Optimal control of a mathematical model for Japanese encephalitis transmission

Abstract

Japanese encephalitis (JE) is a vector-borne disease that causes encephalitis mostly children in Asia and livestock. A mathematical model can be used to predict JE spread in the future. In this paper, we analysed a mathematical model of JE transmission. We also applied several optimal control variables such as vaccination and treatment to the human population, insecticide to mosquito population, and vaccination to pig population. Based on the analysis results, we obtained two equilibriums, namely disease-free equilibrium and endemic equilibrium. The existence and stability of the equilibriums depended on R 0 (basic reproduction ratio). The disease-free equilibrium is locally asymptotically stable if R 0 < 1, while the endemic equilibrium is locally asymptotically stable if R 0 > 1. Furthermore, we determined the existence of the optimal control variables by Pontryagin Maximum Principle. Numerical simulation showed that the control strategies are effective to minimize the number of active JE in human, mosquito and pig population.