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Schistosomiasis models with two migrating human groups. (English) Zbl 1114.92038

Summary: We propose, models of schistosomiasis that incorporate several realistic features including two human habitats, migration between these, negative binomial distribution of schistosomes within human hosts, disease-induced mortality in both human and snail hosts, and others. The qualitative and quantitative mathematical properties are analyzed. Numerical simulations help examine the dynamics and suggest some properties of these models that we were unable to prove mathematically. Partial results are extended to models with multiple human groups, and numerical simulations also support the results. Explicit thresholds for the survival of schistosomes are established. Control strategies derived from these thresholds are also discussed.

MSC:

92C50 Medical applications (general)
34D05 Asymptotic properties of solutions to ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
65C20 Probabilistic models, generic numerical methods in probability and statistics
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