A stochastic SIS infection model incorporating indirect transmission

Journal of Applied Probability

Volumn 42, Issue 3, 2005, Pages 726-737

  Clancy, Damian ^a  

^a UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

Free living infectious stage; Normal approximation; Piecewise deterministic Markov process; Quasi stationary distribution

Indexed keywords

EID: 27944465693     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1127322023     Document Type: Article

References (17)

1. ANDERSON, R. M. AND MAY, R. M. (1981). The population dynamics of microparasites and their invertebrate hosts. Phil. Trans. R. Soc. London B 291, 451-524.
2. ANDERSON, W. J. (1991). Continuous-Time Markov Chains. An Applications-Oriented Approach. Springer, Berlin.
3. ANDERSSON, H. AND DJEHICHE, B. (1998). A threshold limit theorem for the stochastic logistic epidemic. J. Appl. Prob. 35, 662-670.
4. CLANCY, D., O'NEILL, P. D. AND POLLETT, P. K. (2001). Approximations for the long-term behaviour of an open-population epidemic model. Methodology Comput. Appl. Prob. 3, 75-95.
5. DAVIS, M. H. A. (1993). Markov Models and Optimization. Chapman and Hall, London.
6. FERRARI, P., KESTEN, H., MARTÍNEZ, S. AND PICCO, P. (1995). Existence of quasi-stationary distributions. A renewal dynamic approach. Ann. Prob. 23, 501-521.
7. KIJIMA, M., NAIR, M. G., POLLETT, P. K. AND VAN DOORN, E. A. (1997). Limiting conditional distributions for birth-death processes. Adv. Appl. Prob. 29, 185-204.
8. KURTZ, T. G. (1970). Solutions of ordinary differential equations as limits of pure jump Markov processes. J. Appl. Prob. 7, 49-58.
9. KURTZ, T. G. (1971). Limit theorems for sequences of jump Markov processes approximating ordinary differential processes. J. Appl. Prob. 8, 344-356.
10. NÅSELL, I. (1996). The quasi-stationary distribution of the closed endemic SIS model. Adv. Appl. Prob. 28, 895-932.
11. NÅSELL, I. (1999). On the quasi-stationary distribution of the stochastic logistic epidemic. Math. Biosci. 156, 21-40.
12. NÅSELL, I. (1999). On the time to extinction in recurrent epidemics. J. R. Statist. Soc. B 61, 309-330.
13. PAKES, A. G. (1995). Quasi-stationary laws for Markov processes: examples of an always proximate absorbing state. Adv. Appl. Prob. 27, 120-145.
14. POLLETT, P. K. (1990). On a model for interference between searching insect parasites. J. Austral. Math. Soc. Ser. B 31, 133-150.
15. TURNER, J., BEGON, M., BOWERS, R. G. AND FRENCH, N. P. (2003). A model appropriate to the transmission of a human food-borne pathogen in a multigroup managed herd. Prev. Vet. Med. 57, 175-198.
16. WEISS, G. H. AND DISHON, M. (1971). On the asymptotic behaviour of the stochastic and deterministic models of an epidemic. Math. Biosci. 11, 261-265.
17. XIAO, Y., BOWERS, R. G., CLANCY, D. AND FRENCH, N. P. (2005). Dynamics of infection with multiple transmission mechanisms in unmanaged/managed animal populations. Submitted.