Coinfection Dynamics of Tuberculosis with Other Infectious Diseases—A Mathematical Study

Abstract

This study investigates the SEIR mathematical model to examine the co-dynamics of tuberculosis and other infectious diseases. Tuberculosis patients are known to have a higher susceptibility to additional infections due to compromised immunity. As such, understanding the dynamics of co-infections involving tuberculosis is critical, given their significant contribution to the overall disease burden in a population. In this paper, we propose an SEIR model that accounts for saturated treatment and incidence rates. A local stability analysis of the model is conducted, along with the calculation of the basic reproduction number. We also perform a sensitivity analysis of the reproduction number. Furthermore, an optimal control problem is formulated to enhance prevention strategies and minimize the costs associated with managing co-infectious diseases. The findings highlight that providing effective treatment to the infected population is the most impactful and cost-efficient strategy for disease control.