Eco-Epidemiological model and optimal control of disease transmission between humans and animals

Abstract

In this paper, a nonlinear mathematical model is proposed to study the dynamics of disease transmission between human beings and animals. The disease free equilibrium is established and it is locally asymptotically stable if the basic reproduction number R0< 1. To determine how a marginal change in any one of the parameters in R0would impact on the prevalence of the infection, a sensitivity analysis is carried out by using the Forward Normalized Sensitivity Index. We then modify the basic model into an optimal control problem by incorporating three controls to check the spread of the disease. These controls are grouped into curatives and preventives. It shows that a combine effort of both curatives and preventives is necessary to combat the disease. Numerical simulations are also provided to illustrate the mathematical results. Finally, various options of combinations of the controls are examined to determine the most cost effective combination that can control the infection by using the Incremental Cost-Effectiveness Ratio. It indicates that the combine effort of curatives and preventives is preferable but the preventive is better than the curative strategies.