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#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 (I_ss) will go to hospital (H) or even to intensive care units (ICU), and are therefore at risk of dying from COVID-19.

Epidemiological model considering as health states: susceptible (S), latent non-shedding infected (E), incubating shedding infected (I_p), asymptomatic (I_a), pauci-symptomatic (I_ps), moderately symptomatic (I_ms), with severe symptoms (I_ss), 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).

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.

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.