A renewal equation with a birth-death process as a model for parasitic infections

DOI10.1007/BF00288434zbMath0715.92026OpenAlexW2315913076WikidataQ52543015 ScholiaQ52543015MaRDI QIDQ752595

Mirjam E. E. Kretzschmar

Publication date: 1989

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00288434

zbMATH Keywords

boundary conditionsBanach fixed point theoremhost-parasite systemsage structurehost populationExistence and uniquenesslinear birth-death-processmultitype processparasite diseasespersistent solutionsrenewal equation for the host population

Mathematics Subject Classification ID

Epidemiology (92D30) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Applications of branching processes (60J85) Geometric theory, characteristics, transformations in context of PDEs (35A30)

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A schistosomiasis model with an age-structure in human hosts and its application to treatment strategies, Backward bifurcation in epidemic control, Well-posedness of an infinite system of partial differential equations modelling parasitic infection in an age-structured host., Hybrid models for helminth infections with special reference to onchocerciasis, Existence of solutions for a host-parasite model, Predator-prey populations with parasitic infection, Deterministic approximation of a stochastic metapopulation model, Stein factors for negative binomial approximation in Wasserstein distance

Cites Work

• Models for pair formation in bisexual populations
• Persistent solutions in a model for parasitic infections
• Population dynamics of killing parasites which reproduce in the host
• Nonlinear hyperbolic partial differential equations for the dynamics of parasite populations
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