GLOBAL DYNAMICS OF AN SIVS EPIDEMIC MODEL WITH BILINEAR INCIDENCE RATE

Abstract

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 \(\mathcal{R}\)₀ < 1, the disease-free equilibrium is locally and globally asymptotically stable i.e. the disease will be wiped out from population.  When \(\mathcal{R}\)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.