Global results for an SIRS model with vaccination and isolation

Motivation is provided for the development of an SIRS epidemiological model with both vaccination and isolation control strategies. The model is then formulated and analyzed. In particular, the conditions for the existence of multiple endemic equilibria are given. The backward bifurcation, forward bifurcation and saddle–node bifurcation are explored. When the control reproduction numbers are below or over unity, local and global stabilities of the disease-free equilibrium and endemic equilibria are proved under certain parameter conditions. The critical vaccination rate and isolation rate are calculated, which determine the disease’s endemicity.