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Dernière mise à jour : Mai 2018

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Epidemiological modelling and its use to manage COVID-19

Insights into mechanistic models, by the DYNAMO team

Over the next few weeks, we will present some key elements of epidemiological modelling through short educational articles. These articles will help you to better understand and decipher the assumptions underlying the epidemiological models that are currently widely used, and how these assumptions can impact predictions regarding the spread of pathogens, particularly SARS-CoV-2. The objective is to discover the advantages and limitations of mechanistic modelling, an approach that is at the core of the DYNAMO team's work. The examples of models will be inspired by models used in crisis, but sometimes simplified to make them accessible.

#6 – Why represent the heterogeneity of infected individuals in the model ? (2/2)

Other factors explain why the models are sometimes made more complex, particularly with regard to infected individuals. First of all, the diagrams of epidemiological models are the result of discussions between people with different profiles and disciplines: epidemiology, mathematics, computer science, but also virology, medicine, management, etc. These diagrams therefore result from a compromise between parsimony (i.e. the fewest possible parameters) and realism (associated with better readability of the model by non-modellers). To illustrate this, we have decomposed shedder individuals according to the level of excretion (pink vs. red), and the level of disease severity (light or dark blue). We also considered the level of symptom onset (see figure below). Compared to the diagram in article #5, this better reflects what experts in the field know about the infection and the disease. It also makes it possible to adjust the parameters (contacts, shedding levels; see table below) and the transitions according to the health states. Thus, this scheme considers that only individuals with severe symptoms (Iss) will go to hospital (H) or even to intensive care units (ICU), and are therefore at risk of dying from COVID-19.

Schéma de modélisation avec différents états I ("infecté")

Epidemiological model considering as health states: susceptible (S), latent non-shedding infected (E), incubating shedding infected (Ip), asymptomatic (Ia), pauci-symptomatic (Ips), moderately symptomatic (Ims), with severe symptoms (Iss), in hospital (H), in intensive care unit (ICU), cured (R), and dead (M). The strength of infection (λ) takes into account the difference in the contribution of shedding infected persons to new infections (adapted from Di Domenico et al. report).

Table of model parameters (adapted from Di Domenico et al. report).

Parameters

Definitions

Selected values

β

Basal transmission rate (day-1)

1.2

σ

Multiplying factor for reducing the excretion of Ip, Ia, Ips

0.42

v

Multiplying factor to reduce the contact of the Iss, H, ICU

0.25

1/ε

Average latency time (days)

3.7

1/γp

Average duration of the state Ip (days)

1.5

[pa, pps, pms, pss]

Probability of being Ia, Ips, Ims or Iss (sum = 1)

[0.3, 0.2, 0.3, 0.2]

1/γ

Average duration of states Ia, Ips, Ims, Iss (days)

2.3

pICU

Probability of admission to an intensive care unit due to severe symptoms

0.25

1/γH

Average duration at hospital (days)

15

(1-µH)

Proportion of H that recover

0.9

1/γICU

Average duration in intensive care unit (days)

20

(1-µICU)

Proportion of ICU that recover

0.7

These values give a basic reproductive rate R = 3.3 without control.

This type of model makes it possible, for example, to compare a situation without any control with a situation assuming a lockdown of the general population from March 16 to May 11, then a social distancing from May 11 to May 26 (end date of the predictions in the figures below). It is possible to look not only at the number of cumulative deaths (these observations being available and enabling the model to be calibrated), but also at the number of people in intensive care units. Thus, if the model is correctly defined and calibrated, it is possible to identify when to intervene to avoid exceeding hospital capacity. We will detail these aspects in a next article.

Nombre de décès cumulés par jour avec (en noir) et sans (en rouge) confinement
Nombre de personnes en soins intensifs par jour avec (en noir) et sans (en rouge) confinement

Predictions of the model in terms of cumulative number of deaths (top) and number of people in intensive care units (bottom), assuming an introduction of the virus on January 7 in the general French population, and assuming that lockdown reduces contacts by 90%, while social distancing reduces them by 50%. The observation data (cross) correspond to March 16, April 5, May 11 and May 26.

Such models can also help to test interventions that are targeted (e.g., only symptomatic individuals are isolated, with a longer detection time for the pauci-symptomatic), or that would not apply equally to all groups (e.g., social distancing requested from all, but less applied by the asymptomatic). Article #8 will continue this discussion, focusing more specifically on targeted management measures.