Almost periodic positive solutions for a time-delayed SIR epidemic model with saturated treatment on time scales

In this paper, we study a non-autonomous time-delayed SIR epidemic model which involves almost periodic incidence rate and saturated treatment function on time scales. By utilizing some dynamic inequalities on time scales, sufficient conditions are derived for the permanence of the SIR epidemic model and we also obtain the existence and uniform asymptotic stability of almost periodic positive solutions for the addressed SIR model by Lyapunov functional method. Finally numerical simulations are given to demonstrate our theoretical results.

Keywords:

SIR model , time scale , almost periodic incidence rate , almost periodic positive solution , permanence , uniform asymptotic stability