Sensitivity and Optimal Control Analysis of Japanese Encephalitis Disease: A Mathematical Model

Abstract

Japanese encephalitis is caused by flavivirus, which can affect both humans and animals. A Japanese encephalitis disease model is proposed and analyzed to investigate the transmission dynamics of Japanese encephalitis with saturated incident rate and saturated treatment function. Assume that the infected pig populations are growing logistically in the environment. The basic reproduction number R0 of the model is obtained using the next-generation matrix method. The sensitivity analysis is performed to identify the key parameters that affect the basic reproduction number, which can be regulated to control the transmission dynamics of the disease. The model is extended to optimal control model incorporating three time-dependent inputs for the control of transmission route by using Pontryagin's maximum principle. This study is significant as Japanese encephalitis disease poses serious challenges for public health in past few years. Numerical simulation is performed to support our analytical findings.