A co-infection model of dengue and leptospirosis diseases

Abstract

In this paper an SIR deterministic mathematical model for co-infection of dengue and leptospirosis is proposed. We use a compartment model by using ordinary differential equations. The positivity of future solution of the model, the invariant region, and the stability of disease-free equilibrium point as well as endemic equilibrium point are studied. To study the stability of the equilibria, a basic reproduction number is obtained by using the next generation matrix. The robustness of the model is also investigated. To identify the effect of each parameter on the expansion or control of the diseases, sensitivity analysis is performed. The effects of treating dengue infected only, leptospirosis infected only, and co-infected individuals have been identified by using the numerical simulation. Therefore, increasing the rate of recovery and decreasing the contact rate of dengue, leptospirosis, and their co-infection have a great influence in fighting dengue, leptospirosis, and their co-infection in the community.