A SIRS Epidemic Model Incorporating Treatment and Age-Structured of Recovered Period

A SIR model incorporating treatment and ages-tructured of recovered period is investigated. It is assumed that infective ones recover from the disease with temporary immunity. Here the rate at which recovered individual move to susceptible class again, depends upon vaccine age and hence it is assumed to be a variable. By using the existence of root and characteristic values analysis, we show that determines whether the disease will become endemic or die out. From a biological point of view, our results indicate that (1) the disease can be eradicated if the treatment rate is controlled under relatively low threshold provided 0 ≤ I ≤ I₀; (2) When I >; I₀, the equilibrium E₁ is unstable whenever it exists.