An SIS epidemic model with variable population size and a delay.
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.
Hethcote
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Department of Mathematics, University of Iowa, Iowa City 52242, USA.
van den Driessche
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D004196:Disease Outbreaks / Q000706:statistics & numerical data; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D011156:Population Density; D013997:Time Factors