Abstract
Deterministic epidemic models of SIS and SIR type are considered where births and deaths occur at equal rates with all new-borns being susceptible. In an SIS model the effect of births and deaths is to raise the threshold which determines the number of infectives as time approaches infinity. The asymptotic behavior in an SIS model is also indicated when the contact rate is periodic and when carriers are present. Asymptotic stability regions are determined for the equilibrium points in a host and vector SIS model and in an SIR epidemic model.
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© 1974 Springer-Verlag Berlin · Heidelberg
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Hethcote, H.W. (1974). Asymptotic Behavior and Stability in Epidemic Models. In: van den Driessche, P. (eds) Mathematical Problems in Biology. Lecture Notes in Biomathematics, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45455-4_10
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DOI: https://doi.org/10.1007/978-3-642-45455-4_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-06847-1
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