The manuscript analyzes a deterministic compartmental mathematical model for the dynamics of the transmission of Japanese encephalitis with saturated incidence rate and saturated treatment function. For regions with limited resources, the incorporation of the saturation therapy function is ideal. We add the logistic differential equation to the model along with the pig carrying capacity and assume that the pig population is infected and growing logistically in the environment. The model’s different equilibria are thoroughly studied and analysed for their stability. The model’s basic reproduction number, R0, is computed. The model shows the occurrence of backward bifurcation for R0 less than one, suggesting that when R0 less than one is not entirely sufficient for eradicate the disease for the population. The basic reproduction number’s key parameters’ sensitivity analysis is presented. The basic reproduction number R0 can change significantly with even a minor modification in any of these crucial parameters. Using real data, we used curve fitting through using 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.