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In this paper we investigate the effects of variable infectivity on the spread of HIV in a heterosexual population where pair formation and separation are taken into account. We calculate the basic reproduction ratio as a function of the number of new partners during the infectious period, keeping t
The literature on the mathematical modelling of infectious diseases has grown enormously in recent years, both in quantity and quality. Here, we briefly point to the purposes of these modelling exercises and introduce the main ideas behind compartmental models, to act as a guide to the (bio)mathemat
It is shown how one can calculate the basic reproduction ratio R0 for infectious disease models where an arbitrary but finite number of disease states are recognized and where the phenomena of pair formation and separation are taken into account. Several examples are discussed
The expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population is mathematically defined as the dominant eigenvalue of a positive linear operator. It is shown that in certain special cases one can eas
Certain infectious plant diseases are controlled by inspection and subsequent hand removal of diseased parts. In this paper we give two sets of criteria from which one can conclude whether this control effort is adequate or not. These criteria do not require knowledge of the infection- or detection
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