Host spatial heterogeneity and extinction of an SIS epidemic

Journal of Theoretical Biology

Volumn 192, Issue 3, 1998, Pages 351-361

  Caraco, Thomas ^a   Duryea, Maria ^a   Gardner, Geoffrey ^a   Maniatty, William ^b   Szymanski, Boleslaw K ^b  

^a STATE UNIVERSITY OF NEW YORK   (United States)

^b Rensselaer Polytechnic Institute   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EPIDEMIC; EXTINCTION; HOST; MODELLING; SPATIAL DISTRIBUTION; SPATIAL HETEROGENEITY;

ARTICLE; DENSITY; DISEASE PREDISPOSITION; DISPERSION; EPIDEMIC; HOST; NATURAL POPULATION; PRIORITY JOURNAL;

EID: 0032493181     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1006/jtbi.1998.0663     Document Type: Article

References (37)

1. BARTHOLOMEW, D. J. (1982). Stochastic Models for Social Processes (3rd Edn). New York: Wiley.
2. BRAMSON, M., DURRETT, R. & SWINDLE, G. (1989). Statistical mechanics of crabgrass. Ann. Prob. 17, 444-481.
3. BURDON, J. J., JAROSZ, A. M. & KIRBY, G. C. (1989). Pattern and patchiness in plant-pathogen interactions: causes and consequences. An. Rev. Ecol. Syst. 20, 119-136.
4. CAIN, M. L. (1985). Random search by herbivorous insects: a simulation model. Ecology 66, 876-888.
5. CAIN, M. L., ECCLESTON, J. & KAREIVA, P. M. (1985). The influence of food plant dispersion on caterpillar searching success. Ecol. Entomol. 10, 1-7.
6. CLAESSEN, D, & DE ROOS, A. M. (1995). Evolution of virulence in a host-pathogen system with local pathogen transmission. Oikos 74, 401-413.
7. COHEN, J. E. (1971). Casual Groups of Monkeys and Men. Cambridge: Harvard University Press.
8. COX, J. T. & DURRETT, R. (1988). Limit theorems for the spread of epidemics and forest fires. Stock. Proc. Appl. 30, 171-191.
9. DIGGLE, P. (1983). Statistical Analysis of Spatial Point Patterns. New York: Academic Press.
10. DURRETT, R. & LEVIN, S. A. (1994). Stochastic spatial models: a user's guide to ecological applications. Phil. Trans. R. Soc., London B343, 329-350.
11. DURRETT, R. & NEUHAUSER, C. (1991). Epidemics with recovery in D = 2. Ann. Appl. Prob. 1, 189-206.
12. DURYEA, M. (1996). Host spatial heterogeneity and disease dispersal. M.S. Thesis, University at Albany, New York.
13. DWYER, G. (1992). On the spatial spread of insect pathogens: theory and experiment. Ecology 73, 479-494.
14. FELLER, W. (1957). An Introduction to Probability Theory and Its Applications, Vol. 1, 2nd Edn. New York: Wiley.
15. GREIG-SMITH, P. (1979). Pattern in vegetation. J. Ecology 67, 755-779.
16. HETHCOTE, H. W. & VAN ARK, J. W. (1987). Epidemiological models for heterogeneous populations: proportionate mixing, parameter estimation, and immunization programs. Math. Biosci. 84, 85-118.
17. IVES, A. R. (1992). Continuous-time models of host-parasitoid interactions. Am. Nat. 240, 1-29.
18. KAREIVA, P. (1990). Population dynamics in spatially complex environments: theory and data. Phil. Trans. R. Soc., London B30, 175-190.
19. KARMESHU & PATHRIA, R. K. (1979). Co-operative behaviour in a non-linear diffusion of information. Can. J. Physics 57, 1572-1578.
20. KEELING, M. J. & GRENFELL, B. T. (1997). Disease extinction and community size: modeling the persistence of measles. Science 275, 65-67.
21. MANIATTY, W., SZYMANSKI, B. & CARACO, T. (1994). Implementation and performance of parallel ecological simulations. In: Applications in Parallel and Distributed Computing (Girault, C., ed.), pp. 93-102. Amsterdam: North-Holland.
22. MAY, R. M. & ANDERSON, R. M. (1984). Spatial heterogeneity and the design of immunization programs. Math. Biosci. 72, 83-111.
23. MCCAULEY, E., WILSON, W. G. & DE ROOS, A. M. (1993). Dynamics of age-structured and spatially structured predator-prey interactions: individual-based models and population-level formulations. Am. Nat. 142, 412-442.
24. MCELHANY, P., REAL, L. A. & POWER, A. G. (1995). Vector preference and disease dynamics: a study of barley yellow dwarf virus. Ecology 76, 444-457.
25. MOLLISON, D. (1977). Spatial contact models for ecological and epidemic spread. J. R. Statist. Soc. Ser. B 39, 283-326.
26. MOLLISON, D. & KUULASMAA, K. (1985). Spatial epidemic models: theory and simulations. In: Population Dynamics of Rabies in Wildlife (Bacon, P. J., ed.). London: Academic Press.
27. MOLLISON, D. & LEVIN, S. A. (1995). Spatial dynamics of parasitism. In: Ecology of Infectious Diseases in Natural Populations (Grenfell, B. T. & Dobson, A. P., eds). Cambridge: Cambridge University Press.
28. MURRAY, J. D., STANLEY, E. A. & BROWN, D. L. (1986). On the spatial spread of rabies among foxes. Proc. R. Soc., London, B229, 111-151.
29. NAKAMURU, M., MATSUDA, H. & IWASA, Y. (1997). The evolution of cooperation in a lattice-structured population. J. theor. Biol. 184, 65-81.
30. ONSTAD, D. W., MADDOX, J. V., COX, D. J. & KORNKVEN, E. A. (1990). Spatial and temporal dynamics of animals and the host-density threshold in epizootiology. J. Invert. Path. 55, 76-84.
31. PACALA, S. W. & TILMAN, D. (1994). Limiting similarity in mechanistic and spatial models of plant competition in heterogeneous environments. Am. Nat. 143, 222-257.
32. POST, W. M., DEANGELIS, D. L. & TRAVIS, C. C. (1983). Endemic disease in environments with spatially heterogeneous host populations. Math. Biosci. 63, 289-302.
33. RHODES, C. J. & ANDERSON, R. M. (1996). Persistence and dynamics in lattice models of epidemic spread. J. theor. Biol. 180, 125-133.
34. ROSS, S. M. (1983). Stochastic Processes. New York: Wiley.
35. RUXTON, G. D. (1996). Synchronisation between individuals and the dynamics of linked populations. J. theor. Biol. 183, 47-54.
36. SWINTON, J. & ANDERSON, R. M. (1995). Model frameworks for plant-pathogen interactions. In: Ecology of Infectious Diseases in Natural Populations (Grenfell, B. T. & Dobson, A. P., eds), pp. 280-294. Cambridge: Cambridge University Press.
37. SZYMANSKI, B. & CARACO, T. (1994). Spatial analysis of vector-borne disease: a four-species model. Evol. Ecol. 8, 299-314.