On the problem of minimizing the epidemic final size for SIR model by social distancing
Résumé
We revisit the problem of minimizing the epidemic final size in the SIR model through social distancing of bounded intensity. In the existing literature, this problem has been considered imposing a priori interval structure on the time period when interventions are enforced. We show that when considering the more general class of controls with an L1 constraint on the confinement effort that reduces the infection rate, the support of the optimal control is still a single time interval. This shows that, for this problem, there is no benefit in splitting interventions on several disjoint time periods. However, if the infection rate is known beforehand to change with time once from one value to another one, then we show that the optimal solution could consist in splitting the interventions in at most two disjoint time periods.
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