The Qualitative analysis of a mathematical model in the transmission of Japanese Encephalitis with saturated treatment

Abstract

The analysis of a compartmental deterministic mathematical model for the dynamics of Japanese encephalitis transmission that includes a saturated incidence rate and saturated treatment function is presented in the manuscript. The saturation therapy feature should be included in areas with low resources. We assume that the pig population is diseased and logistically expanding in the environment and include the logistic differential equation in the model along with the pig carrying capacity. The model's different equilibria are thoroughly studied and analyzed for their stability. The model's basic reproduction number, $\mathcal R_0$, is computed. The model shows the occurrence of backward bifurcation for $\mathcal R_0$ less than one, suggesting that when $\mathcal R_0$ less than one is not entirely sufficient for eradicating the disease for the population. The basic reproduction number's key parameters' sensitivity analysis is presented. The basic reproduction number $\mathcal R_0$ can change significantly with even a minor modification in any of these crucial parameters. Using real data, we used curve fitting by using the least squares method, contour plots, and box plots to show the number of infected patients in two different Indian states. In order to support our analytical findings, numerical simulation is shown.