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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Supported in part by NSERC grant A-8965, the University of Victoria Committee on Faculty Research & Travel, and the Institute for Mathematics and its Applications, Minneapolis, MN, with funds provided by NSF
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Derrick, W.R., van den Driessche, P. A disease transmission model in a nonconstant population. J. Math. Biol. 31, 495–512 (1993). https://doi.org/10.1007/BF00173889
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DOI: https://doi.org/10.1007/BF00173889