Advances in Applied Probability

Convergence and monotonicity for a model of spontaneous infection and transmission

Eric Foxall

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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

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

Dates
First available in Project Euclid: 29 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.aap/1401369707

Digital Object Identifier
doi:10.1239/aap/1401369707

Mathematical Reviews number (MathSciNet)
MR3215546

Zentralblatt MATH identifier
1310.60108

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

Keywords
Continuous-time Markov process interacting particle system SIS model

Citation

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. https://projecteuclid.org/euclid.aap/1401369707


Export citation

References

  • Berman, A. and Plemmons, R. J. (1994). Nonnegative Matrices in the Mathematical Sciences. Society for Industrial and Applied Mathematics, Philadelphia, PA.
  • Bubley, R. and Dyer, M. (1997). Path coupling: a technique for proving rapid mixing in Markov chains. In Proc. 38th Annual Symp. Foundations of Computer Science, pp. 223–231.
  • Harris, T. E. (1974). Contact interactions on a lattice. Ann. Prob. 2, 969–988.
  • Harris, T. E. (1978). Additive set-valued Markov processes and graphical methods. Ann. Prob. 6, 355–378.
  • Krone, S. M. (1999). The two-stage contact process. Ann. Appl. Prob. 9, 331–351.
  • Levin, D., Peres, Y. and Witmer, E. L. (2006). Markov Chains and Mixing Times. American Mathematical Society.
  • Neuhauser, C. (1992). Ergodic theorems for the multitype contact process. Prob. Theory Relat. Fields 91, 467–506.
  • Norris, J. R. (1997). Markov Chains. Cambridge University Press.
  • Van Mieghem, P., Omic, J. and Kooij, R. (2009). Virus spread in networks. IEEE/ACM Trans. Networking 17, 1–14.