Dynamics of Japanese encephalitis - A study in mathematical epidemiology

An S --> I --> R --> S (susceptible-infective-recovered-susceptible) epidem iological model coupling the dynamics of the spread of Japanese encephaliti s (JE) in two populations, human and reservoir animals (pigs, cattle, equin es, birds, etc.) through a vector population (a particular species of mosqu itos, Culex vishnui, Culex tritaeniorhynchus, etc.) is discussed. We assume that there is a constant recruitment rate of the susceptibles into both th e populations, whereas the death rates are proportional to the population s izes, which are hence variables. We also assume that the human population i s regulated by the disease. Conditions for the existence of a unique endemi c equilibrium were found, and the endemicity of the disease is discussed. T he 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 compu ter simulation. The dynamics of disease transmission of JE during 1948-1956 in Japan were also investigated with the help of available data.