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Endemic infections in growing populations. (English) Zbl 0586.92018
For a homogeneously mixing population, the authors consider the effects of an increasing population upon the incidence of a particular infection. This feature of an increasing population differs from most epidemic models with assumption of constant host population.
An age-structured compartmental model is formulated with susceptible, infectious, and recovered/immune categories. The population growth occurs in a fixed finite region so that density and infection rates are increasing over time. The density dependent tranmission has the form $$\beta$$ XY, where X is the number of susceptibles and Y is the total number of infectious individuals per unit area.
Asymptotic expressions for the force of infection are obtained explicitly when the death rate is given by (1) everyone dies at age L, or (2) an age-independent mortality rate $$\mu$$. For type (1) survivorship, explicit analytic and numerical examples are given to illustrate the age-specific patterns of susceptibility as functions of time.
Reviewer: S.M.Lenhart

##### MSC:
 92D25 Population dynamics (general)
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##### References:
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