Strong approximations for mobile population epidemic models

Annals of Applied Probability

Volumn 6, Issue 3, 1996, Pages 883-895

  Clancy, Damian ^a  

^a UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

Birth and death processes; Coupling; Migration processes; Multigroup epidemics; Threshold theorems

Indexed keywords

EID: 0030488552     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1034968231     Document Type: Article

References (20)

1. BAILEY, N. T. J. (1975). The Mathematical Theory of Infectious Diseases and its Applications, 2nd ed. Griffin, London.
2. BALL, F. G. (1983). The threshold behavior of epidemic models. J. Appl. Probab. 20 227-241.
3. BALL, F. G. (1991). Dynamic population epidemic models. Math. Biosci. 107 299-324.
4. BALL, F. G. and CLANCY, D. (1993). The final size and severity of a generalised stochastic multitype epidemic model. Adv. in Appl. Probab. 25 721-736.
5. BALL, F. G. and DONNELLY, P. J. (1995). Strong approximations for epidemic models. Stochastic Process. Appl. 55 1-21.
6. BALL, F. G. and O'NEILL, P. D. (1994). Strong convergence of stochastic epidemics. Adv. in Appl. Probab. 26 629-655.
7. BARTLETT, M. S. (1955). An Introduction to Stochastic Processes. Cambridge Univ. Press.
8. CLANCY, D. (1996). Carrier-borne epidemic models incorporating population mobility. Math. Biosci. 132 185-204.
9. ETHIER, S. N. and KURTZ, T. G. (1986). Markov Processes: Characterization and Convergence. Wiley, New York.
10. KENDALL, D. G. (1948). On the generalized "birth-and-death" process. Ann. Math. Statist. 19 1-15.
11. KENDALL, D. G. (1956). Deterministic and stochastic epidemics in closed populations. Proc. Third Berkeley Symp. Math. Statist. Probab. 4 149-165. Univ. California Press, Berkeley.
12. METZ, J. A. J. (1978). The epidemic in a closed population with all susceptibles equally vulnerable: some results for large susceptible populations and small initial infections. Acta Biotheoretica 27 75-123.
13. MODE, C. J. (1971). Multitype Branching Processes. North-Holland, Amsterdam.
14. MOLLISON, D. (1977). Spatial contact models for ecological and epidemic spread. J. Roy. Statist. Soc. Ser. B 39 283-326.
15. O'NEILL, P. D. (1996). Strong approximations for some open population epidemic models. J. Appl. Probab. 33 448-457.
16. PURI, P. S. (1968). Interconnected birth and death processes. J. Appl. Probab. 5 334-349.
17. RAMAN, S. and CHIANG, C. L. (1973). On a solution of the migration process and the application to a problem in epidemiology. J. Appl. Probab. 10 718-727.
18. SCALIA-TOMBA, G. (1985). Asymptotic final size distribution for some chain-binomial processes. Adv. in Appl. Probab. 17 477-495.
19. SCALIA-TOMBA, G. (1990). On the asymptotic final size distribution of epidemics in heterogeneous populations. In Stochastic Processes in Epidemic Theory. Lecture Notes in Biomath. 86 189-196. Springer, New York.
20. SENETA, E. (1973). Non-negative Matrices: An Introduction to Theory and Applications. Allen and Unwin, London.