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Theor Popul Biol. 2001 Aug;60(1):59-71.

Realistic distributions of infectious periods in epidemic models: changing patterns of persistence and dynamics.

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Program in Theoretical Biology, Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540, USA.


Most mathematical models used to study the epidemiology of childhood viral diseases, such as measles, describe the period of infectiousness by an exponential distribution. The effects of including more realistic descriptions of the infectious period within SIR (susceptible/infectious/recovered) models are studied. Less dispersed distributions are seen to have two important epidemiological consequences. First, less stable behaviour is seen within the model: incidence patterns become more complex. Second, disease persistence is diminished: in models with a finite population, the minimum population size needed to allow disease persistence increases. The assumption made concerning the infectious period distribution is of a kind routinely made in the formulation of mathematical models in population biology. Since it has a major effect on the central issues of population persistence and dynamics, the results of this study have broad implications for mathematical modellers of a wide range of biological systems.

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