22.07.2020

Modeling Infectiology

Djidjou-Demasse R et al

Pre-prints

The authors show that there is an attenuation strategy for an epidemic until production of a vaccine, and that such strategies greatly reduce the number of deaths over that period. It is worth noting that the optimal strategy (with the chosen parameters) seems to be to keep the number of severe infections at a low level (1/100th of the capacity of intensive care units), then to lift containment measures just before the deployment of the vaccine. The authors also show that these results are relatively robust. Thus, reinstating containment measures at regular intervals according to data from the previous time period provides effective control over the number of deaths linked to the pandemic.

This article determines optimal control methods for an epidemic over a fixed period of time (while waiting for a vaccine). The goal is to control the epidemic while minimizing the number of deaths caused, directly and indirectly, by saturation of the health system, as well as the cost associated with the control strategy.

This is a very interesting optimization result. The authors take into account the saturation of the medical system and the number of associated deaths due to an epidemic.

The model used by the authors is fairly complex, with a large number of parameters. It is worth noting that the time T before the vaccine is distributed is assumed to be known, which has a non-negligible impact on the optimal solution (containment measures are released a defined time before T, because those newly infected would otherwise die after T).

It would also be interesting to study the effect of a parameter measuring the relative cost of containment measures with respect to the number of deaths.

The objective of this study is to determine strategies that permit control of an epidemic by limiting the maximum number of deaths due to the epidemic, as well as the cost associated with the control policy. Specifically, the article incorporates increases in mortality due to saturation of the health care system. Different “actualized” strategies are also considered, such as a control policy unrolled at regular intervals, a constant control policy, or alternation between periods of maximal (complete containment) and minimal control.

The authors consider a relatively complex SEAIR-type model with differentiation between moderate and severe infection. Individuals can be Susceptible (S) to infection, then become Exposed (E) if they are infected. After a latency period, these individuals become Asymptomatic carriers (A), during which period they infect others, then Infected (I) and symptomatic, and finally Recovered (R). A fraction of infected individuals develop severe disease. If these individuals are few enough in number that all can be treated, their death rate remains low. On the other hand, if their number is high enough, their death rate, as well as that of all individuals ill for other reasons, increases greatly due to saturation of the health care system. The authors utilize classic methods of differential equations and optimization to determine the optimal strategy to control the epidemic (based on infected cases), which simultaneously minimizes the total number of deaths and the duration and stringency of the control policy. Using numerical analysis, the authors can simulate these optimal values and the progression of the epidemic under these optimal strategies.

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