Abstrak RSS

A Condition for Stability in an SIR Age Structured Disease Model with Decreasing Survival Rate

A Condition for Stability in an SIR Age Structured Disease Model with Decreasing Survival Rate
Asep K. Supriatna
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In this paper we present an SIR model for disease transmission with an assumption that individuals in the under-laying demographic population experience a monotonically decreasing survival rate. We show that the results in an analogous SI model for disease transmission are the special case of the SIR model in this paper. We found that there is a threshold for the disease transmission determining the existence and the absence of the endemic equilibrium. We investigate the stability of this equilibrium via a Gronwall-like inequality theorem. Unlike in the SI model, the threshold for the existence is not equivalent to the threshold for the stability of the equilibrium. We provide an additional condition which consistently generalizes the results in the SI model.

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