Application of various control strategies to Japanese encephalitic: A mathematical study with human, pig and mosquito.

Japanese encephalitis (JE) is a public health problem that threats the entire world today. Japanese Encephalitis virus (JEV) mostly became a threat due to the significant number of increase of susceptible mosquito vectors and vertebrate hosts in Asia by which around 70,000 cases and 10,000 deaths per year took place in children below 15 years of age. In this paper, a mathematical model of JE due to JEV from the vector source (infected mosquito) and two vertebrate hosts (infected human and infected pig) is formulated. The disease can be controlled by applying several control measures such as vaccination, medicine and insecticide to the JE infection causing species. The model has been formulated as an optimal control problem and has been solved using Pontryagin's maximum principle. Also, the stability of the system has been studied with the help of basic reproduction number for disease free and endemic equilibrium. The results of fixed control for endemic equilibrium is presented numerically and depicted graphically. The effects of different control strategies on human, pig and mosquito has been analyzed using Runge-Kutta 4th order forward and backward techniques and presented thereafter graphically.