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A note on the coexistence times for two competing SIS epidemics
Stockholm University, Faculty of Science, Department of Mathematics.
##### Abstract [en]

The stochastic SIS logistic epidemic process is a well-known continuous-time Markov chain with finite state space, describing the spread of an epidemic in a homogeneously mixing  population of size N. This process  eventually reaches an absorbing state (extinction'') and its extinction time is well-understood.  Namely, we can identify a phase transition depending on the infectious rate of the epidemic. There is a \textit{subcritical} phase where the process goes extinct in  time $O_{P}(\log N)$, and a \textit{supercritical} phase where the extinction time grows exponentially in the population size. In this work we consider two SIS epidemics with distinct supercritical infectious rates competing under cross-immunity, i.e. during its infectious period an infective individual is immune to the other infection. We show that with high probability the process with the lower infectious rate dies out first and the two epidemics coexist for a time that is $O_{P}(\log N)$. Furthermore, we conjecture the limiting distribution of the coexistence time.

##### Keywords [en]
SIS epidemic model, competitive Lotka-Volterra systems, extinction times
Natural Sciences
##### Identifiers
OAI: oai:DiVA.org:su-106730DiVA, id: diva2:738456
Available from: 2014-08-18 Created: 2014-08-18 Last updated: 2014-08-22Bibliographically approved
##### In thesis
1. Spatial Marriage Problems and Epidemics
Open this publication in new window or tab >>Spatial Marriage Problems and Epidemics
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

This thesis consists of four papers covering three different topics on the modeling of large real networks and phenomena thereon. In Papers I and II, we propose and study the properties of a bipartite version of the model introduced by Deijfen, Holroyd and Häggström for generating translation-invariant spatial random graphs with prescribed degree distribution. In particular, we focus our attention on spatial random graphs generated by a matching scheme based on the Gale-Shapley stable marriage problem. In paper III, we propose a random graph model for generating edge-weighted graphs with prescribed degree and weight distributions, and tunable degree-degree correlation. We then study a simple inhomogeneous epidemic model on such graphs, where the infection probabilities are functions of the edge-weights, and investigate how the epidemic threshold is affected by the degree-degree correlation. In paper IV, we study a simple stochastic model aimed at representing a competition between two virus strains in a population. A longstanding principle in ecology known as the competitive exclusion principle predicts that when one of the strains has even the slightest advantage over the other, the one with the advantage will either drive the competitor to extinction or lead to a transformation in the ecological niche. We investigate how long it will take for the strain to drive its competitor to extinction.

##### Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University, 2014. p. 25
Mathematics
##### Research subject
Mathematical Statistics
##### Identifiers
urn:nbn:se:su:diva-106796 (URN)978-91-7447-970-6 (ISBN)
##### Public defence
2014-09-24, sal 14, hus 5, Kräftriket, Roslagsvägen 101, Stockholm, 13:00 (English)
##### Note

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 1: In press. Paper 4: Manuscript.

Available from: 2014-09-02 Created: 2014-08-20 Last updated: 2015-03-27Bibliographically approved

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##### By organisation
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