Modeling and Analysis of the Spread of Japanese Encephalitis with Environmental Effects

A nonlinear mathematical model for the spread of Japanese Encephalitis, caused by infected mosquito feeding on susceptible human population incorporating demographic and environmental factors is proposed and analyzed. In the modeling process, it is assumed that the growth rates of reservoir animal population and vector mosquito population are enhanced due to environmental discharges caused by human population related factors. The model is analyzed by stability theory of differential equations and computer simulation. Both the disease-free and the endemic equilibria are found and their stability is investigated. It is found that whenever the disease-free equilibrium is locally asymptotically stable, the endemic equilibrium does not exist. The analysis of the model shows that if the growth rates of reservoir animal population and vector mosquito population caused by environmental factors increase, the spread of Japanese Encephalitis increases and the disease becomes more endemic due to human immigration. Numerical simulations are also carried out to investigate the influence of certain parameters on the spread of disease, to support the analytical results and illustrate possible behavioral scenario of the model.