Optimal Control Solution for Rabies Disease Transmission within Free-ranging Dog Population
Eti D. Wiraningsih1, a), Z. Jamaludin2,b), A. P. Ramadhan2,c), M. Misbach2,d) and Asep K. Supriatna2,e)
1Department of Mathematics, Faculty of Mathematics and Natural Sciences, State University of Jakarta, DKI-Jakarta, Indonesia
2Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Padjadjaran, Bandung-West Java, Indonesia
a)Corresponding author: etidwi[at]gmail.com
Abstract
This paper considers deterministic model for transmission dynamics of rabies virus in the free-ranging dog population. The endemic equilibrium is found and its existence depends on the value of the basic reproduction number. 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. Some numerical example are presented to show the properties of the optimal control solution.
Keywords: Rabies mathematical model, effective reproduction number, optimal control.
Topic: Mathematics