Well-posedness of an infinite system of partial differential equations modelling parasitic infection in an age-structured host.
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 \((p_i(a,t), i\in N)\).
infinite system of first-order partial differential equations
scientific article; zbMATH DE number 1974964