An Optimal Control Approach for Public Health Interventions on an Epidemic-Viral Model in Deterministic and Stochastic Environments

Abstract

Dynamical models for within-host infectious diseases and between-host propagation behave differently with respect to time scale. Although, they represent a challenge for learning more about the impact of a viral load on the behavior of an epidemic model in a certain population. In this paper, we investigate pharmaceutical and non-pharmaceutical interventions in a framework that couples a viral and an epidemic model. We propose an optimal control for both deterministic and stochastic models, where we show the existence of deterministic and stochastic optimal controls for public health interventions with quarantine. Then, using Pontryagin’s maximum principle, we characterize an optimal control for non-pharmaceutical interventions, vaccination campaigns, and treatment strategies. Finally, numerical simulations and sensitivity analysis are conducted to illustrate our theoretical results.