Abstract
In this paper, our main purpose is to investigate mathematical aspects of the Pease’s evolutionary epidemic model for type A influenza. First we formulate the Pease model as an abstract semilinear Cauchy problem and construct the semigroup solution. Next we prove existence and uniqueness of the endemic steady state and show endemic threshold phenomena. Subsequently by using semigroup approach, we investigate the local stability of endemic steady state. We prove that the endemic steady state is locally asymptotically stable if its prevalence is greater than fifty percent. Finally we discuss some possible extensions of the Pease’s model and open problems.
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Inaba, H. (2002). Endemic Threshold and Stability in an Evolutionary Epidemic Model. In: Castillo-Chavez, C., Blower, S., van den Driessche, P., Kirschner, D., Yakubu, AA. (eds) Mathematical Approaches for Emerging and Reemerging Infectious Diseases: Models, Methods, and Theory. The IMA Volumes in Mathematics and its Applications, vol 126. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0065-6_19
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DOI: https://doi.org/10.1007/978-1-4613-0065-6_19
Publisher Name: Springer, New York, NY
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