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Zbl 0836.92022
Hethcote, Herbert W.; van den Driessche, P.
(van den Driessche, P.)
An SIS epidemic model with variable population size and a delay. (English)
[J] J. Math. Biol. 34, No.2, 177-194 (1995). ISSN 0303-6812; ISSN 1432-1416/e

Summary: The SIS epidemiological model has births, natural deaths, disease-related deaths and a delay corresponding to the infectious period. The thresholds for persistence, equilibria and stability are determined. The persistence of the disease combined with the disease-related deaths can cause the population size to decrease to zero, to remain finite, or to grow exponentially with a smaller growth rate constant. For some parameter values, the endemic infective-fraction equilibrium is asymptotically stable, but for other parameter values, it is unstable and a surrounding periodic solution appears by Hopf bifurcation.

MSC 2000:: *92D30 Epidemiology
45M10 Stability theory of integral equations
45M05 Asymptotic theory of integral equations

Keywords: SIS epidemiological model; delay; thresholds; persistence; equilibria; stability; endemic infective-fraction equilibrium; periodic solution; Hopf bifurcation

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Zentralblatt MATH Berlin [Germany]