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Dynamics of Evolutionary Epidemiological SIR Model with Varying Total Population Size.

Infectious diseases have often had a big impact on population sizes and historical events. Therefore, the constant population size models are not often suitable when the natural births and deaths are not balanced or when the disease-related deaths are significant. Moreover mutation of Pathogens is an important phenomenon of the disease dynamics, as pathogens can reproduce quickly. As a consequence, in this paper the evolutionary behavior of SIR model considering variable population size has been studied. The resident strain and mutant strain have been introduced with the SIR model considering varying population size and analyzed their behavior of dynamics. It has shown the disease free equilibrium is locally asymptotically stable if 1 0 < r R and 1 0 < m