Threshold methods for threshold models in age dependent population dynamics and epidemiology
type: Item
instance of: scholarly article
title: Threshold methods for threshold models in age dependent population dynamics and epidemiology
zbMATH Open document ID: 0795.92023
DOI: 10.1007/BF02576762
published in: Calcolo
publication date: 1993-05-24T00:00:00Z
review text: This paper considers two models: the Gurtin and MacCamy model in nonlinear, age-dependent population dynamics, and an epidemic model of S.I.S type with age structure. First-order finite differences along the characteristics of the differential operator are used to construct a first-order numerical method for approximating the solution of the Gurtin-MacCamy model. Boundedness and monotonicity are assumed for the birth and death rate functions (instead of Lipschitz continuity) to prove convergence of the method. The numerical approach is based on the observation that the solution of a certain differential-delay problem approaches the solution of the original one as the delay tends to zero. Stability of the numerical method is discussed. It is also proved that the solution of the discrete model stabilizes asymptotically towards the solution of a discretization of the differential equation for the equilibrium distribution. The other model describes the spread of a mild epidemic through the population described by the first model. Both intracohort and intercohort transmissions of the infection are considered. A first order method is constructed by extending suitably the one for the Gurtin-MacCamy model. The authors prove again that the discrete solution of the difference scheme has a similar large time behavior as the solution of the continuous model.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 92-08
Mathematics Subject Classification ID: 92D30
zbMATH DE Number: 165191
zbMATH Keywords: age-structured SIS-model
zbMATH Keywords: McKendrick equations
zbMATH Keywords: boundedness
zbMATH Keywords: threshold methods
zbMATH Keywords: threshold models
zbMATH Keywords: Gurtin and MacCamy model
zbMATH Keywords: nonlinear, age- dependent population dynamics
zbMATH Keywords: finite differences
zbMATH Keywords: first-order numerical method
zbMATH Keywords: monotonicity
zbMATH Keywords: differential-delay problem
zbMATH Keywords: discretization
zbMATH Keywords: equilibrium distribution
zbMATH Keywords: intracohort and intercohort transmissions
author: Thierry Lafaye
author: M. Langlais
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 165191