A Distributed Optimal Control Model Applied to COVID-19 Pandemic

In this paper, a distributed optimal control epidemiological model is presented. The model describes the dynamics of an epidemic with social distancing as a control policy. The model belongs to the class of continuous-time models, usually involving ordinary/partial differential equations, but has a novel feature. The core model---a single integral equation---does not explicitly use transition rates between compartments. Instead, it is based on statistical information on the disease status of infected individuals, depending on the time since infection. The approach is especially relevant for the coronavirus disease 2019 (COVID-19) in which infected individuals are infectious before onset of symptoms during a relatively long incubation period. Based on the analysis of the proposed optimal control problem, including necessary optimality conditions, this paper outlines some efficient numerical approaches. Numerical solutions show some interesting features of the optimal policy for social distancing, depending on the weights attributed to the number of isolated individuals with symptoms and to economic losses due to the enforcement of the control policy. The general nature of the model allows for inclusion of additional epidemic features with minor adaptations in the basic equations. Therefore, the modeling approach may contribute to the analysis of combined intervention strategies and to the guidance of public health decisions.