Advances in Applied Probability

Convergence and monotonicity for a model of spontaneous infection and transmission

Eric Foxall

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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.

Article information

Adv. in Appl. Probab., Volume 46, Number 2 (2014), 560-584.

First available in Project Euclid: 29 May 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 92B99: None of the above, but in this section

Continuous-time Markov process interacting particle system SIS model


Foxall, Eric. Convergence and monotonicity for a model of spontaneous infection and transmission. Adv. in Appl. Probab. 46 (2014), no. 2, 560--584. doi:10.1239/aap/1401369707.

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