Stochastic optimal control model for COVID-19: mask wearing and active screening/testing

The main objective of this article is to study the effectiveness of wearing masks and implementing active screening and testing to contain the spread of COVID-19 during stages when the disease has already started to spread. This work innovates by focusing on the basic measures of mask use and active screening and testing, which are frequently overlooked in the literature in favor of more expensive interventions like travel bans and vaccinations. We study their effectiveness and determine the optimal way to implement them. To achieve this goal, we develop a stochastic SEIR model that includes four populations: susceptible, exposed, infected, and recovered individuals. We integrate two control functions into the model to represent mask-wearing and active screening and testing interventions. Using an adapted formulation of Pontryagin’s maximum principle suitable for the stochastic context, we aim to find the optimal approach to implementing these controls. We combine the Forward-Backward Sweep Method (FBSM) with a special Runge–Kutta scheme for stochastic differential equations to solve the optimality system for our stochastic optimal control problem. Our study demonstrates that even when the disease has begun to spread, using both mask-wearing and active screening and testing can lead to significant reductions in the numbers of exposed and infected individuals, offering a cost-effective strategy for countries with limited resources.