Limits of a multi-patch SIS epidemic model

Journal of Mathematical Biology

Volumn 45, Issue 5, 2002, Pages 419-440

  Arrigoni, F ^a   Pugliese, A ^a  

^a UNIVERSITY OF TRENTO   (Italy)

Author keywords

Markov population processes; Metapopulation; SIS epidemic; Weak convergence of measures

Indexed keywords

ANIMAL; ARTICLE; BIOLOGICAL MODEL; EPIDEMIC; EPIDEMIOLOGY; HUMAN; MATHEMATICAL COMPUTING; POPULATION DENSITY; POPULATION DYNAMICS; STATISTICS;

ANIMALS; DISEASE OUTBREAKS; EPIDEMIOLOGIC METHODS; HUMANS; MODELS, BIOLOGICAL; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; POPULATION DENSITY; POPULATION DYNAMICS; STOCHASTIC PROCESSES;

EID: 0345959467     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s002850200155     Document Type: Article

References (22)

1. Ball, F.: Stochastic and deterministic models for SIS epidemics among a population partitioned into households, Math. Biosciences, 156, 41 (1999)
2. Ball, F., Mollison, D., Scalia Tomba, G.P.: Epidemics with two levels of mixing, Annals of Applied Probability, 7, 46 (1997)
3. Barbour, A.D.: Density dependent Markov population processes, in Biological growth and spread (Proc. Conf., Heidelberg, 1979), (eds.), Springer Berlin 36-49 (1980)
4. Barbour, A.D.: On a functional central limit theorem for Markov population processes, Advances in Appl. Probability, 6, 21-39 (1974)
5. Barbour, A.D., Kafetzaki, M.: A host parasite model yielding heterogenous parasite loads, J. Math. Biol., 31, 157 (1993)
6. Billingsley, P.: Probability and measure, John Wiley & Sons, New York 1995
7. Billingsley, P.: Convergence of probability measures, John Wiley & Sons, New York 1968
8. Capasso, V.: Mathematical structures of epidemic systems. Lecture Notes in Biomathematics, 97. Springer-Verlag, Berlin, 1993
9. Diekmann, O., Gyllenberg, M., Metz, J.A.J., Thieme, H.R.: On the formulation and analysis of general deterministic structured population models. I. Linear theory. J. Math. Biol., 36, 349-388 (1998)
10. Diekmann, O., Gyllenberg, M., Huang, H., Kirkilionis, M., Metz, J.A.J., Thieme, H.R.: On the formulation and analysis of general deterministic structured population models. II. Nonlinear theory. J. Math. Biol., 43, 157-189 (2001)
11. 0 in models for infectious diseases in heterogeneous populations. J. Math. Biol., 28, no. 4, 365-382 (1990)
12. Diekmann, O., Heesterbeek, J.A.P.: Mathematical Epidemiology of Infectiuos Diseases. Wiley, New York 2000
13. Dunford, N., Schwartz, J.T.: Linear operators. Part I. Interscience publishers, inc. New York 1957
14. Ethier, S.N., Kurtz, T.G.: Markov Processes. Characterization and Convergence, John Wiley & Sons, New York 1986
15. Grenfell, B., Harwood, J.: (Meta)population dynamics of infectious diseases. TREE, 12, 395-399 (1997)
16. Gyllenberg, M., Hanski, I.A.: Structured metapopulation models. In I.A. Hanski and M.E. Gilpin (eds.) Metapopulation biology: ecology, genetics and evolution, pp. 93-122. Academic Press
17. Gyllenberg, M., Hanski, I.A., Hastings, A.: Single-species metapopulation dynamics: a structured model. Theor. Pop. Biol., 42, 35-62 (1992)
18. Gyllenberg, M., Metz, J.A.J.: On fitness in structured metapopulations J. of Math. Biol., 43, no. 6, 545-560 (2001)
19. Gyllenberg, M., Silvestrov, D.: Quasi-stationary distributions of a stochastic metapopulation model J. Math. Biol., 33, 35-70 (1994)
20. Kurtz, T.G.: Approximation of population processes, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa., (1981)
21. Lajmanovich, A., Yorke, J.A.: A deterministic model for gonorrhea in a nonhomogeneous population. Math. Biosci., 28, 221-236 (1976)
22. Pollett, P.K.: On a model for interference between searching insect parasites, J. Austral. Math. Soc. Ser. B, 32, 133 (1990)