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In this article, a nonlinear mathematical model used for the impact of vaccination on the control of infectious disease, Japanese encephalitis with a standard incidence rate of mosquitoes, pigs and humans has been planned and analyzed. During the modeling process, it is expected that the disease spreads only due to get in touch with the susceptible and infected class only. It is also assumed that due to the effect of vaccination, the total human population forms a separate class and avoids contact with the infection. The dynamical behaviors of the system have been explored by using the stability theory of differential equations and numerical simulations. The local and global stability of the system for both equilibrium states under certain conditions has been studied. We have set up a threshold condition in the language of the vaccine-induced reproduction number   R  (   α  1   )   , which is fewer than unity, the disease dies in the absence of the infected population, otherwise, the infection remains in the population. Furthermore, it is found that vaccine coverage has a substantial effect on the basic reproduction number. Also, by continuous efforts and effectiveness of vaccine coverage, the disease can be eradicated. It is also found a more sensitive parameter for the transmission of Japanese encephalitis virus by using sensitivity analysis. In addition, numerical results are used to investigate the effect of some parameters happening the control of JE infection, for justification of analytical results.

The influence of vaccination on the control of JE with a standard incidence rate of mosquitoes, pigs and humans