Dynamics of Japanese encephalitis - A study in mathematical epidemiology

An S --> I --> R --> S (susceptible-infective-recovered-susceptible) epidemiological model coupling the dynamics of the spread of Japanese encephalitis (JE) in two populations, human and reservoir animals (pigs, cattle, equines, birds, etc.) through a vector population (a particular species of mosquitos, Culex vishnui, Culex tritaeniorhynchus, etc.) is discussed. We assume that there is a constant recruitment rate of the susceptibles into both the populations, whereas the death rates are proportional to the population sizes, which are hence variables. We also assume that the human population is regulated by the disease. Conditions for the existence of a unique endemic equilibrium were found, and the endemicity of the disease is discussed. The threshold values determine whether the disease dies out or approaches an endemic equilibrium. The persistence of disease and disease-related death can lead to a new equilibrium population size. The criteria for eradication of the disease have been worked out. The analytical results corresponding to the solutions of our system are verified by numerical analysis and computer simulation. The dynamics of disease transmission of JE during 1948-1956 in Japan were also investigated with the help of available data.