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Convergence and Monotonicity for a Model of Spontaneous Infection and Transmission

Part of: Mathematical biology in general Markov processes

Published online by Cambridge University Press:  22 February 2016

Eric Foxall
Eric Foxall*
Affiliation:
University of Victoria
*
∗ Postal address: Department of Mathematics and Statistics, University of Victoria, PO Box 3060 STN CSC, Victoria BC, V8W 3R4, Canada. Email address: e.t.foxall@gmail.com
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Abstract

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A version of the contact process (effectively an SIS model) on a finite set of sites is considered in which there is the possibility of spontaneous infection. A companion process is also considered in which spontaneous infection does not occur from the disease-free state. Monotonicity with respect to parameters and initial data is established, and conditions for irreducibility and exponential convergence of the processes are given. For the spontaneous process, a set of approximating equations is derived, and its properties investigated.

Keywords

Continuous-time Markov processinteracting particle systemSIS model

MSC classification

Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 92B99: None of the above, but in this section
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 46 , Issue 2 , June 2014 , pp. 560 - 584
Copyright
© Applied Probability Trust 

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