AN SIS EPIDEMIC MODEL WITH VARIABLE POPULATION-SIZE AND A DELAY

The SIS epidemiological model has births, natural deaths, disease-rela ted deaths and a delay corresponding to the infectious period. The thr esholds for persistence, equilibria and stability are determined. The persistence of the disease combined with the disease-related deaths ca n cause the population size to decrease to zero, to remain finite, or to grow exponentially with a smaller growth rate constant. For some pa rameter values, the endemic infective-fraction equilibrium is asymptot ically stable, but for other parameter values, it is unstable and a su rrounding periodic solution appears by Hopf bifurcation.