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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.
Table des matières
1. Introduction.- 2. Host Models.- 3. Transmission Models for Malaria.- 4. Transmission Models for Hermaphroditic Helminthiasis.- 5. Transmission Models for Schistosomiasis.- Appendices.- I. The Recovery Probability in the Superinfection Process.- II. The Incidence and the Recovery Probability in the Superinfection Process with Monogamous Mating.- III. Control Efficiency Functions for the Ross Malaria Model.- IV. Local Stability Results for Equilibrium Solutions of Systems of Differential Equations and of Differential-Difference Equations.- V. A Proof of Sierpinski's Inequality.- References.
