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.