A DISEASE TRANSMISSION MODEL IN A NONCONSTANT POPULATION

A general SIRS disease transmission model is formulated under assumpti ons that the size of the population varies, the incidence rate is nonl inear, and the recovered (removed) class may also be directly reinfect ed. For a class of incidence functions it is shown that the model has no periodic solutions. By contrast, for a particular incidence functio n, a combination of analytical and numerical techniques are used to sh ow that (for some parameters) periodic solutions can arise through hom oclinic loops or saddle connections and disappear through Hopf bifurca tions.