Comparison of an infinite dimensional model for parasitic diseases with a related 2-dimensional system

DOI10.1006/jmaa.1993.1211zbMath0774.92019OpenAlexW2004750844MaRDI QIDQ1260860

Mirjam E. E. Kretzschmar

Publication date: 5 September 1993

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.1993.1211

zbMATH Keywords

overdispersionsteady statesinvariant distributionstwo-dimensional systemexponential solutionsthreshold valuesparasitic diseasesinfinite system of ordinary differential equationsendemic steady statevariance to mean ratio

Mathematics Subject Classification ID

Epidemiology (92D30) Bifurcation theory for ordinary differential equations (34C23) Growth and boundedness of solutions to ordinary differential equations (34C11) Dynamical systems and ergodic theory (37-XX)

Related Items (10)

A structured population model with diffusion in structure space ⋮ Laws of large numbers for epidemic models with countably many types ⋮ Backward bifurcation in epidemic control ⋮ Well-posedness of an infinite system of partial differential equations modelling parasitic infection in an age-structured host. ⋮ A new approach to mathematical modeling of host-parasite systems ⋮ Aggregation, stability, and oscillations in different models for host-macroparasite interactions. ⋮ Individual and patch behaviour in structured metapopulation models ⋮ Hybrid models for helminth infections with special reference to onchocerciasis ⋮ Coexistence of macroparasites without direct interactions ⋮ A law of large numbers approximation for Markov population processes with countably many types

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