A model of spatial epidemic spread when individuals move within overlapping home ranges

Bulletin of Mathematical Biology

Volumn 68, Issue 2, 2006, Pages 401-416

  Reluga, Timothy C ^a   Medlock, Jan ^a   Galvani, Alison P ^a  

^a YALE UNIVERSITY SCHOOL OF MEDICINE   (United States)

Author keywords

Distributed contacts; Distributed infectives; Epidemics; Invasions

Indexed keywords

ALGORITHM; ANIMAL; ARTICLE; BIOLOGICAL MODEL; COMMUNICABLE DISEASE; COMPUTER SIMULATION; DISEASE TRANSMISSION; EPIDEMIC; EPIDEMIOLOGY; HUMAN; LOCOMOTION; STATISTICS;

ALGORITHMS; ANIMALS; COMMUNICABLE DISEASES; COMPUTER SIMULATION; DISEASE OUTBREAKS; EPIDEMIOLOGIC METHODS; HUMANS; LOCOMOTION; MODELS, BIOLOGICAL;

EID: 33746595344     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-005-9027-y     Document Type: Article

References (53)

1. Allen, L., Ernest, R., 2002. The impact of long-range dispersal on the rate of spread in population and epidemic models. In: Castillo-Chavez, C., Blower, S., van den Driessche, P., Kirschner, D., Yakubu, A.-A. (Eds.), Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction. Springer, New York, pp. 183-197.
2. Alt, W., 1980. Biased random-walk models for chemotaxis and related diffusion approximations. J. Math. Biol. 9, 147-177.
3. Anderson, R.M., May, R.M., 1991. Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, New York.
4. Arino, J., van den Driessche, P., 2003. A multi-city epidemic model. Math. Pop. Stud. 10, 175-193.
5. Bailey, N.T.J., 1975. The Mathematical Theory of Infectious Diseases, 2nd ed. Griffin, London.
6. Bauch, C.T., Galvani, A.P., 2003. Using network models to approximate spatial point-process models. Math. Biosci. 184, 101-114.
7. Bian, L., 2004. A conceptual framework for an individual-based spatially explicit epidemiological model. Environ. Plan. B-Plan. Design 31, 381-395.
8. Busenberg, S.N., Travis, C.C., 1983. Epidemic models with spatial spread due to population migration. J. Math. Biol. 16, 181-198.
9. Caraco, T., Glavanakov, S., Chen, G., Flaherty, J.E., Ohsumi, T.K., Szymanski, B.K., 2002. Stage-structured infection transmission and a spatial epidemic: A model for Lyme disease. Am. Natural. 160, 348-359.
10. Clark, J.S., Lewis, M., Horvath, L., 2001. Invasion by extremes: Population spread with variation in dispersal and reproduction. Am. Natural. 152, 204-224.
11. Daniels, H.E., 1975. The deterministic spread of a simple epidemic. In: Gani, J. (Ed.), Perspectives in Probability and Statistics: Papers in Honour of M. S. Bartlett on the Occasion of his Sixty-Fifth Birthday. Academic Press, London, pp. 373-386.
12. Doran, R.J., Laffan, S.W., 2005. Simulating the spatial dynamics of foot and mouth disease outbreaks in feral pigs and livestock in Queensland, Australia, using a susceptible-infected-recovered cellular automata model. Prev. Vet. Med. 70, 133-152.
13. Durrett, R., 1999. Stochastic spatial models. SIAM Rev. 41, 677-718.
14. Durrett, R., Levin, S., 1994. The importance of being discrete (and spatial). Theor. Pop. Biol. 46, 363-394.
15. Eubank, S., Guclu, H., Kumar, V.S.A., Marathe, M.V., Srinivasan, A., Toroczkai, Z., Wang, N., 2004. Modelling disease outbreaks in realistic urban social networks. Nature 429, 180-184.
16. Evans, M., Hastings, N., Peacock, B., 2000. Statistical Distributions, 2nd ed. Wiley, New York.
17. Fenner, F., Henderson, D.A., Arita, I., Jezek, Z., Ladnyi, I., 1988. Smallpox and Its Eradication. World Health Organization, Geneva.
18. Fife, P.C., 1979. Mathematical Aspects of Reacting and Diffusing Systems. Lecture Notes in Biomathematics. Springer-Verlag, New York.
19. Filipe, J.A.N., Maule, M.M., 2003. Analytical methods for predicting the behaviour of population models with general spatial interactions. Math. Biosci. 183, 15-35.
20. Fuks, H., Lawniczak, A.T., 2001. Individual-based lattice model for spatial spread of epidemics. Discrete Dyn. Nat. Soc. 6, 191-200.
21. Goel, N.S., Richter-Dyn, N., 1974. Stochastic Models in Biology. Academic Press, New York.
22. Hadeler, K.P., 2003. The role of migration and contact distributions in epidemic spread. In: Banks, H.T., Castillo-Chavez, C. (Eds.), Bioterrorism: Mathematical Modeling Applications in Homeland Security. SIAM, Philadelphia, pp. 199-210.
23. Hillen, T., Othmer, H.G., 2000. The diffusion limit of transport equations derived from velocity-jump processes. SIAM J. Appl. Math. 61, 751-775.
24. Keeling, M.J., Gilligan, C.A., 2000. Bubonic plague: A metapopulation model of a zoonosis. Proc. R. Soc. Lond. B 267, 2219-2230.
25. Kendall, D.G., 1965. Mathematical models of the spread of infection. In Mathematics and Computer Science in Biology and Medicine. H. M. Stationary Office, London, pp. 213-225.
26. Kot, M., 2001. Elements of Mathematical Ecology. Cambridge University Press, New York.
27. Kot, M., Medlock, J., Reluga, T., Walton, D.B., 2004. Stochasticity, invasions, and branching random walks. Theor. Pop. Biol. 66, 175-184.
28. Lewis, M.A., 2000. Spread rate for a nonlinear stochastic invasion. J. Math. Biol. 41, 430-454.
29. Lewis, M.A., Pacala, S., 2000. Modeling and analysis of stochastic invasion processes. J. Math. Biol. 41, 387-429.
30. Lloyd, A.L., Jansen, V.A.A., 2004. Spatiotemporal dynamics of epidemics: Synchrony in metapopulation models. Math. Biosci. 188, 1-16.
31. McKean, H.P., 1975. Application of Brownian motion to the equation of Kolmogorov-Petrovskii-Piskunov. Commun. Pure Appl. Math. 28, 323-331.
32. Medlock, J., Kot, M., 2003. Spreading disease: Integro-differential equations old and new. Math. Biosci. 184, 201-222.
33. Méndez, V., 1998. Epidemic models with an infected-infectious period. Phys. Rev. E 57, 3622-3624.
34. Metz, J.A.J., Mollison, D., van den Bosch, F., 1999. The Dynamics of Invasion Waves. Technical Report IR-99-039, International Institute for Applied Systems Analysis. Laxenburg, Austria.
35. Metz, J.A.J., van den Bosch, F., 1995. Velocities of epidemic spread. In: Mollison, D. (Ed.), Epidemic Models: Their Structure and Relation to Data. Cambridge University Press, Cambridge, UK, pp. 150-186.
36. Meyers, L.A., Pourbohloul, B., Newman, M.E.J., Skowronski, D.M., Brunham, R.C., 2005. Network theory and SARS: Predicting outbreak diversity. J. Theor. Biol. 232, 71-81.
37. Mollison, D., 1972. The rate of spatial propagation of simple epidemics. In: Proceedings of the 6th Berkeley Symposium on Mathematical Statistics and Probability, vol. 3. University of California Press, Berkeley, CA, pp. 579-614.
38. Mollison, D., 1977. Spatial contact models for ecological and epidemic spread. J. R. Stat. Soc. B 39, 283-326.
39. Mollison, D., 1991. Dependence of epidemic and population velocities on basic parameters. Math. Biosci. 107, 255-287.
40. Newman, M.E.J., 2002. Spread of epidemic disease on networks. Phys. Rev. E 66, 016128.
41. Noble, J.V., 1974. Geographic and temporal development of plagues. Nature 250, 726-729.
42. Othmer, H.G., Dunbar, S.R., Alt, W., 1988. Models of dispersal in biological-systems. J. Math. Biol. 26, 263-298.
43. Othmer, H.G., Hillen, T., 2002. The diffusion limit of transport equations II: Chemotaxis equations. SIAM J. Appl. Math. 62, 1222-1250.
44. Read, J.M., Keeling, M.J., 2003. Disease evolution on networks: the role of contact structure. Proc. R. Soc. Lond. B 270, 699-708.
45. Riley, S., Fraser, C., Donnelly, C.A., Ghani, A.C., Abu-Raddad, L.J., Hedley, A.J., Leung, G.M., Ho, L.M., Lam, T.H., Thach, T.Q., Chau, P., Chan, K.P., Leung, P.Y., Tsang, T., Ho, W., Lee, K.H., Lau, E.M.C., Ferguson, N.M., Anderson, R.M., 2003. Transmission dynamics of the etiological agent of SARS in Hong Kong: Impact of public health interventions. Science 300, 1961-1966.
46. Schinazi, R., 1996. On an interacting particle system modeling an epidemic. J. Math. Biol. 34, 915-925.
47. Schwetlick, H.R., 2000. Travelling fronts for multidimensional nonlinear transport equations. Ann. Inst. Henri Poincare Phys. Theor. 17, 523-550.
48. Snyder, R.E., 2003. How demographic stochasticity can slow biological invasions. Ecology 84, 1333-1339.
49. Thomson, N.A., Ellner, S.P., 2003. Pair-edge approximation for heterogeneous lattice population models. Theor. Pop. Biol. 64, 271-280.
50. Uhlenbeck, G.E., Ornstein, L.S., 1930. On the theory of the Brownian motion. Phys. Rev. 36, 823-841.
51. van den Bosch, F., Metz, J., Zadoks, J., 1999. Pandemics of focal plant disease, a model. Phytopathology 89, 495-505.
52. van den Bosch, F., Verhaar, M., Buiel, A., Hoogkamer,W., Zadoks, J., 1990. Focus expansion in plant disease. IV: Expansion rates in mixtures of resistant and susceptible hosts. Phytopathology 80, 598-602.
53. van den Bosch, F., Zadoks, J., Metz, J., 1988. Focus expansion in plant disease. I: The constant rate of focus expansion. Phytopathology 78, 54-58.