Slow convergence to equilibrium for an evolutionary epidemiology integro-differential system
| Autor: | Arnaud Ducrot, Ramsès Djidjou-Demasse, Jean-Baptiste Burie |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques Appliquées du Havre (LMAH), Université Le Havre Normandie (ULH), Normandie Université (NU)-Normandie Université (NU), Institut de Recherche pour le Développement (IRD) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Work (thermodynamics)
Applied Mathematics 010102 general mathematics Variance (accounting) System of linear equations Space (mathematics) 01 natural sciences 010101 applied mathematics Mutation (genetic algorithm) Quantitative Biology::Populations and Evolution Discrete Mathematics and Combinatorics Slow convergence [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Statistical physics 0101 mathematics Dispersion (water waves) Selection (genetic algorithm) ComputingMilieux_MISCELLANEOUS Mathematics |
| Zdroj: | Discrete and Continuous Dynamical Systems-Series B Discrete and Continuous Dynamical Systems-Series B, American Institute of Mathematical Sciences, 2019, 22 (11), ⟨10.3934/dcdsb.2019225⟩ Discrete and Continuous Dynamical Systems-Series B, American Institute of Mathematical Sciences, 2020, 25 (6), pp.2223-2243. ⟨10.3934/dcdsb.2019225⟩ |
| ISSN: | 1531-3492 1553-524X |
| DOI: | 10.3934/dcdsb.2019225⟩ |
| Popis: | This work is devoted to the study of an integro-differential system of equations modelling the genetic adaptation of a pathogen by taking into account both mutation and selection processes. Using the variance of the dispersion in the phenotype trait space as a small parameter we provide a complete picture of the dynamical behaviour of the solutions of the problem. We show that the dynamics exhibits two main and long regimes – those durations are estimated – before the solution finally reaches its long time configuration, the endemic equilibrium. The analysis provided in this work rigorously explains and justifies the complex behaviour observed through numerical simulations of the system. |
| Databáze: | OpenAIRE |
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