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arXiv · 2405.06628

Optimal epidemic control by social distancing and vaccination of an infection structured by time since infection: the covid-19 case study

Alberto d'Onofrio·Mimmo Iannelli·Piero Manfredi·Gabriela Marinoschi
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Abstract

Motivated by the issue of COVID-19 mitigation, in this work we tackle the general problem of optimally controlling an epidemic outbreak of a communicable disease structured by time since exposure, by the aid of two types of control instruments namely, social distancing and vaccination by a vaccine at least partly effective in protecting from infection. Effective vaccines are assumed to be made available only in a subsequent period of the epidemic so that - in the first period - epidemic control only relies on social distancing, as it happened for the COVID-19 pandemic. By our analyses, we could prove the existence of (at least) one optimal control pair, we derived first-order necessary conditions for optimality, and proved some useful properties of such optimal solutions. A worked example provides a number of further insights on the relationships between key control and epidemic parameters.

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Alberto d'Onofrio, Mimmo Iannelli, Piero Manfredi, Gabriela Marinoschi. 2024-05-10. Optimal epidemic control by social distancing and vaccination of an infection structured by time since infection: the covid-19 case study. https://doi.org/10.1137/22m1499406

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