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These notes are an extended version of lectures given in the
Symposium on Mathematics and Development arranged by the School of
Mathematical Sciences of the University of Khartoum, Sudan, in
1982. The purpose of the notes is to discuss some models for the
transmission of tropical infections. This area of mathematical
epidemiology has previously received only minor attention by
mathematicians, but is now growing in importance. The term "hybrid
model" is used to denote a model with both stochastic and
deterministic ingredients. We describe how a hybrid model approach
can be used to formulate and study both some classical models for
malaria and schistosomiasis and some extensions of these models.
The formulation of the models requires some familiarity with Markov
chains in continuous time and discrete state space. The analysis of
the models uses concepts and methods in the qualitative theory of
ordinary differential equations. The presentation is aimed at the
senior undergraduate or beginning graduate level.
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