GLOBAL DYNAMICS OF AN SIVS EPIDEMIC MODEL WITH BILINEAR INCIDENCE RATE

An SIS type epidemic model with variable population size is considered. The model includes a temporary vaccination program to prevent individuals from infection and to eradicate the disease. If R-0 < 1, the disease-free equilibrium is locally and globally asymptotically stable i.e. the disease will be wiped out from population. When R-0 > 1, the endemic equilibrium is locally asymptotically stable employing a result in stability of the second additive compound matrix. In addition, by using a geometric approach it is shown that this equilibrium is also globally asymptotically stable. So in this case, the disease will persist in population permanently. Also, a briefly discussion is made on the minimum amount of vaccination which is necessary to eradicate the disease. Finally, some numerical examples are given to confirm the obtained results.