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A core group model for disease transmission. (English) Zbl 0832.92021
Summary: Models for sexually transmitted diseases generally assume that the size of the core group is fixed. Publicly available information on disease prevalence may influence the recruitment of new susceptibles into highly sexually active populations. It is assumed that the recruitment rate into the core population is low while disease prevalence is high, core group members mix only with each other, disease levels outside the core are negligible, and some core group members reduce their risk through the use of a partially effective vaccine or prophylactics.
A demographic-epidemic model is formulated in which the combined size of the core and non-core population is constant. A simpler version models the epidemic in an isolated core population of constant size under the influence of educational programs and measures that reduce susceptibility. The threshold condition for an endemic infection is determined. Backward bifurcations, multiple infective stationary states, and hysteresis phenomena can be observed even in the simplified version. Abrupt changes in disease prevalence levels may result from small changes in the disease management parameters and do not occur in the absence of such a program. The general conclusion is that partially effective vaccination or education programs may increase the total number of cases while decreasing the relative frequency of cases in the core group.
The study throws some new light on the role of the reproduction number in connection with elimination attempts. It shows that although the reproduction number defines the threshold for the spread of the disease in a susceptible population, it is of limited value when elimination of an existing epidemic is planned.

MSC:
92D30 Epidemiology
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