Optimal control for a discrete model of hepatitis C with latent, acute and chronic stages in the presence of treatment

Abstract

In this article, we consider a discrete mathematical model of viral hepatitis C (HCV). The population we will study is divided into six compartments: the unawareness susceptible, awareness susceptible, exposed individuals, individuals with acute infection, individuals with chronic infection and the individuals undergoing treatement. Our objective is to find the best strategy to reduce the number of the unawareness susceptible, individuals with chronic infection and exposed individuals through three controls, respectively, education and awareness, access to early detection and treatment. We study the impact of each control mechanism individually and the impact of combinations of these strategies in the control of HCV. A discret version of Pontryagin’s maximum principle was used to characterize the optimal controls obtained. Numerical simulation of the results, using MATLAB software, showed the effectiveness of the proposed controls, and the results confirm the performance of the proposed optimization strategies.