Optimal Control of an Epidemic Model of Leptospirosis with Nonlinear Saturated Incidences

Abstract

In this paper, we consider a leptospirosis epidemic model with non-linear saturated incidence by applying the optimal control techniques to eradicate the infection in the human population. Leptospirosis is the disease which effects human as well as Cattle. Our aim is to find such optimal control techniques for the eradication of leptospira in the host population. To do this, we define three control variables, one for human and the second and third one for Vector population. First we find the existence of the control problem and then we characterize the optimal control problem by using the well-known method of Pontryagin’s Maximum Principle. The numerical simulations of both the system are solving by using backward Runge-kutta order four schemes. Finally, the numerical results of both the systems are presented for comparison.