TRANSMISSION OF JAPANESE ENCEPHALITIS IN A 3-POPULATION MODEL

The model considered for the spread of Japanese Encephalitis (JE) in a human population of varying size from a reservoir population (pigs, c attle, equines, birds, etc.) through a vector population (particular s pecies of mosquitos) is of SIRS (susceptible-infective-recovered-susce ptible) type for the human and reservoir populations and SIS (suscepti ble-infective-susceptible) type for the vector population. We have con sidered the logistic differential equation with density-dependent birt h rate for the vector population whereas the reservoir population is o f constant size. We assume that the human population is regulated by t he disease, We also assume that there is a constant recruitment rate o f susceptibles into the human population. We perform an equilibrium an d stability analysis to find a threshold condition. If the threshold i s exceeded, then there is a unique equilibrium with disease present wh ich is locally stable to small perturbations and global stability depe nds on death rates and the ratio Of the equilibrium population sizes o f the infected vector and total human populations.