Analysis On An SIRS Epidemic Model With Age-structured

The main contents of this paper consist of two parts.The first part, an SIRS epidemic model with infection age is considered. The model isinvestigated by means of theories in di?erential and integral equation and the basic reproductivenumber is founded. We prove that the disease-free equilibrium is globally asymptotically stablewhen the basic reproduction number is less than one. When the basic reproductive number isgreater than one, the disease-free equilibrium is unstable, but an endemic equilibrium exists.The second part, an SIRS epidemic model with age-structured is discussed. By using thetheories and methods of di?erential and integral equation, we obtain the explicit expressionof the basic reproduction number. It is proved that the disease-free equilibrium is globallyasymptotically stable if the basic reproduction number is less than one, and at least one endemicequilibrium exists if the basic reproductive number is greater than one. Furthermore, theconditions on stability of endemic equilibrium are also given.