The co-dynamics of malaria and tuberculosis with optimal control strategies

Abstract

Malaria and Tuberculosis are both the severe and causing death diseases in the world. The occurrence of TB and malaria as a coinfection is also an alarming threat to the human. Therefore, we consider a mathematical model of the dynamics of malaria and tuberculosis coinfection and explore its theoretical results. We formulate the model and obtain their basic properties. We show that at the disease free case each model is locally asymptotically stable, when the basic reproduction number less than unity. Further, we analyze the phenomenon of backward bifurcation for coinfection model. For the sub models, we present the local stability for the disease free case whenever the basic reproduction number less than 1. Further, an optimal control problem is presented to investigate the dynamics of malaria and tuberculosis coinfection. The numerical results with different scenarios are presented. The mathematical model with and without control problemare solved numerically using the Runge-Kutta backward and forward scheme of order four.