Stability analysis of infectious diseases model in a dynamic population

Abstract

The stability analysis of infectious disease model in a dynamic population is studied.The recruitment rate into the susceptiblepopulation is introduced since the population is dynamic thereby allowing a varying pouplation as a result of migration and birth.Themodel exhibited two equilibria: the disease free and endemic. The local stability of the model is asymptotically stable when R0 < 1 andunstable when R0 > 1. The global stability analysis of the disease free shows that the system is globally stable when the first derivativeof Lyapunov function is negative.