Global Dynamics and Optimal Control of a Viral Infection Model with Generic Nonlinear Infection Rate

Abstract

This paper is devoted to exploring the combined impact of a generic nonlinear infection rate and infected removable storage media on viral spread. For that purpose, a novel dynamical model with an external compartment is proposed, and the explanations of the main model assumptions (especially the generic nonlinear infection rate) are also examined. The existence and global stability of the unique equilibrium of the model are fully investigated, from which it can be seen that computer virus would persist. On this basis, a next-best approach to controlling the level of infected computers is suggested, and the theoretical analysis of optimal control of the model is also performed. Additionally, some numerical examples are given to illustrate the main results.