Patterns in the effects of infectious diseases on population growth.
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.
Diekmann
O
O
Centrum voor Wiskunde en Informatica, Amsterdam.
Kretzschmar
M
M
D001723:Birth Rate; D003141:Communicable Diseases / Q000453:epidemiology*; D004196:Disease Outbreaks; D005298:Fertility; D006801:Humans; D008433:Mathematics; D015233:Models, Statistical; D009026:Mortality; D010272:Parasitic Diseases / Q000453:epidemiology*; D011158:Population Growth