Analysis of a nonautonomous epidemic model with density dependent birth rate

In this paper, a nonautonomous SIRS epidemic model with density dependent birth rate is proposed and studied. Threshold conditions for the permanence and extinction of the disease are established. Some new threshold values of integral form are obtained. We prove that the disease is permanent if R0∗>0, and extinct if R1∗⩽0 or R2∗<0. For the periodic and almost periodic cases, these threshold conditions act as sharp threshold values for the permanence and extinction of the disease. Global asymptotic stability of periodic solution for the periodic system is derived. Some examples are given to illustrate the main results of this paper.