A Mathematical Framework for the Transmission Dynamics and Optimal Control of HCV-HIV Coinfection and Superinfection

This paper proposes a compartmental mathematical model to study the transmission dynamics of coinfection and superinfection caused by HCV-HIV. Initially, the model is analyzed without any control measure. The disease-free and endemic equilibrium points are determined, and also their local and global stability is examined using the Direct Lyapunov Method. The model is then extended by incorporating optimal controls representing treatment strategies for HCV and HIV. An optimal control problem is formulated, and the existence of optimal controls is established. Necessary conditions for optimality are derived using Pontryagin’s maximum principle. Numerical simulations, along with local and global sensitivity analyses, are performed to demonstrate the impact of various treatment strategies and to identify the most influential factors contributing to the spread of the infection. The results show that infection parameters are contributing to the prevalence while optimal controls significantly reduce the prevalence of both coinfection and superinfection. Further, it is pointed out that there is a chance of permanent cure in case of HCV since reinfection in general does not occur. However, in case of HIV and AIDS, there is no permanent cure; therefore, coinfection and superinfection remain a significant risk, making permanent eradication unlikely. Hence, it is recommended to continue applying the control strategies for suppressing and managing these infections effectively.