CoVprehension

Question 17.1 : Qualité des tests et recherche de stratégie optimale

2020-05-12T00:00:00+00:00

Tests de dépistage

Dès le 16 mars 2020, l’OMS recommande de tester tous les cas suspects. Cependant, il a fallu du temps pour mettre au point des tests de qualité.

Qualité des tests

La qualité des tests de dépistage dépend de 2 facteurs :

La sensibilité du test indique la probabilité que le test soit positif si la personne testée est réellement malade, c’est-à-dire la proportion de vrais positifs. Un test 100% sensible appliqué à une personne malade sera toujours positif (pas de faux négatifs).
La spécificité du test indique la probabilité que le test soit négatif si la personne testée n’est pas malade, c’est-à-dire la proportion de vrais négatifs. Un test 100% spécifique appliqué à une personne saine sera toujours négatif (pas de faux positifs).

Cependant, il est impossible de fabriquer des tests parfaits sur ces deux critères, ni même sur un seul. Les tests de dépistage ont toujours une marge d’erreur. Les tests ne pouvant avoir à la fois une sensibilité et une spécificité très élevées, nous devons choisir la stratégie que nous préférons adopter :

soit avoir une sensibilité très élevée, et donc réduire le plus possible la proportion de faux positifs : ceci permet d’éviter de confiner des personnes qui n’étaient en réalité pas infectées
soit avoir une spécificité très élevée, et donc réduire le plus possible la proportion de faux négatifs : ceci permet d’éviter de laisser circuler des personnes infectées

Les premiers tests étaient relativement spécifiques (de l’ordre de 95 à 98% de vrais négatifs) mais encore peu sensibles (parfois 30 à 40% de faux négatifs. Il est donc parfois nécessaire de faire un deuxième test pour confirmer un résultat.

Dans le modèle présenté précédemment, nous simulons des tests ayant une sensibilité et une spécificité de 90%. Il pourrait être intéressant de faire varier ces deux paramètres pour observer l’impact qu’ils ont sur la reconstruction de la courbe épidémique, cela fera peut-être l’objet d’un post ultérieur !

Types de tests

Il existe deux types de tests permettant de détecter le SARS-CoV-2 :

les tests dits PCR, pour réaction en chaîne par polymérase, sont réalisés à partir de prélèvements nasopharyngés (dans le nez) et permettent de déterminer si une personne est porteuse du virus au moment où le prélèvement est effectué
les tests sérologiques sont réalisés à partir de prélèvements sanguins et permettent de déterminer si une personne possède des anticorps contre le virus, ce qui indique une infection plus ou moins récente selon le type d’anticorps détectés

Les tests PCR sont des tests de diagnostic permettant d’identifier les personnes qui sont actuellement porteuses du virus, tandis que les tests sérologiques indiquent uniquement la présence d’anticorps mais ne permettent pas de conclure sur le fait qu’une personne soit porteuse du virus, et donc potentiellement contagieuse.

Pour plus d’informations sur les différents types de tests et leur fiabilité, le collectif KezaCovid a réalisé une infographie explicative très bien faite.

Recherche de la stratégie optimale dans notre modèle

Afin de déterminer la stratégie qui permet d’obtenir le résultat le plus satisfaisant, nous avons exécuté un algorithme d’optimisation sur notre modèle. Cet algorithme simule le modèle un très grand nombre de fois en faisant varier les valeurs des paramètres d’entrée, dans le but d’optimiser les critères qui nous paraissent les plus importants pour caractériser la réussite de la campagne de tests.

Nous avons fait varier les trois paramètres d’entrée suivants :

Stratégie de test utilisée (aléatoire, travailleurs, personnes âgées, personnes symptomatiques)
Nombre de tests quotidiens (entre 0,5 et 7 fois la stratégie française)
Seuil de déclenchement de la campagne de test (entre démarrage immédiat et démarrage à 50% de personnes infectées dans la population)

Dans le but de minimiser les trois critères de sortie suivants :

Nombre total de tests effectués (leur nombre étant limité, on cherche à en utiliser le moins possible)
Nombre de résultats faux positifs (qui entraînent des quarantaines inutiles)
Nombre de personnes infectées non détectées (qui continuent à propager le virus - que ce soit parce qu’elles n’ont pas été testées, ou à cause de faux négatifs)

Comme nous avons plusieurs critères de sortie, il n’existe pas une solution unique qui sera la meilleure, mais plusieurs solutions équivalentes qui permettent de mieux minimiser l’un ou l’autre des critères de sortie. C’est ce qu’on appelle un front de Pareto.

Pour une population de 10 000 agents, toutes les meilleures solutions trouvées par l’algorithme :

utilisent la stratégie de test qui cible les personnes symptomatiques
commencent à tester dès l’apparition du premier cas (le plus tôt possible en somme, comme recommandé par l’OMS)

En outre, les paramètres sélectionnés par ces meilleures solutions montrent que plus on fait de tests, plus on détecte de personnes infectées (voir figure ci-dessous). Ce résultat peut sembler évident mais il est toujours bon de confirmer qu’un modèle se comporte de la manière attendue !

Cela confirme donc aussi que la stratégie de tester massivement la population le plus tôt possible fonctionne et peut éviter un confinement, à condition bien sûr de disposer de suffisamment de tests et de personnels pour les réaliser. C’est d’ailleurs la stratégie adoptée en Corée du Sud.

Rappel : les modèles développés sur ce site sont des modèles pédagogiques, bien plus simples que les modèles construits et mis en oeuvre par d’autres équipes scientifiques travaillant sur la COVID-19. Ils ne se substituent pas à ces modèles de référence et ne peuvent pas être utilisés à leur place pour mener des expertises, diagnostics ou pronostics. Notre objectif est de contribuer à la création, au sein de la population, d’une meilleure connaissance des moteurs de cette épidémie qui nous concerne toutes et tous.

Question 17: Let’s test people! Sure, but who, when and how?

2020-05-12T00:00:00+00:00

Now that lockdown measures are lifting, it is important to pick a strategy which will prevent a second epidemic wave (a rebound). It is estimated that only a very small share of the population is currently immune (between 3 and 7% of the French population for example on 11th May), which is not enough to talk about herd immunity.

Because herd immunity is not achievable quickly and without a high human cost (we tackle this issue in Q16), we should have a system where infected people self-isolate to avoid contaminating other people (similarly to the strategy adopted at the beginning of the epidemic or in Sweden, instead of the total lockdown, cf. Q13). However, this might not be enough. Since the incubation time with COVID-19 is long (a week on average, but sometimes up to 20 days), infected people have the time to infect their contacts before they are detected and put in quarantine. This is why we plan on tracking and tracing contracts (cf. Q14). Besides, the share of asymptomatic cases is still mostly unknown but estimated around 30%, which means that we cannot rely entirely on symptomatic displays to isolate infected people. It is therefore necessary to test the population more broadly.

The World Health Organisation (WHO) was already advocating this strategy on 16th May, recommending that we test all suspicious cases. France however started testing late and slowly: it took some time to design reliable tests and the small number of such available tests was thus limited to healthcare workers and people at risk. For more details about the different types of test, see Going further at the bottom of this page.

We now have better quality tests, but in order to successfully lift the lockdown measures, we will have to broaden the testing conditions. The goal of the French government is to be able to test 700,000 people per week. For now, France never tested more than 150,000 people per week, so the goal of 700,000 seems too ambitious for several reasons:

the lack of Personal Protective Equipment (PPE), testing kits, staff;
the limited number of non-medical laboratories requisited to administer the tests, which are under-used compared to medical laboratories;
the lack of connections between the testing laboratories and the government database in order to centralise results.

Testing robots have been ordered to China to increase the testing capacity, but operating them requires staff who to be recruited and trained. These robots also consume a lot of consumable and delivery times are very long. It will thus take some time before we reach this testing capacity. Also, with France’s 67 million citizens, it would take about two years (96 weeks) to test everyone at this rate. This is way too long, given that a person tested negative on one given week can become sick the next week.

The goal is therefore twofold: we want to know as precisely as possible what is the current state of the epidemic in the country and we want to control the spread of the virus as well as possible with adapted measures (neither too strong nor too lax), under the constraint that testing kits are in limited supply. The question then is: who should we test in priority?

If we pick the people we test at random, given the small share of people infected in the total population, we risk having very few positive tests and “wasting” them (the chances of finding infected people are low). For this reason, we tend to test suspicious cases (the symptomatic ones), but this strategy ignores all the asymptomatic cases who are also contagious, and most probably numerous. At the beginning of the epidemic, healthcare workers were tested in priority, since they were the most exposed to the virus. As it aims to reopen schools, the government considers testing teachers and school workers. More generally, we should test people who work outside of home and therefore have a higher chance of being infected. But you can also be contaminated outside of work (when shopping for example). Since we now know the profile of high-risk people, we could also consider testing them in priority in order to treat them early and prevent serious complications. But the results would then not be representative of the general circulation of the epidemic in the general population.

It is clear that finding the best strategy on all accounts is not easy if only using our intuition. A simulation can help, by allowing us to compare different strategies and to measure their effects.

In our model

Characteristics of the population

We have modelled a population of 2,000 individuals, distributed in several age categories. This influences their sensitivity to the virus (people at-risk) as well as their mobility. For instance, 50% of people aged 20 to 65 have work outside their home (“essential” workers) whereas the rest stay at home (remote work, furloughed workers, family carers, etc.). People aged < 20 and 65+ are considered homebound (by respectively remote schooling and retirement).

Individuals in our population can be in one of five distinct states regarding the virus, as shown in the figure below:

Susceptible: they have never been infected and are therefore not immune either
In incubation: they have been infected but are not yet sick (it lasts 6 days on average)
Asymptomatic: they are sick but display no symptom. Only a test will reveal them (30% of patients below 65, for an average of 21 days)
Symptomatic: they are sick and display symptoms. (70% of patients below 65 and 100% of 65+ patients, for an average of 21 days)
Recovered: they are immune and cannot get infected again (this is a hypothesis of this model, we do not know yet if it is the case in reality).

When they move in the simulation world, individuals can come into contact with one another. Infected people (in incubation, asymptomatic and symptomatic) are all contagious and can therefore transmit the virus to susceptible people they are in contact with. Individuals working from home do not move but they can be in contact with people passing by their home (deliveries, postal services, etc.). However, they have less contacts on average than people who have to work outside of home.

Testing strategies

Our goal is to find out how we can best use the tests available each day to reach the two main objectives of a massive testing campaign: to monitor the epidemic and to control it. In the model, we can act on several parameters:

The number of tests available each day: the testing strategy of the French government plans for 500,000 to 700,000 tests per week, which corresponds to about 2 to 3 tests per day for the population of 2,000 in our model
When the testing campaign starts, i.e. the moment from which we start testing the population. It is defined in the model by the threshold X of the proportion of symptomatic people in the population: when more than X% of the population is symptomatic, we start the testing campaign.
The population being tested: do we pick individuals at random? Do we aim for symptomatic people, or older people (since they are more at risk), or people working outside of home?

In order to reduce the spread of the virus, people who tested positive are put into quarantine and are completely isolated: they cannot transmit the virus any further.

Inference of the epidemic curve

Using the number of tests performed, we can reconstruct the curve of the number of cases: the number of positive tests in the total number of tests provides an estimation of the proportion of cases in the general population. One of the advantages of our model is that we know the “true” number of people infected over time since we know the status of all of the agents. We can therefore compare the estimated curve using tests and the “true” curve to verify the correctness of the estimations.

In order to compute this estimation, we could intuitively think that a simple cross multiplication suffices: for instance, if we test 700,000 people and that 1,000 of them are infected, then we deduce that out of the 70,000,000 residents of France, 100,000 are infected. But this simple proportionality rule does not work well in epidemiology, especially when the number of people tested or the prevalence of the epidemic (i.e. the total number of cases at a given time) is too low, as is the case at the beginning and at the end of an epidemic, or when tests are not entirely reliable. Another method for estimating the total number of infected people is to compute the predictive values of the test, which depend on three elements: the prevalence of the epidemic, the rate of false positives and the rate of false negatives obtained with the test.

The number of confirmed cases given each day by the French government is a combination of the test results and the expertise of health professionals, since we do not know the “true” number of infected people (as we do in simulation). The computation method is more complex than the one we use in our model, which is a simplification of reality, but it also has, like all statistical estimations do, some error margins and potential biases.

Testing scenarios for 2,000 individuals

Comparison of estimated cases for the different samples of population

Let us look at what happens when we choose a daily number of cases equivalent to that of the French government, i.e. 3 tests for 2,000 individuals, and when we start testing as soon as the first case appears. We compare the curves representing the number of cases estimated by the proportionality rule (in red), the number of cases estimated by computing the predictive values (in blue) and the “true” number of cases (in black), for each sample of population.

By testing at random	By testing symptomatic people

By testing elderly people	By testing people who work outside of home

Firstly, we note that the blue and red curves (the estimated cases) vary a lot more than the black curves (the “true” cases). Indeed, they depend on the number of positive tests each day, which varies greatly depending on who is tested. In general, we choose to “smooth” this estimation by computing the mean result of tests over several days (here, a mean over 7 days), but there is always a larger variability depending on who is tested each week. For example, a lot of negative tests may result in an estimation of a decreasing epidemic which is not necessarily true (maybe we just tested non-infected people, which does not mean that no one is sick anymore).

We also note that the blue curves (with predictive values) are better estimators than the red curves (proportionality rule), especially at the beginning and at the end of the epidemic when the prevalence of the virus is low, and especially for symptomatic people, who are less representative of the total population.

Secondly, we find that the worst estimation happens when we only test symptomatic people (top right figure): since we only test symptomatic people, who therefore have a high probability of being infected by COVID-19, we overestimate the “true” number of cases in the general population. Given that the tests we model are diagnostic ones, it is really not sound to extrapolate the number of cases in the general population from the tests performed on symptomatic people. The model confirms this. Such tests allow to control the epidemic by confirming and confining infected people, but they do not allow to monitor its spread in the population.

Comparison given the number of daily available tests

Let us now look at what happens when we choose to increase the number of daily tests: we start with 3 tests for 2,000 peoples on the top left corner, then up to 6 tests for 2,000 on the top right corner, then 9 for 2,000 at the bottom. Simulations were done on the random sample only, with a beginning of the testing campaign as soon as the first case appears. The following figures show only the estimation by predictive values since it is better than the proportionality method.

3 tests for 2,000 people	6 tests for 2,000 people

9 tests for 2,000 people

We notice that the higher the number of tests, the better the estimation of the number of cases in the general population. After an initial overestimation, when there are very few cases in the population and very little tests performed, the reconstructed curve follows rather precisely the actual epidemic curve, in particular around the peaking time, the key moment of the epidemic.

Comparison given the activation of the testing campaign

If we want for 15% of people to be infected to activate the testing campaign, the knowledge of the epidemic we get is strongly diminished, even if we ramp up the number of tests available daily. Simulations are run for the random sample.

immediate start - 3 tests/2,000	start at 15% - 3 tests/2,000

immediate start - 9 tests/2,000	start at 15% - 9 tests/2,000

We notice that with 3 tests for 2,000 people (first line), the reconstructed curve cannot capture the epidemic peak when we started the testing after 15% of infections (right hand side figure). Similarly, despite increasing the number of tests to 9 for 2,000 people on the second line, we notice that the peak identification is very uncertain and it leads to a strong overestimation of the number of cases once the peak is past (right hand side figure). This only happens when the number of cases is very low on the left hand side figure (when testing happens from the start).

Over to you

In the simulator below, we have several tools available to:

Modify the number of tests available each day, and therefore the time necessary to test all the targeted population
Modify the starting date of the testing campaign: from the start of the epidemic or later on
Choose who is tested: people working outside of home, older people, people at random or people already showing symptoms of COVID-19

Your goals:

To minimize the total number of tests used
To minimize the spread of the epidemic: i.e. the total number of people infected
To minimize the number of people quarantined for no reason, i.e. the number of false positive tests
To follow at much as possible the “true” curve in order to monitor precisely the epidemic over time

Nota Bene To see the results of the optimal strategy obtained with an algorithm: Going further!

If the simulator window is truncated, try to zoom out.

Simulate different testing strategies

To conclude

We saw that organising testing is a complex question. It is important to start early, but designing a reliable test takes time and the first tests are not very informative (too many false positives / negatives).

Nota Bene For more information on the quality of tests and its importance in the estimation of case numbers: Going further!

It is necessary to test a representative sample of the population, but the constraints on the number of available tests lead to testing people who are most probably positive. This strategy offers the best control over the epidemic (testing and putting into quarantine all suspicious cases), but it leads to an overestimation of the number of cases in the population, and therefore towards a set of measures which are too restrictive.

As often, the truth is about finding the right balance.

Reminder: the models developed on this website are for educational purposes only. They are a lot simpler than models built and deployed by other teams working on COVID-19. They are not substitutes for these reference models and cannot be used to make diagnoses or forecasts. Our goal instead is to raise awareness about this epidemic and its drivers.

Going further

Question 18: The people with whom we interact daily reflect our interpersonal network: what is the influence of this network’s shape on the spread of the virus?

2020-05-12T00:00:00+00:00

Coming soon!

Question 16: Herd immunity, miracle strategy?

2020-04-28T00:00:00+00:00

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Simuler l’impact du confinement sur la courbe épidémique

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C’est aussi simple que ça.

Going further

Question 15: Are we all equal in the face of the virus?

2020-04-15T00:00:00+00:00

INTRODUCTION

Since the emergence of COVID-19 in Europe, the social characteristics of patients makes us wonder who is more affected. The virus originated in China.The first cases were “imported” either by Chinese nationals travelling overseas, or by foriegn travelers coming back home from China, then from the first other affected countries (Egypt, Iran, Italy…). It is no mystery that tourists and professionals traveling beyond Europe are mostly from privileged classes (diplomats, sales representatives, etc). (diplomates, commerciaux…).
In France, and in Paris in particular, one of the first instances of the epidemic was within the House of Commons, then in Cabinet. The media coverage over the infection of celebrities and royals in the world could suggest that COVID-19 was somewhat a “rich people disease”. The same analysis was made in the coverage of different national media outlets (in (Russia, Ukraine, but also Brasil, Mexico and Uruguay).

At the same time, many commentators stated that the virus was blind to socioeconomic differences. The Atlantic for example claimed, regarding Boris Johnson’s situation, that his infection illustrated the fact that the disease was universal, since it touched all groups of society regardless of wealth and size. Indeed, when the disease started spreading, all categories of population seemed affected equally, as the virus does not discriminate directly between its hosts in terms of social class or income.

However, the consequences of the disease are not the same for everyone. One’s state of health at the time of infection (co-morbidities especially), or one’s age make certain infected people more at risk and cause their symptoms to be more serious. Depending on the quality of life of the person infected, their professional activities or their usual mode of transport, “basic protective measures” are more or less easy to observe strictly. We can add the difference in access to healthcare and information, which vary significantly with the social status of people and their socialisation (as was shown for example in Sweden, where the spread of the virus was faster among foreigners who did not have access to information broadcasted in Swedish in the mainstream national media).

In this post, we present a model which illustrates the social and spatial spread of the virus among individuals from three social classes with distinct characteristics, and between different cities. The way the virus is transmitted from one individual to another is the same for all social classes: a close contact suffices (with a non-zero probability of transmission, as in the previous questions). However, the situations where people from different social classes come into contact with other people (and therefore can be contaminated) vary depending on elements which are directly linked to the social class they belong to. Social reality is very complex and social classes are defined along fuzzy and multiple lines, including levels of income and education. Here, we focus on only two elements, which we think have a particular role on the current epidemic dynamic:

The geographical amplitude of usual professional activities (that is, roughly, the distance between home and work as well as the frequency of business trips) and the fact that the person can work from home or not in case of a lockdown.
The residential situation:
- regarding the main residence: in collective or individual housing.
- the possibility to use a secondary residence in an isolated location. The difference induced during lockdown and its level of comfort and bearability are made stark and immediately perceived.

n general, the social position of people combines these two dimensions so that typically (and especially so in cities): the most privileged have a large geographical amplitude (they travel more often and further away, for business as well as for pleasure, etc.), they can work from home (as these first numbers about American cities by income level suggest), they reside more frequently than others in an individual housing setting, and own more frequently than others a secondary residence. Of course, there exists surgeons who live in collective housing and have to work on site, in the same way that some office clerks can work from their detached home. But on average and to simplify, we here define “privileged” people (represented by triangles) as those who can work remotely from an individual housing setting (a detached house for example). On the contrary, we define “working class” people (represented by circles) as those who cannot work from home (such as nurses, cashiers, police officers, cleaners, etc.) and who live in collective housing (typically, a flat). Their professional and residential settings mean that they can catch and transmit the virus when they go to work, but also when they come back home. Indeed, we assume that sharing a lift, a digicode or a communal bin cupboard, and interacting with neighbors makes the transmission of the virus possible at home. In our model, some individuals have an intermediary status (the “middle class”) and are represented by squares. They share a single characteristics with each of the two previous groups. For example, they live in collective housing but can work from home, or they live in a detached house but have to work on site. Their social position is intermediate between the privileged and the working class

DESCRIPTION OF THE MODEL

In the simulation, 1 working person (selected randomly) out of 2 has to keep working on site whereas the other half of people can work from home. If we add the weights of the health sector (7.1% of jobs), the social sector (7.4%), the commerce sector (12.9%), administration (9.1%), transports (5.5%) and finance (4.6%), we end up (for France at least), to roughly this figure of 50% of jobs having to be operated on site. Similarly, 1 person (selected randomly) out of 2 lives in individual housing whereas the other half resides in collective housing (this figure can vary greatly by city, region, country). If we combine these two dimensions, we obtain a simulated society where 1 in 4 on average is considered “privileged”, 1 in 4 is considered “working class” and 2 out of 4 are considered “middle class”.

The mobility of people operates on two scales: mobility within the city where people live (intra-urban scale), and mobility between cities (inter-urban scale). Indeed, some privileged people may work in a different city from the one where they live.

The model represents a typical region, where there is one big city and some smaller cities linked together by transport infrastructure which allows travel from one to the other. As in most countries, the bigger the city, the more densely it is populated (cf. Illustration below). For instance, there are approximately 4 people per patch in the big city and 1 person per patch in the smallest one.

Each day, a person can visit a maximum of 3 different locations:

Their workplace. Workplaces are represented by:
- black flags for jobs which cannot be done remotely (for example: hospitals, waste management sites, supermarkets)
- grey flags for jobs in workplaces that will be closed during lockdown (some can be accessed virtually). We have reproduced in the simulation the “real-life” regularity by which workplaces are more concentrated in large cities than residence. Therefore, some people have to go to work in a city larger than the one they live in.
The location of an additional activity (like shopping or going to the doctor), that is a public space where the person has to go, but which also corresponds to someone else’s non-remote workplace. Such locations are visited on average every four days. To simplify, we keep the same frequency of visits before and after lockdown, even though such a frequency must certainly be higher before the lockdown.
The place of residence (in collective or individual housing).

Infection can happen in any of these locations, except home for people living in individual housing. People living in collective housing thus have an extra risk to get infected every day compared to other people.

At the beginning of a simulation, someone at random is picked to carry the virus. The model then represents the spread of the epidemic in the population.

When the threshold of 10 deaths is reached, a mandatory lockdown is imposed: everyone who can work remotely has to, whereas other people keep working from their usual workplace.

IS THE EPIDEMIC TRULY BLIND TO SOCIAL CLASS DIFFERENCES?

Let us look at the evolution of the epidemic in each social class of the population, by stopping the simulation regularly to update our view of the situation. After 35 days (the first series of graphs), the epidemic is still in its starting phace: on the left-hand side graph (“global epidemic situation”), the teal curve representing infected people is still below the beige curve representing susceptible people, and the number of people carrying the disease is not very high. When we disentangle this information by social class, we see that privileged people are proportionately more infected than others (the purple curve on the left-hand side graph is above the other curves) in this specific simulation, although it can vary depending on where the virus first appears (chance intervenes a little in the model as in reality). At this point, not many have died and there is no lockdown. If we look at where people got infected, we see that about a third (regardless of class) got it from going to work.

Day 35

Let us run the simulation until day 70. Since we last looked, the threshold of 10 deaths has been crossed and lockdown has been imposed. We can now observe its first effects on the epidemic. Privileged people do not have to go to work anymore, and since they live in individual housing, they only have one opportunity to get infected: going to an additional activity every four days on average. Their infection level thus decreases very fast (right-hand side graph, purple curve). If the lockdown lowers the number of contacts made during the day for everyone, the amplitude of the decrease is not the same for each social class. Those who cannot work remotely and those who live in flats (and thus firstly the working class) still have several contacts a day and are increasingly infected by the virus (the green curve keeps going up and above the other two classes). They do not benefit as much from the lockdown.

Day 70

At day 350 of this simulation, the epidemic is over. The proportion of infected people in the working class has been higher than the proportion of privileged people infected for about 250 says, with the middle class figure sitting in between. About 5.5% of all working class individuals have died, whereas it is less than 4% for privileged and middle class individuals. These figures can vary with the different simulations but the trend is always the same after the lockdown. Also, among those who got infected, less than 1 in 5 did because of work in the privileged class, whereas it is almost 3 in 4 in the working class.

Day 350

OVER TO YOU!

As with previous questions on this website, a simulation allows you to explore the simulation for yourself. To set up the simulation, click on the blue banner below, and when you see the model’s interface, click “Initialise”. To start the simulation, press “Simulate”. You will see the graphs and the map change as time passes. The simulation will automatically cease when the epidemic is over. This can take several minutes.

If the simulator window appears truncated, just zoom out.

Simulate the impact of the epidemic on the different social classes

WHAT ABOUT SECONDARY RESIDENCES?

We heard a lot about secondary homes right after lockdown was imposed: it might have been authorised to use them as in Russia, or discouraged as in France, but many people fled the cities to isolate themselves in the country. Some early estimations.(based on mobile phone activity) suggest for example that Paris and its region have lost about 17% of their inhabitants. The media abundantly commented on the bourgeois populations who fled to their seaside homes, at the expense of risking the health of locals in touristic regions where the healthcare system is not calibrated for such a population increase. Of course, reality is more complex and the “Parisian exodus” includes secondary homeowners (from central Paris mostly) as well as students going back to their family homes, or people caring for family in other regions…

In the model presented here, we simplify the phenomenon as follows: we assume that people from the working class do not own secondary home, whereas 5% of middle class people and 10% of privileged people do (in France, 10% of housing units on average are secondary residences, although it does not mean that 10% of the population own a secondary residence, since some people own or co-own multiple properties. We keep the 10% figure for privileged people, and half of that number of the middle class). Secondary residences are located outside of cities, in isolation. Once people are confined in their secondary home, we assume that they do not come out anymore.

When clicking on “Secondary-houses?” in the lower left part of the simulator before initialising the model, you can see by yourself the impact of secondary residences on the spread of the epidemic…

The presence of secondary homes slightly reduces the number of infections, and therefore also the number of deaths, but only for privileged people. They always help to contain the epidemic, but only for privileged people (and parts of the middle class). The lockdown on the other hand benefits everyone by limiting all contacts in the population (cf. question 9), even though working class individuals benefit less from it than others because they still maintain contacts at their workplace and place of residence.

The virus is blind, but the chance of escaping it is not. When looking at two discriminating elements (residence and remote working), we see that the less privileged in society systematically pay a higher price in this epidemic. So we hope that the social redistribution measures will live up to the expectations…

It is (almost!) as simple as that.

NB. The question of social inequalities in the face of the virus is vast and all dimensions were not discussed here. Social variations in the use of public transportation, unequal comfort at home during lockdown, inequality in access to health care and to information play a very important role on the consequences of the current epidemic on society. These questions will be addressed in further publications. Stay tuned!

Reminder: the models developed on this website are for educational purposes only. They are a lot simpler than models built and deployed by other teams working on COVID-19. They are not substitutes for these reference models and cannot be used to make diagnoses or forecasts. Our goal instead is to raise awareness about this epidemic and its drivers.

Question 14: Can backtracking contacts with a mobile app make a difference?

2020-04-14T00:00:00+00:00

Taper texte directement ici. Quelques astuces, à commencer par les listes :

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EXEMPLE SIMULATEUR INTEGRE

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Simuler l’impact du confinement sur la courbe épidémique

TEXTE BAS DE PAGE

C’est aussi simple que ça.

Going further

Question 13: Some countries have opted for a targeted lockdown instead of a total lockdown: is it possible to contain the epidemic this way?

2020-04-08T00:00:00+00:00

Several countries, including Sweden, decided against a total lockdown of the population. Even now, Swedes can decide by themselves if they should stay home or pursue their business as usual. The rationale behind this approach is economic, although it allows individuals to participate in the fight against the virus, at their own scale. It can be thought of as a decentralisation of decisions and agent based modelling, which is the technique used on this website, is often used to deal with this kind of question.

Recommendations given to the Swedish population are the following:

Respect the basic protective measures during in each interaction.
Go into quarantine as soon as you suspect you might have the virus.
Don’t come out of quarantine until a few days after you feel recovered.
Avoid public gathering (gatherings of 50+ people have been banned).

In order to implement such a policy, two prerequisites have to be met, and they are not universal: first the population has to know about the symptoms of COVID-19, even in its mildest form, so that each person can decide if they suspect they have been infected; then each worker has to trust the State’s support to negotiate the possibility to work from home or be on sick leave whilst access to a doctor is not always immediate.

These prerequisites allow us to assume in our model that individuals are really autonomous in their behaviour management.

Presentation of the model

The model is based on the one presented for question 6, where the lockdown mechanism has been adapted to include the possibility of a targeted lockdown. The population size has been upped to 1000: this makes the model less readable visually but it allows to observe more phenomena on the long run. The transmission mechanism has also been slightly modified. A final modification is that each agent is considered to be immune (after having had the virus) and does not have to stay in and can resume their life as usual.

At the beginning of the simulation, there is a unique infected agent: “agent zero”. Each day, an agent has up to three interactions out of the house and up to one interaction per person at home.

A “reasonable” agent is an agent whose interactions are less contagious thanks to basic protective measures and who goes into quarantine while they fall sick - they will therefore only be in contact with their household.

The rule for basic transmission is that: at each time step, an agent A interacts at random with an agent B when in proximity. If A and B are already infected or if none of them are, nothing happens. If B is infected and A is not, then A becomes infected with a probability of 20%. This probability changes if agents are reasonable: if only A or B is reasonable, then the probability is divided by 2; if both of them are reasonable, then the probability is divided by 4.

We can now test this model

Let’s start by testing the model with two extreme situations: with no lockdown at all (which allows to highlight the basic epidemic curve) and then with a perfectly followed set of rules where all agents use basic protected measures and go into quarantine upon their first suspicion of being sick.

Illustration - The situation of no lockdown. Infected agents who seem to appear spontaneously at the middle of the image have been contaminated at home, by an agent from their household.

The situation of a lockdown and 100% of reasonable agents is not shown here because then the disease does not spread. Indeed, “agent zero” goes into quarantine immediately and so do the members of their household, leaving the epidemic to die down. This holds true only if we assume that agents can recognise the disease as soon as they become contagious (see infra).

Now imagine that not all agents are reasonable: let’s see what could happen if only 80% of them were. We discover a subtle situation: if agent zero (the first to become sick) is reasonable, then there is no spreading. On the contrary, if agent zero is not reasonable, then the epidemic starts but spreads slower than if no quarantine was put in place. We notice that during the epidemic, a large number of agents keep working, and that if we manage to create a herd immunity where the number of immune people is higher that the number of susceptible people, then the epidemic flattens quite rapidly.

Illustration - Targeted lockdown with 80% of “reasonable” agents. “Non-reasonable” agents are shown as triangles.

Illustration - When we reach 85% of reasonable agents, we see that a small difference in proportion transforms the dynamics significantly and drastically reduces the number of people affected by the virus in the course of the epidemic.

Things are not as simple as that though. One of the most complicated aspects to manage with COVID-19 is that it is hard to recognise, even for reasonable agents: they don’t always know that they are sick. This happens because the incubation period can last several days and also because a large number of cases are asymptomatic and hard to interpret. When they ignore their level of threat to others, “reasonable” agents use basic protective measures but stay active. In the model, we will assume that agents do not realise straight away that they are sick. We can see the impact on the curves.

Illustration - Diffusion curve of the epidemic if the disease is too discreet to be perceivable by the agent for 1, 4 or 7 days (from left to right).

With 100% of “reasonable” agents, the targeted lockdown stops the spread of the disease (in the model) even if agents stay asymptomatic for several days. From a delay of 7+ days between infection and first symptoms, the disease will spread even with quarantine:

With 85% of “reasonable” agents, we see that the epidemic can spread in the population even when the delay between infection and first symptoms is only of 1 day:

A remaining question is that of the possibility of a delay between the start of the epidemic and the reaction from the government with any lockdown or quarantine. Such a scenario is plausible with insufficient anticipation. We notice how this delay might become decisive for economic activity, the speed of transmission and the total number of infected agents.

Illustration - 85% “reasonable” agents with no delay between infection and symptoms, and quarantine recommended immediately, or after 7, 10 or 14 days.

NB: Much like our own day, a day in the model corresponds to a set of interactions that an agent can have outside or inside their household. However the analogy stops here since a week in the model cannot be compared with a week in the world we know. What matters here is to explore the impact of the timing of a targeted lockdown on the dynamics of the epidemic and the economy..

Finally, we have to recall an essential hypothesis of the model, the effect of which is only visible at the macroscopic scale. Part of the behavioural rules of the agents is that they come out of quarantine once they are fully recovered. Regarding COVID-19, it seems a lot simpler to identify the end of the disease compared to its start - we can therefore assume that agents will be able to detect when they are recovered. This has a significant impact on the spread of the disease. We can understand this as a decrease in potentially contagious interactions: if immune agents come out of quarantine, susceptible agents have more opportunities to have safe contacts than if recovered people had stayed home. Each interaction therefore has less chance to be a contagious one.

Illustration - 100% “reasonable” agents, 7 days between infection and symptoms. In black, recovered agents go out of quarantine, in teal recovered agents stay in quarantine.

To conclude, we note that it is theoretically very simple to mainly contain an epidemic with a targeted lockdown, even when the disease is not easy to detect immediately. Nevertheless, the number of completely asymptomatic patients of COVID-19 and the incubation period (which is not perfectly known to this day but seems to last up to 20 days) should be taken into account if we wish to better model and understand the current epidemic. We could imagine more systematic testing to reveal infections, which would probably require the household and colleagues of someone visibly sick to go into quarantine. This simple model can however illustrate this political option, and show that it prevents a relapse of the disease at the end of lockdown, as it is feared will happen after lifting a total lockdown.

Jouer avec le modèle :

If the simulator window appears truncated, just zoom out.

Simulate the impact of a targeted lockdown

Question 12: How come nobody saw this epidemic coming?

2020-04-06T00:00:00+00:00

If the plague, cholera or typhus seem to belong to the past for many societies in the world - the big names of those who revolutionized the field of infectious diseases in the 19th century are now fronting their institutions: Pasteur in France, Koch in Germany for example - the big book of infectious diseases cannot yet be closed.

The Asian flu of 1957-1958 claimed more than a million victims in the world, and so did the Hong Kong flu between 1968 and 1970. The beginning of the 1980s will never be dissociated from the emergence of HIV / AIDS, which claimed between 25 and 35 million victims until this day. Cholera has kept flaring up in waves of varying intensity since the 1990s. It affects between 1.3 and 4 million people according to the World Health Organisation (WHO). Finally, around 50,000 cases of plague have been recorded since the 1990s. A particularity of this disease is that it can circulate unnoticed for years and suddenly reappear in the form of epidemic outbreaks (such as in the Surat region in India in 1994, seasonal outbreaks in Madagascar…).

After World War II, the golden age of victory over infectious diseases proved an illusion. It had been fueled by the hopes following scientific discoveries, technological progress and the benefits from hygienist practices of the end of the 19th century. Things have changed however with time: the resisting capacity of societies and their weaknesses are not exactly of the same nature. On one hand, the knowledge and tools used to fight the diseases are way more elaborate today than they were in 1900, which allowed unprecedented victories (smallpox for example was eradicated in 1980). On the other hand, a significant demographic growth in a more mobile and interconnected world, the acceleration of urbanisation, the emergence of antimicrobial resistance, the persistence of poverty, the destruction of biodiversity… are all risk factors in the (re)appearance of global infectious diseases.

Risk is a complex concept. It is difficult to apprehend. It comprises two dimensions, both difficult to evaluate: the probability of the feared event occuring and the severity of its consequences. In the case of COVID-19, the pandemic seems to have come as a surprise, because of its unexpected outbreak, because of the conditions for its rapid spread from the most central parts of the global economic space, and because of its dramatic consequences.

What are the elements which favoured this surprise effect? Was it the probability that a global pandemic might occur underestimated? Is it the severity of the health, social, economic and environmental consequences of such an event which was underestimated? Or both? Even though the information flow has never been so intense and fast, it is hard to understand why national and international political responses failed to assess the right level of risk associated with this pandemic outbreak. We suggest some elements to answer these questions, relying on both the characteristics of recent epidemics and the characteristics of COVID-19.

Understanding the epidemic risks of the past twenty years.

Following the Severe Acute Respiratory Syndrome (SARS) pandemic in 2003, six epidemics have triggered public health emergency of international concern (PHEIC) from the World Health Organisation: 1/ Influenza AH1N1 in 2009; 2/ Ebola hemorrhagic fever in 2014; 3/ the fever epidemic from the Zika virus in 2016; 4/ Ebola again in 2018; 5/ the resurgence of polio in 2019; and 6/ COVID-19 in 2020. Since 2005, PHEIC refers to an extraordinary event qualified as such because of the risk it represents to international health and to which a coordinated action is required from national States. The recent global public health emergencies were characterised by two features: the diversity and extent of spaces affected on the one hand, and the mortality attributed to them on the other.

For example, new polio cases have only been located so far in poor regions of the world undergoing geopolitical conflicts, whereas the Zika virus appeared in South America with a rapid spread to the whole intertropical zone. Similarly, the transmission of the SARS pandemic was contained but this virus demonstrated an ability to spread very rapidly to large urban spaces (Hanoi in Vietnam, Hong Kong, Singapore or Toronto in Canada). For the past twenty years, new or re-emerging pathogens have shown their ability to spread fast and globally.

The impact of such global health emergencies on general mortality may have seemed limited in time (less than ten weeks for influenza H1N1 for instance) and in terms of the age categories affected: with an increased severity for populations aged 50+ (H1N1 or SARS), in conjunction with risk factors such as heart and dietary conditions or not. The carriers (symptomatic or asymptomatic) exhibited similar profiles, and the consequences on global mortality remained limited, but the effects of handling patients were considerable for health systems locally and regionally (SARS, Ebola, Zika).

COVID-19: a rather quiet switch from epidemic to pandemic

The geographic spread and mortality attributable to COVID-19 leave no doubt as to the severity of this global crisis. But when exactly did the infectious episode of the pathogen, initially compared to the seasonal flu by some political and scientific actors, become a threatening global pandemic requiring half of humanity to lock down?

A study shows that the circulation of the virus in the Italian province of Lombardy started at least in the beginning of January 2020 (or a month before the first cases officially recorded), and that the first cases of a still unknown viral pneumopathy seem to have been recorded in November 2019 in China, the warnings about an epidemic risk happened much later in China, in Asia and then throughout the world. On 23rd January 2020, the WHO emergency committee upped their threat level, [declaring](https://www.who.int/news-room/detail/23-01-2020-statement-on-the-meeting-of-the-international-health-regulations-(2005)-emergency-committee-regarding-the-outbreak-of-novel-coronavirus-(2019-ncov): “there exists an interhuman transmission of the virus (…) Some infected cases in China were exported to the United States, to Thailand, to Japan and the Republic of Korea.”

Starting in Wuhan, the virus transmission happened quietly, infecting a large number of people, most of them remaining asymptomatic. The sporadic cases qualified as “imported” - because they were linked directly to the original centre of the epidemic - led to more and more cases of local contamination. This process was accelerated by asymptomatic forms of the disease whose silent spread was reinforced by a rather long incubation period (up to two weeks). Besides, the mortality of 2%, estimated at the beginning of the epidemic in China, was not considered high enough to raise the alarm (the mortality rate of SARS or MERS-COV were estimated to be respectively 9.8 and 34%). Many comparisons, sometimes unfortunate, with the seasonal flu, introduced a confusion and underestimation of the risk.

Transmission routes have followed the channels of a globalised world. Wuhan, with over 11 million inhabitants, is the most populated city of Central China and the capital city of the Hubei province. It is an industrial, commercial financial and scientific centre. It is linked to the largest Chinese metropolises (Beijing, Shanghai, Guangzhou), all located within a 1000 kilometer range. Imported by airways, the epidemic then spread to different countries. From these first imported cases, local and community chains of transmission emerged. The characteristics of the first communities to be affected reflect their role in the globalised economy. In early February, Singapore had the highest number of infections outside of China and was planning to take restrictive measures as its financial centre was impacted; then Northern Italy, cradle of the “Made in Italy” luxury brands, became a new epidemic centre. Most cities in the world, being interconnected with China but also with each other, became affected by this epidemic because the symptomatic and asymptomatic characteristics of the disease made it hard to detect.

The possible organisational dysfunction in the relay of information about COVID-19

The identification of a new pathogen by the World Health Organisation relies on the national State’s sharing of information and on the representative WHO bureaus, which are not present in every country. Delays in information transmission from some of the States to the WHO may exist for several reasons: a will to downplay the severity or danger of the epidemic to preserve economic activities or political stability; a weakness of the health system and its ability to notify and register new risks and new diseases; some lags between the identification of the disease and the sharing of this information between difference administrative levels of a country, then to the WHO; the fact that a country might no be represented at WHO.

The ability of health systems to identify and to respond to epidemics is a crucial factor in case of emergencies. Over the past thirty or so years in most countries, healthcare systems have been profoundly transformed along two lines: a financial logic coupled with the contractualisation of means and objectives, and a multiplication of actors in charge of health. These changes may have pushed health systems to reorganise or reduce some programs, in particular those dealing with risk prevention, but also to extend the chain of actors in charge of health, making responses more complicated in case of health emergencies. Such dysfunction in the face of critical situations question the way States are organised.

For instance, in France - a country whose healthcare sector is still centralised, as is Spain despite an older dynamic of decentralisation - criticisms against national health structures have been sparked by the lack of anticipation regarding both prevention and the protection of people, healthcare workers and carers. In a federal system such as the United States, lockdown measures taken by some State governors have been criticized by Federal power. In Germany, where the Länder (or “regions”) cater for healthcare, the federal system was praised for its ability to offer tailor made responses to differentiated challenges, but it was also criticized for the delays imposed by coordination and competition on decision making and information transfer between administrative levels in times of crisis.

COVID-19: an epidemic so far removed…

Quite obviously, for a large number of rulers in the world, the risk of an epidemic seemed far removed at first. The first sources noting the novelty and danger of COVID-19 were sporadic, hard to trace and to evaluate because they were transmitted on Chinese social media, where information is tightly controlled by the central political power. Initially shared within scientific communities (through journals, blogs, etc.), the information was then relayed by national political actors while new sources of information appeared, through more official channels and at varying rhythms, seemingly at odds or quite late compared to the health situation.

In the end, it took the WHO about two and a half months to declare the situation as a pandemic, after a large number of countries were already affected. As a comparison, it took less than a month during the H1N1 epidemic between the identification of the first cases in Mexico on 5th May 2009 and the pandemic declaration on 2nd June 2009.

The initial resources produced by national governments were confusing because the different messages shared at the international level did not provide national level decision makers with real answers, but also because other political events closer to home delayed action on this information, such as pensions reforms and municipal elections in France, inter-community riots in India, etc.

Such ignorance of the actual risk level continued even during the first contaminations in each country. Information from China, Northern Italy or the first epidemic centres in each country could support the impression that the disease was spatially contained and only affected particular groups of people. It took the national lockdown measures for the whole population to regard the epidemic as immediate and dangerous. The change is illustrated by Google searches of the term “coronavirus between the 31/12/2019 (when the WHO received the first notification about the pneumopathy) and mid-April 2020 in four countries who chose to opt for strict or very strict national lockdowns.

Each country has its own epidemic curve, and similarly its own curve of relative interest in the term on the most popular search engine. We can see that “coronavirus” searches only become popular at the end of February 2020, so two months after the official declaration in China. Furthermore, WHO announcements and decisions about the risk level associated with COVID-19 seem to have had very little impact on the web searches. The epidemic remained far removed despite WHO alarms and announcements. However, the search peaks coincide with the chronology of lockdown announcements in all four countries: first Italy (step by step), then Spain, then France, then the UK.

Chronology (31/12/2019-12/04/2020) of the search for “coronavirus” on Google in four european countries. “Google trends” gives the number of keyword searches as a ratio of the total searches made on Google at the given time. It highlights a particular interest for a given subject. Values represent the level of this interest by country and by day: 100 at the peak of term popularity, 50 when the term is half as popular and 0 when the number of searches is not high enough compared to other searches to represent a trend.

Conclusion

The “once in a century pandemic” announced in 2009 after the emergence of the A-H1N1 influenza virus generated a general and early mobilisation of national and international healthcare systems, whereas it seems that COVID-19, which we now know is more dangerous, has suffered from a combination of epidemiological and sociopolitical factors which made it more of a surprise epidemic.

The risk of an infectious disease with a potential to spread across the world was foreseen, but the international and national structures supposed to respond to it were not equally prepared. Scientific reports on global risks had not waited until 2020 to agree on the complexity and interdependence between multiple risks threatening the world equilibrium, a pandemic being one of the least negligible risks foreseen. The probability of such an event occurring is hard to estimate, but the potential severity of its consequences was already known as a hard fact. 2018, the unfortunate 100th anniversary of the “Spanish” flu, was an opportunity for scientists to recall that many epidemiological risks threaten our societies, and that they are never far away - in time or in space. During a conference titled “Are we ready for the next pandemic?”, Peter Piot, professor of public health and then director of the London School of Hygiene & Tropical Medicine was clear: our societies were insufficiently prepared for the new threats associated with infectious diseases. He offered several routes for improvement:

Local capacities for detection and fast reaction should be reinforced within countries;
Global health governance, represented by the WHO, should be strengthened;
Partnerships and communication between communities, NGOs and the private sector should be more systematic;
Data and sample sharing between scientific organisation and public healthcare systems should be automatic in due time;
The Research & Development system should function independently from market incentives.

These five points were already part of the essential reforms sketched after Ebola in 2015. Even though Ebola did not manage to transform the rules enough to help with the current epidemic, will COVID-19 transform governance and practices in both national and international healthcare systems?

Question 10: How can modelling tools help predict the inflections of the epidemic curve?

2020-04-02T00:00:00+00:00

Many phenomena can help flatten the epidemic curve and it is therefore very important to include them in our models. Practically, how do we do that?

We are going to answer this question using the tools and practices of mathematical epidemiology. In all simplicity of course.

Let’s take the textbook case of a model where individuals of a given population can be either healthy (and so susceptible to being infected), infected, or recovered. We find here the main components of most models developed on this website. In the jargon of epidemic modelling, we talk of the SIR (S for Susceptible, I for Infected and R for Recovered) model. This type of model is a classic of mathematical modelling.

In most of the questions already answered on this website, we were interested in a limited number of interacting individuals, whose individual behaviour was represented. In case we want to model entire populations (at the scale of France as a whole, or Europe or the world for example), it makes little sense to represent each individual’s behaviour, unless there are particular reasons to.

We instead consider population clusters to be homogenous in respect to their characteristics and behaviours, and purposefully limit the number of parameters: besides the initial population in each state S, I and R, we keep the contact rate, the rate of transmission, and the recovery rate.

Naturally, the rate of transmission and the recovery rate are parameters which depend on the disease as well as one the protected measures deployed. They are estimated from empirical or theoretical data collected from different countries since the beginning of the epidemic.

This type of model, which assumes (the strong hypothesis) that everyone will behave, get infected and develop the disease in the same way, is mostly expressed as mathematical equations. However, it is sometimes very useful to express it graphically.

The basic idea is very simple in theory (even though it is less so in practice): from an initial situation (for example 100,000 healthy people and 1 infected person) we compute the evolution of the number of healthy, infected and recovered people from their known quantity at the previous step in time as well as our two mechanisms of transmission and recovery.

Once the model is built, we find the epidemic curves we are looking for by solving the model analytically: we can now follow the evolution of the number of susceptible, infected and recovered people as a function of time.

From there and by fixing the initial conditions (i.e. the same quantities of susceptible, infected and recovered people at the start of the simulation), we can play with each parameter (the contact rate, contagiousness rate and recovery rate) to study its effect on the shape of the curves obtained.

A lockdown scenario will lead us to define a contact rate below the one used as a benchmark, in the hypothesis that things run otherwise “normally”. This way, setting a period of lockdown during our virtual epidemic will disrupt the epidemic curve.

If the simulator window appears truncated, just zoom out.

Simulate the impact of lockdow on the epidemic curve

You might wonder how we estimated the contact rate before and after lockdown: come this way!

Everything we’ve presented so far may look easy on paper… Except this: how do we actually estimate this contact rate before and during lockdown?

It is a peculiar question, isn’t it? On average, how many interactions do we have each day with other people? Obviously, we only consider interactions which imply a physical proximity with other people, thus allowing transmission of the virus. It seems obvious at first sight that this value has to vary enormously between a Parisian (or a New Yorker, a Shanghaian, etc.) who takes the metro/tube/subway at peak hour and someone who lives as a hermit in Lozère (or Idaho, or the Sichuan). However, we have to find an order of magnitude which can characterise our population as widely as possible (remember: we assume that all individuals behave in a similar way).

A study conducted in several European countries in 2007 brought an interesting statistic to light. It surveyed 7290 participants picked at random. Using logbooks of their interactions over a single day, participants reported a total of 97,904 close interactions. The main result was therefore that the average number of proximate contacts was 13.4 per person and per day. This is an interesting one for our model isn’t it?

What about the same parameter during lockdown? If people comply strictly, they spend most of their time at home and respect social distancing when they have to go out, so the contact rate should tend to zero shouldn’t it? If you have read questions 2 and 6, you already know that it is not that simple…

We are not able to find a precise answer to this question in the literature. Therefore we fix a default value of one, a single contact per person and per day on average during lockdown, so ten times less than usual.

How do we translate these two values (~10 and ~1 contact) to our model? Let’s see.

We already know that at each step of the simulation, a certain number of people will leave the stock of susceptible people to be counted as infected. This quantity depends on four elements:

The number of susceptible people in the population
The number of infected people in the population
The contact rate
The rate of transmission

The number of contacts an infected person will have with a susceptible individual at each step of the simulation corresponds to the multiplication of three terms: Number of Susceptible x Number of Infected x Contact rate.

If we go back to our initial situation (100,000 Susceptible and 1 Infected), in order to arrive at 10 contacts between an infected person and susceptible others at each time step, we have to define a contact rate of 0.0001 since 100,000 x 1 x 0.0001 = 10.

Of course, this value does not account for the interactions among susceptible people and among infected people. The interactions within groups (susceptible, infected or recovered) or with recovered people are not part of this computation.

Besides, the number of susceptible people evolve with time, and so does the number of infected or recovered people. The number of interactions will thus naturally evolve during the epidemic. This is easy to grasp, because the less susceptible people, the less interactions there can be between infected and susceptible people (this is, by the way, one of the principles behind herd immunity, as you will see in question 8).

If you have read our explanation carefully, another question might arise… Do you have it?

This computation is indeed updated “at each step of the simulation”. But what does the time of the simulation represent in our case?

This could (maybe) be the subject of another post ;)

In the meantime, if you want to know more about mathematical modelling of epidemics, we recommend you read this report written by one of the best research teams in the field.

It is as simple as that.

Question 11: COVID-19, a disease of the anthropocene?

2020-04-02T00:00:00+00:00

The concept of anthropocene was developed in the natural sciences and reappropriated by the humanities and social sciences in a more critical and political perspective. There is no consensus in the scientific debate. However, the general idea is that the Earth has entered a phase of its evolution which is irremediably determined by human activities that impact geological and climatic history. The beginning of this period is still largely debated by researchers. Did this start with the industrial revolution? With the first nuclear trials?

In the question, the use of the anthropocene concept seems to refer to the way human beings organise their habitat as well as the impact of their activities on Earth. With regards to COVID-19 and previous pandemics, there are several elements that we need to consider in order to understand the emergence and spread of these viruses.

The general mortality dynamics of populations at the global scale is not linear in time or space, but it is characterised instead by catch-up phases and breaks in variable rhythms. While noting a strong trend towards an increase in life expectancy at birth since the end of the 20th century, especially after WWII for a majority of the world population, we also notice breaks in this trend which coincide with the appearance of new diseases and forms of resistance to known diseases. The second half of the 20th century has seen a reduction of infectious, parasitic and deficiency diseases - at various speeds depending on the world regions - and by the appearance and identification of 1/ new pathogens (HIV/AIDS, viral hemorrhagic fever like EBOLA for example); 2/ former pathogens we thought were highly contained, if not eliminated, which have mutated (cholera 0139, multidrug resistant tuberculosis…) or whose expansion area has changed (insect-borne viral diseases such as dengue fever or yellow fever).

The causes for the emergence or re-emergence of pathogens are diverse (resistance to anti-infectious drugs, abandonment of health campaigns, reduction of vaccination…). The ones that are linked to transformations and developments of environments by humans are crucial (urbanisation, new modes of land use, actions on ecosystems and the climate…). These changes imply on one hand that pathogens, hosts, and vectors adapt one way or another to such new environments, transformed or built, and on the other hand, that the probability of interactions increases between wild and domesticated animal species, but also with humans.

The role of these transformations in pathogens crossing “the species divide” (from animal to man) is essential but it is also important to understand how they vary in time and why they spread geographically. For example, the Ebola hemorrhagic fever epidemic has occurred brutally and sporadically in parts of West Africa since 1976, when it was identified. Almost 30 years later, in December 2013, it spread wider and more regularly to specific regions of Africa, including in cities.

In general, the diffusion depends on the possibilities of movement by vectors and reservoirs, may they be animals or humans, and of their interactions. Some vectors like the mosquitoes take advantage of air or maritime transportation to settle outside of their regions of origin. They can also benefit from more favorable environmental conditions, including in other regions of the globe because of global warming.

With diseases where man is the vector, like the flu or the coronavirus, two factors are decisive geographically. Firstly, it is important to understand the organisation of circulation routes and the actors using them because they both play a role in connecting places. Secondly, it is necessary to identify how populations and settlements are organised: are they dispersed? Concentrated? Do people live in large global metropolises? In enclaved territories? These questions imply that differences in density and mobility (high or low? Over a large/small distance?) have consequences on the probabilities of interaction between places.

One of the most cited examples in the scientific literature is the appearance and diffusion of the “Black” plague in Europe between 1348 and 1352. It illustrates the importance of circulations along continental routes in the Middle Ages between Asia and Europe (Silk roads) and along maritime regional routes (Black sea and the Mediterranean), as well as fault lines and command centres of political and economic powers such as the Mongol Empire and its role in the development and strengthening of relations between Europe and Eastern Asia. The second pandemic of cholera (1829-1837) starting from South Asia (Bengal region), shows the intensification of connexions between places which has happened in the 19th century because of how large colonial empires (the Russian, Ottoman, British Empires…) expanded their maritime and railway networks, in rivalry and conflict with one another. Indeed, the pandemic started from colonial ports and then spread to hinterlands. It flourished with the acceleration and expansions of conflicts.

What about the COVID-19 pandemic? Even though it is too early to give a final explanation given the many unknowns about the disease, we can formulate a hypothesis about the conditions under which the virus was introduced. The potentials for circulation and diffusion seem to be higher in places which combine a high accessibility (1) and a high connexity (2). Several arguments are in favour of this hypothesis. The first one regards to the characteristics of the Hubei province and its capital city Wuhan: a large industrial Chinese centre and a flagship region for the economy (within the “Go West” programme of the Chinese government), with a large number of foreign companies (automobile, high-tech and biotech, steel industry, chemicals…). The region also stands in a central position inside the Beijing – Shanghai – Guangdong/Hong Kong triangle which serves more than 400 million people; it is a logistics platform located at one end of the large continental and maritime project of the “New Silk Roads” supported by China and other Asian countries.

It is in this economic and industrial hub of international influence, with a high development potential and therefore large environmental transformation, that the first COVID-19 victim was identified.

The second argument reflects the role of air travel. Wuhan is an important hub which has direct connexions with several larger capital cities in East Asia, the Middle East, Western Europe and North America. These capital cities’ hinterlands have served as gateways of the pandemic with airports acting as crossroads for the spread of the virus. The third argument is that among the first confirmed positive cases (the “tip of the iceberg”), many resided, were in contact with or worked in the centres and peripheries of large metropolises, and especially in places which host and connect the activities of the global production chain: the peripheries of Milano in Italy, of Seattle in the USA, of Munich in Germany, of Incheon in South Korea, of Mumbai in India, of Sidney in Australia, of Durban in South Africa…

These regions all have a very high potential for economic development linked with international investments. Among the first confirmed cases, many were very internationally mobile individuals who had circulated in affected areas (Hubei in China, Lombardy in Italy, the Qom province in Iran…). These individuals were, additionally, part of generally large social networks spread over large distances. Therefore, once they got infected, they contributed to the accelerated diffusion of the virus worldwide as well as the multiplication of local transmissions.

All in all, the high connexion of places has facilitated the spread of the virus at the global scale and has accelerated its diffusion in territories particularly well connected and accessible at the regional scale. This general dynamic has furthermore been amplified by various events: religious gatherings (in France, India and South Korea for example), folk festivals (the carnival in Germany), political rallies as in Spain and tourism in Austria. All these events both accelerated the local rate of transmission and spread the virus to more distant places.

The COVID-19 pandemic highlights the complex interactions between pathogens and fauna, land use changes, resources, human activities and mobility, even though these transformations have not suddenly appeared in the last 150 or 50 years. Plagues, cholera, flus… have tagged along throughout the human history of exchange, although the rhythm of environmental change and epidemics is faster nowadays. For some, the frequency of epidemics will inevitably increase as a consequence of the acceleration of alterations on the climate and the environment. To conclude, asking if COVID-19 is a disease of the anthropocene amounts to question the political responses that governments will make after this phase of crisis management. Some scientists worry already about the devastating effects that this crisis will have on the climate. Will sustainable development measures be slashed in order to prioritise the economy, with a renewed boost of fossil energy and a renewed pressure on natural resources? What will the political response be to the social and geographical inequalities that the epidemic reveals?

Footnotes

(1) It represents the availability of transportation options to connect places

(2) In a transportation network, places are well connected to one another.