A disease transmission model in a nonconstant population
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Updated: Nov 8, 2026

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
Published on: July 4, 2007
W R Derrick1, P van den Driessche
1Department of Mathematics, University of Montana, Missoula 59812.
Abstract:
A general SIRS disease transmission model is formulated under assumptions that the size of the population varies, the incidence rate is nonlinear, and the recovered (removed) class may also be directly reinfected. For a class of incidence functions it is shown that the model has no periodic solutions. By contrast, for a particular incidence function, a combination of analytical and numerical techniques are used to show that (for some parameters) periodic solutions can arise through homoclinic loops or saddle connections and disappear through Hopf bifurcations.
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