Optimal Control Solution for Rabies Disease Transmission within Free-ranging Dog

Abstract

This paper considers deterministic model for transmission dynamics of rabies virus in the free-ranging dog population. The stability of system near by Disease Free Equilibrium point is analized using Next Generation Matrix. The effect of vaccination in susceptible dog population is considered on the model. We then present the effective reproduction number in the present of the vaccination. Further we developed the formula to obtain the optimal vaccination to eliminate the endemic equilibrium, via the Pontryagin Maximum Principle. Numerical example are presented  to show the properties of the optimal control solution.