Abstract
An infectious disease may reduce or even stop the exponential growth of a population. We consider two very simple models for microparasitic and macroparasitic diseases, respectively, and study how the effect depends on a contact parameter kappa. The results are presented as bifurcation diagrams involving several threshold values of kappa. The precise form of the bifurcation diagram depends critically on a second parameter xi, measuring the influence of the disease on the fertility of the hosts. A striking outcome of the analysis is that for certain ranges of parameter values bistable behaviour occurs: either the population grows exponentially or it oscillates periodically with large amplitude.
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