Modelling zoonotic diseases with treatment in both human and animal populations

Abstract

This paper proposes and analyzes a nonlinear mathematical model to study the factors responsible for transmission of zoonotic diseases and how effectively the zoonotic diseases can be managed. The disease free equilibrium of the system is established and the effects of the model parameters on the disease transmission dynamics are equally assessed. We then modify the basic model into an optimal control problem by incorporating three control variables into the model which are categorized into curative and preventive strategies. Numerical simulations of the optimal control problem are also carried out to determine the most cost-effective of various options of combinations of the controls. The results indicate that the combined effort of curatives and preventives is the most cost-effective strategy to combat the spread of the zoonotic disease.

https://doi.org/10.28919/cmbn/3236