On emergence times of competition processes
Résumé
Competition processes are natural extensions of birth-death processes in higher dimensions. At any time, for any type, a birth, a death or a mutation to another type can occur. This work is concerned with the time $S$ at which a particular type emerges in the population through spontaneous birth or mutation. We give some bounds for the tail of the distribution of $S$. Then using properties of quasi-stationary distributions, we give conditions for the existence of an initial law under which $S$ is exponentially distributed. Finally, we provide some examples of applications to the emergence time of pathogen mutants overcoming host resistance in a host-pathogen system.
Origine | Fichiers produits par l'(les) auteur(s) |
---|