SIS Epidemic Models with Multiple Pathogen Strains

Journal of Difference Equations and Applications

Volumn 10, Issue 1, 2004, Pages 53-75

  Allen, Linda J S ^a   Kirupaharan, Nadarajah ^a   Wilson, Sherri M ^a  

^a TEXAS TECH UNIVERSITY   (United States)

Author keywords

Competitive exclusion; Lotka Volterra competition model; Patch model; SIS epidemic model

Indexed keywords

EID: 0842346795     PISSN: 10236198     EISSN: None     Source Type: Journal    
DOI: 10.1080/10236190310001603680     Document Type: Article

References (37)

1. A. Ackleh and L. J. S. Allen, Competitive exclusion and coexistence for pathogens in an epidemic model with variable population size, J. Math. Biol., (2003), In press.
2. L. J. S. Allen, Some discrete-time SI, SIR, and SIS epidemic models, Math. Biosci., 124 (1994), 83-105.
3. L. J. S. Allen and A. M. Burgin, Comparison of deterministic and stochastic SIS and SIR models in discrete time, Math. Biosci., 163 (2000), 1-31.
4. R. M. Anderson and R. M. May, Coevolution of hosts and parasites, Parasitology, 85 (1982), 411-426.
5. R. M. Anderson and R. M. May, Infectious Diseases of Humans Dynamics and Control, Oxford Univ. Press, Oxford, 1992.
6. V. Andreasen, J. Lin and S. A. Levin, The dynamics of cocirculating influenza strains conferring partial cross-immunity, J. Math. Biol., 35 (1997), 825-842.
7. V. Andreasen and A. Pugliese, Pathogen coexistence induced by density dependent host mortality, J. Theor. Biol., 177 (1995), 159-165.
8. H. J. Bremermann and H. R. Thieme, A competitive exclusion principle for pathogen virulence, J. Math. Biol., 27 (1989), 179-190.
9. C. Castillo-Chavez, W. Huang and J. Li, Competitive exclusion in gonorrhea models and other sexually transmitted diseases, SIAM J. Appl. Math., 56 (1996), 494-508.
10. C. Castillo-Chavez, W. Huang and J. Li, The effects of females' susceptibility on the coexistence of multiple pathogen strains of sexually transmitted diseases, J. Math. Biol., 35 (1997), 503-522.
11. C. Castillo-Chavez, W. Huang and J. Li, Competitive exclusion and coexistence of multiple strains in an SIS STD model, SIAM J. Appl. Math., 59 (1999), 1790-1811.
12. C. Castillo-Chavez and A.-A. Yakubu, Dispersal, disease and life-history evolution, Math. Biosci., 173 (2001), 35-53.
13. C. Castillo-Chavez and A.-A. Yakubu, Intraspecific competition, dispersal, and disease dynamics in discrete-time patchy environments, In: C. Castillo-Chavez, S. Blower, P. van den Driessche, D. Kirschner and A.-A. Yakubu, eds, Mathematical Approaches for Emerging and Reemerging Infectious Diseases. An Introduction, Springer-Verlag, New York, 2002, pp. 165-181.
14. M. Doebeli and G. D. Ruxton, Stabilization through spatial pattern formation in metapopulations with long-range dispersal, Proc. R. Soc. Land. B, 265 (1998), 1325-1332.
15. S. N. Elaydi, An Introduction to Difference Equations, 2nd Ed., Springer-Verlag, New York, 1999.
16. Z. Feng and J. X. Velasco-Hernández, Competitive exclusion in a vector-host model for the dengue fever, J. Math. Biol., 35 (1997), 523-544.
17. I. Hanski, Metapopulation Ecology, Oxford Univ. Press, Oxford, 1999.
18. H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev., 42 (2000), 599-653.
19. M. E. Hochberg and R. D. Holt, The coexistence of competing parasites I, The role of cross-species infection, Am. Nat., 136 (1990), 517-541.
20. P. J. Hudson, A. Rizzoli, B. T. Grenfell, H. Heesterbeek and A. P. Dobson, The Ecology of Wildlife Diseases, Oxford Univ. Press, Oxford, 2002.
21. C. L. Lehman and D. Tilman, Competition in spatial habitats, In: D. Tilman and P. Kareiva, eds, Spatial Ecology: The Role of Space in Population Dynamics and Interspecific Interactions, Princeton Univ. Press, Princeton, NJ, 1997, pp. 185-203.
22. S. A. Levin, Community equilibria and stability, and an extension of the competitive exclusion principle, Am. Nat., 104 (1970), 413-423.
23. S. A. Levin, Dispersion and population interactions, Am. Nat., 108 (1974), 207-221.
24. S. Levin and D. Pimentel, Selection of intermediate rates of increase in parasite-host systems, Am. Nat., 117 (1981), 308-315.
25. R. M. May, Spatial chaos and its role in ecology and evolution, In: S. A. Levin, ed, Frontiers in Mathematical Biology, Springer-Verlag, Berlin and Heidelberg, 1994, pp. 326-344.
26. R. M. May and R. M. Andersen, Epidemiology and genetics in the coevolution of parasites and hosts, Proc. R. Soc. Land. B, 219 (1983), 281-313.
27. R. May and M. A. Nowak, Superinfection, metapopulation dynamics, and the evolution of virulence, J. Theor. Biol., 170 (1995), 95-114.
28. R. M. May and M. A. Nowak, Coinfection and the evolution of parasite virulence, Proc. R. Soc. Land. B, 261 (1995), 209-215.
29. J. Mosquera and F. R. Adler, Evolution of virulence: a unified framework for coinfection and superinfection, J. Theor. Biol., 195 (1998), 293-313.
30. M. A. Nowak and R. M. May, Superinfection and the evolution of parasite virulence, Proc. R. Soc. Land. B, 255 (1994), 81-89.
31. A. Okubo and S. A. Levin, Diffusion and Ecological Problems, 2nd Ed., Springer-Verlag, New York, Berlin, and Heidelberg, 2001.
32. S. W. Pacala and S. A. Levin, Biologically generated spatial pattern and the coexistence of competing species", In: D. Tilman and P. Kareiva, eds, Spatial Ecology: The Role of Space in Population Dynamics and Interspecific Interactions, Princeton Univ. Press, Princeton, NJ, 1997, pp. 204-232.
33. A. Pugliese, On the evolutionary coexistence of parasite strains, Math. Biosci., 177 and 178 (2002), 355-375.
34. P. R. Rohani, R. M. May and M. P. Hassell, Metapopulations and equilibrium stability: the effects of spatial structure, J. Theor. Biol., 181 (1996), 97-109.
35. C. Schmaljohn and B. Hjelle, Hantaviruses: a global disease problem, Emerg. Infect. Dis., 3(2) (1997), 95-104.
36. M. van Baalen and M. W. Sabelis, The dynamics of multiple infection and the evolution of virulence, Am. Nat., 146 (1995), 881-910.
37. P. Yodzis, In: S. Levin, ed, Competition for Space and The Structure of Ecological Communities, Springer-Verlag, Berlin, Heidelberg, New York, 1978.