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For parasites with a clearly defined life-cycle we give threshold quantities that determine the stability of the parasite-free steady state for autonomous and periodic deterministic systems formulated in terms of mean parasite burdens. We discuss the biological interpretations of the quantities, how
In this paper the dynamics and control of nematode parasites of farmed ruminants are discussed via a qualitative analysis of a differential equation model. To achieve this a quantity, 'the basic reproduction quotient' (Q0), whose definition coincides with previous definitions of R0 for macroparasite
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 o
An explicit algorithm is given for the computation of the basic reproduction ratio R0 (of the net reproduction ratio R in the case of a not wholly susceptible population) for a class of discrete-time epidemic models. These models allow for a finite number of different individual types, type changes
In this paper we present a generalization of a finite dimensional singular perturbation theorem to Banach spaces. From this we obtain sufficient conditions under which a faithful simplification by a time-scale argument is justified for age-structured models of slowly growing populations. An explicit
In this note we show how to derive, by a mechanistic argument, an expression for the saturating contact rate of individual contacts in a population that mixes randomly. The main assumption is that the individual interaction times are typically short as compared to the time-scale of changes in, for e
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