Translator Disclaimer
December 2020 Extinction time for the weaker of two competing SIS epidemics
Fabio Lopes, Malwina Luczak
Ann. Appl. Probab. 30(6): 2880-2922 (December 2020). DOI: 10.1214/20-AAP1576


We consider a simple Markov model for the spread of a disease caused by two virus strains in a closed homogeneously mixing population of size $N$. The spread of each strain in the absence of the other one is described by the stochastic SIS logistic epidemic process, and we assume that there is perfect cross-immunity between the two strains, that is, individuals infected by one are temporarily immune to re-infections and infections by the other. For the case where one strain is strictly stronger than the other, and the stronger strain on its own is supercritical, we derive precise asymptotic results for the distribution of the time when the weaker strain disappears from the population. We further extend our results to certain parameter values where the difference between the basic reproductive ratios of the two strains may tend to 0 as $N\to\infty$.

In our proofs, we illustrate a new approach to a fluid limit approximation for a sequence of Markov chains in the vicinity of a stable fixed point of the limit differential equation, valid over long time intervals.


Download Citation

Fabio Lopes. Malwina Luczak. "Extinction time for the weaker of two competing SIS epidemics." Ann. Appl. Probab. 30 (6) 2880 - 2922, December 2020.


Received: 1 April 2019; Revised: 1 March 2020; Published: December 2020
First available in Project Euclid: 14 December 2020

Digital Object Identifier: 10.1214/20-AAP1576

Primary: 60J27 , 92D30

Keywords: competing SIS epidemics , near-critical epidemic , Stochastic SIS logistic epidemic , time to extinction

Rights: Copyright © 2020 Institute of Mathematical Statistics


This article is only available to subscribers.
It is not available for individual sale.

Vol.30 • No. 6 • December 2020
Back to Top