Optimal and Nonlinear Dynamic Countermeasure under a Node-Level Model with Nonlinear Infection Rate

Abstract

This paper mainly addresses the issue of how to effectively inhibit viral spread by means of dynamic countermeasure. To this end, a controlled node-level model with nonlinear infection and countermeasure rates is established. On this basis, an optimal control problem capturing the dynamic countermeasure is proposed and analyzed. Specifically, the existence of an optimal dynamic countermeasure scheme and the corresponding optimality system are shown theoretically. Finally, some numerical examples are given to illustrate the main results, from which it is found that (1) the proposed optimal strategy can achieve a low level of infections at a low cost and (2) adjusting nonlinear infection and countermeasure rates and tradeoff factor can be conductive to the containment of virus propagation with less cost.