Well-posedness of an infinite system of partial differential equations modelling parasitic infection in an age-structured host.
type: Item
instance of: scholarly article
title: Well-posedness of an infinite system of partial differential equations modelling parasitic infection in an age-structured host.
zbMATH Open document ID: 1039.35130
DOI: 10.1016/S0022-247X(03)00295-6
author: Lorenza Tonetto
author: Andrea Pugliese
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-09-04T00:00:00Z
review text: A model for the dynamics of a population of individuals (hosts) infected by one species of macroparasites is studied. The host population is age structured; for each \(i\in N\) , \(p_i(a,t)\) denotes the density of hosts of age \(a\) harbouring \(i\) parasites at time \(t\). The model consists of an infinite system of first-order partial differential equations with the unknowns \(p_i(a,t)\), \(i\in N \), and initial and boundary conditions. Starting from this system, an abstract Cauchy problem is considered; then, the results obtained for this problem are applied to prove the existence and uniqueness of a positive solution \((p_i(a,t), i\in N)\).
reviewed by: Ion Onciulescu
Mathematics Subject Classification ID: 35Q80
Mathematics Subject Classification ID: 92D30
zbMATH DE Number: 1974964
zbMATH Keywords: infinite system of first-order partial differential equations
zbMATH Keywords: Cauchy problem
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: population dynamics
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1974964