Endemic behaviour of sis epidemics with general infectious period distributions

Advances in Applied Probability

Volumn 46, Issue 1, 2014, Pages 241-255

  Neal, Peter ^a  

^a LANCASTER UNIVERSITY   (United Kingdom)

Author keywords

Branching process with immigration; Gaussian process; Quasistationary distribution; SIS epidemic

Indexed keywords

PROBABILITY DISTRIBUTIONS;

BRANCHING PROCESS; ENDEMIC EQUILIBRIUM; EPIDEMIC MODELING; GAUSSIAN LIMIT; GAUSSIAN PROCESSES; INFECTIOUS PERIOD; QUASI-STATIONARY DISTRIBUTION; SIS EPIDEMIC;

EPIDEMIOLOGY;

EID: 84903765376     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1396360112     Document Type: Article

References (24)

1. Aldous, D. (1978). Stopping times and tightness. Ann. Prob. 6, 335-340.
2. Andersson, H. and Britton, T. (2000). Stochastic epidemics in dynamic populations: quasi-stationarity and extinction. J. Math. Biol. 41, 559-580.
3. Andersson, H. and Djehiche, B. (1998).A threshold limit theorem for the stochastic logistic epidemic. J. Appl. Prob. 35, 662-670. (Pubitemid 128356773)
4. Arrigoni, F. and Pugliese, A. (2007). Global stability of equilibria for a metapopulation S-I-S model. In Math Everywhere, Springer, Berlin, pp. 229-240.
5. Ball, F. (1999). Stochastic and deterministic models for SIS epidemics among a population partitioned into households. Math. Biosci. 156, 41-67. (Pubitemid 29157685)
6. Ball, F. and Donnelly, P. (1995). Strong approximations for epidemic models. Stoch. Process. Appl. 55, 1-21.
7. Billingsley, P. (1968). Convergence of Probability Measures. JohnWiley, NewYork.
8. Britton, T. and Neal, P. (2010). The time to extinction for a stochastic SIS-household-epidemic model. J. Math. Biol. 61, 763-779.
9. Clancy, D. (2012). Approximating quasistationary distributions of birth-death processes. J. Appl. Prob. 49, 1036-1051.
10. Clancy, D. and Mendy, S. T. (2011). Approximating the quasistationary distribution of the SIS model for endemic infection. Methodol. Comput. Appl. Prob. 13, 603-618.
11. Clancy, D. and Pollett, P. K. (2003). A note on quasistationary distributions of birth-death processes and the SIS logistic epidemic. J. Appl. Prob. 40, 821-825. (Pubitemid 37374299)
12. Ghoshal, G., Sander, L. M. and Sokolov, I. M. (2004). SIS epidemics with household structure: the self-consistent field method. Math. Biosci. 190, 71-85. (Pubitemid 38692824)
13. Kryscio, R. and Lefèvre, C. (1989). On the extinction of the S-I-S stochastic logistic epidemic. J. Appl. Prob. 26, 685-694.
14. Kurtz, T. G. (1971). Limit theorems for sequences of jump Markov processes approximating ordinary differential processes. J. Appl. Prob. 8, 344-356.
15. Lindvall, T. (1973).Weak convergence of probability measures and random functions in function space on D(0,∞). J. Appl. Prob. 10, 109-121.
16. Nåsell, I. (1996). The quasistationary distribution of the closed endemic SIS model. Adv. Appl. Prob. 28, 895-932. (Pubitemid 126499161)
17. Nåsell, I. (1999a). On the quasistationary distribution of the stochastic logistic epidemic. Math. Biosci. 156, 21-40. (Pubitemid 29157684)
18. Nåsell, I. (1999b). On the time to extinction in recurrent epidemics. J. R. Statist. Soc. B 61, 309-330.
19. Nåsell, I. (2003). An extension of the moment closure method. Theoret. Pop. Biol. 64, 233-239. (Pubitemid 38042768)
20. Neal, P. (2006). Stochastic and deterministic analysis of SIS household epidemics. Adv. Appl. Prob. 38, 943-968. (Correction: 44 (2012), 309-310.) (Pubitemid 46242865)
21. Neal P. (2008). The SIS great circle epidemic model. J. Appl. Prob. 45, 513-530.
22. Rogers, L. C. G. andWilliams, D. (1994). Diffusions, Markov Processes, and Martingales,Vol. 1, Foundations. 2nd edn. JohnWiley, Chichester.
23. Scalia-Tomba, G. (1990). On the asymptotic final size distribution of epidemics in heterogeneous populations. In Stochastic Processes in Epidemic Theory, Springer, NewYork., pp. 189-196.
24. Weiss, G. H. and Dishon, M. (1971). On the asymptotic behavior of the stochastic and deterministic models of an epidemic. Math. Biosci. 11, 261-265.