Modelling and Optimal Control of Multi Strain Epidemics, with Application to COVID-19

Abstract: This work introduces a novel epidemiological model that simultaneously considers multiple viral strains, reinfections due to waning immunity response over time and an optimal control formulation. This enables us to derive optimal mitigation strategies over a prescribed time horizon under a more realistic framework that does not imply perennial immunity and a single strain, although these can also be derived as particular cases of our formulation. The model also allows estimation of the number of infections over time in the absence of mitigation strategies under any number of viral strains. We validate our approach in the light of the COVID-19 epidemic and present a number of experiments to shed light on the overall behaviour under one or two strains in the absence of sufficient mitigation measures. We also derive optimal control strategies for distinct mitigation costs and evaluate the effect of these costs on the optimal mitigation measures over a two-year horizon. The results show that relaxations in the mitigation measures cause a rapid increase in the number of cases, which then demand more restrictive measures in the future.