Slow convergence to equilibrium for an evolutionary epidemiology integro-differential system. (English) Zbl 1436.35041
Summary: 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.
MSC:
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35R09 | Integro-partial differential equations |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 92D10 | Genetics and epigenetics |
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