In this short note we give threshold quantities that determine the stability of the infection-free steady state for periodic deterministic systems that describe the spread of infectious diseases in populations whose individuals can be divided into a finite number of distinct groups. We concentrate on "micro-parasitic" infections, but the theory was originally developed for helminth infections. As an example, we treat a simple model of a vector transmitted infection with periodic recruitment in the vector population.
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Heesterbeek et al. (1995) studied this question.
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