Robust uniform persistence and competitive exclusion in a nonautonomous multi-strain SIR epidemic model with disease-induced mortality

Journal of Mathematical Biology

Volumn 68, Issue 1-2, 2014, Pages 453-475

  Ackleh, Azmy S ^a   Salceanu, Paul L ^a  

^a UNIVERSITY OF LOUISIANA AT LAFAYETTE   (United States)

Author keywords

Competitive exclusion; Disease induced mortality; Nonautonomous multi strain SIR model; Nonlinear host mortality; Uniform persistence

Indexed keywords

AMPHIBIA; ANIMAL; ARTICLE; BIOLOGICAL MODEL; CHYTRIDIOMYCETES; COMMUNICABLE DISEASE; COMPUTER SIMULATION; EPIDEMIC; IMMUNOLOGY; MICROBIOLOGY; MORTALITY; POPULATION DYNAMICS; SEASON;

AMPHIBIANS; ANIMALS; CHYTRIDIOMYCOTA; COMMUNICABLE DISEASES; COMPUTER SIMULATION; EPIDEMICS; MODELS, IMMUNOLOGICAL; POPULATION DYNAMICS; SEASONS;

EID: 84891749174     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-012-0636-4     Document Type: Article

References (47)

1. Ackleh AS, Allen LJS (2003) Competitive exclusion and coexistence for pathogens in an epidemic model with variable population size. J Math Biol 47: 153-168.
2. Ackleh AS, Allen LJS (2005) Competitive exclusion in SIS and SIR epidemic models with total cross immunity and density-dependent host mortality. Discrete Cont Dyn B 2: 175-188.
3. Ackleh AS, Deng K, Huang Q (2011) Stochastic Juvenile-adult models with application to a green tree frog population. J Biol Dyn 5: 64-83.
4. Ackleh AS, Carter J, Deng K, Huang Q, Pal N, Yang X (2012) Fitting a structured Juvenile-adult model for green tree frogs to population estimates from capture-mark-recapture field data. Bull Math Biol 74: 641-665.
5. Ahmad S (1993) On the non autonomous Volterra-Lotka competition equations. Proc Am Math Soc 117: 199-204.
6. Ahmad S, Montes de Oca F (1998) Extinction in nonautonomous T-periodic competitive Lotka-Volterra system. Appl Math Comput 90: 155-166.
7. Ahmad S, Lazer AC (2005) Average growth and extinction in a competitive Lotka-Volterra system. Nonlinear Anal 62: 545-557.
8. Anderson RM, May RM (1982) Coevolution of hosts and parasites. Parasitology 85: 411-426.
9. Andreasen V, Pugliese A (1995) Pathogen coexistence induced by density dependent host mortality. J Theor Biol 177: 159-165.
10. Battaaz A, Zanolin F (1998) Coexistence states for periodic competitive Kolmogorov systems. J Math Anal Appl 219: 179-199.
11. Berger L, Marantelli G, Skerratt LF, Speare R (2005) Virulence of the amphibian chytrid fungus Batrachochytrium dendrobatidis varies with the strain. Dis Aquat Org 68: 47-50.
12. Bremermann HJ, Thieme HR (1989) A competitive exclusion principle for pathogen virulence. J Math Biol 27: 179-190.
13. Brucker RM, Harris RN, Schwantes CR, Gallaher TN, Flaherty DC, Lam BA, Minbiole KP (2008a) Amphibian chemical defense: antifungal metabolites of the microsymbiont Janthinobacterium lividum on the salamander Plethodon cinereus. J Chem Ecol 34: 1422-1429.
14. Brucker RM, Baylor CM, Walters RL, Lauer A, Harris RN, Minbiole KP (2008b) The identification of 2, 4-diacetylphloroglucinol as an antifungal metabolite produced by cutaneous bacteria of the salamander Plethodon cinereus. J Chem Ecol 34: 39-43.
15. Castillo-Chavez C, Huang W, Li J (1996) Competitive exclusion in gonorrhea models and other sexually transmitted diseases. SIAM J Appl Math 56: 494-508.
16. Castillo-Chavez C, Huang W, Li J (1999) Competitive exclusoin and coexistence of multiple strains in an SIS STD model. SIAM J Appl Math 56: 1790-1811.
17. Cook SM, Glass RI, Lebaron CW, Ho MS (1990) Global seasonality of rotavirus infections. Bull World Health Organ 68: 171-177.
18. Cushing JM (1980) Two species competition in a periodic environment. J Math Biol 10: 385-400.
19. Cushing JM (1986) Periodic Lotka-Volterra competition equations. J Math Biol 24: 381-403.
20. Feng Z, Velasco-Hernandez JX (1997) Competitive exclusion in a vector-host model for the dengue fever. J Math Biol 35: 523-544.
21. Fine P, Clarkson J (1982) Measles in England and Wales-I: an analysis of factors underlying seasonal patterns. Int J Epidemiol 11: 5-14.
22. Grassly NC, Fraser C (2006) Seasonal infectious disease epidemiology. Proc R Soc B 273: 2541-2550.
23. Hethcote, HW, Yorke JA (1984) Gonorrhea transmission dynamics and control. Lecture notes in biomathematics, vol. 56, p. 105. Springer, Berlin.
24. de Jong M, Diekmann O, Heeserbeek H (1995) How does transimission of infection depend on population size? In: Mollison D (ed) Epidemic models: their structure and relation to data. Cambridge University Press, Cambridge.
25. Kaiser K, Pollinger J (2012) Batrachochytrium dendrobatidis shows high genetic diversity and ecological niche specificity among haplotypes in the Maya Mountains of Belize. PLoS One 7: e32113.
26. Levin SA, Pimentel D (1981) Selection of intermediate rates increase in parasite-host systems. Am Nat 117: 308-315.
27. Li J, Zhou Y, Ma Zh, Hyman JM (2004) Epidemiological models for mutating pathogens. SIAM J Appl Math 65: 1-23.
28. Lipsitch M, Siller S, Nowak MA (1996) The evolution of virulence in pathogens with vertical and horizontal transmission. Evolution 50: 1729-1741.
29. Lisena B (2004) Global stability in periodic competitive system. Nonlinear Anal RWA 5: 613-627.
30. Martcheva M (2009) A non-autonomous multi-strain SIS epidemic model. J Biol Dyn 3: 235-251.
31. May R, Nowak M (1994) Superinfection, metapopulation dynamics, and the evolution of diversity. J Theor Biol 170: 95-114.
32. May R, Nowak M (1995) Coinfection and the evolution of parasite virulence. Proc Roy Soc Lond B 261: 209-215.
33. Mitchell KM, Churcher TS, Garner TWJ, Fisher MC (2008) Persistence of the emerging pathogen Batrachochytrium dendrobatidis outside the amphibian host greatly increases the probability of host extinction. Proc Roy Soc B 275: 329-334.
34. Mounts AW, Ando T, Koopmans M, Bresee JS, Noel J, Glass RI (2000) Cold weather seasonality of gastroenteritis associated with Norwalk-like viruses. J Infect Dis 181(suppl 2): S284-S287. doi: 10. 1086/315586.
35. Nkashama MN (2000) Dynamics of logistic equations with non-autonomous bounded coefficients. Electron J Differ Equ 2: 1-8.
36. Nowak M, May R (1994) Superinfection and the evolution of parasite virulence. Proc Royal Soc Lond B 255: 81-89.
37. Pham L, Boudreaux S, Karhbet S, Price B, Ackleh AS, Carter J, Pal N (2007) Population estimates of Hyla cinerea (Schneider) (Green Treefrog) in an urban environment. Southeastern Nat 6: 203-216.
38. Pugliese A (2002) On the evolutionary coexistence of parasite strains. Math Biosci 177-178: 255-275.
39. Salceanu PL (2013) Robust uniform persistence in discrete and continuous nonautonomous systems. J Math Anal Appl 398: 487-500. doi: 10. 1016/j. jmaa. 2012. 09. 005.
40. Smith HL (1986) Periodic solutions of periodic competitive and cooperative systems. SIAM J Math Anal 17: 1289-1318.
41. Smith HL, Waltman P (1995) The theory of the chemostat. Cambridge University Press, Cambridge.
42. Smith HL, Zhao X-Q (2001) Robust persistence for semi-dynamical systems. Nonlinear Anal 47: 6169-6179.
43. Smith HL, Thieme H (2011) Dynamical systems and population persistence, Graduate studies in mathematics, 118. American Mathematical Society, Providence, RI.
44. Thieme HR (2000) Uniform persistence and permanence for non-autonomous semiflows in population biology. Math Biosci 166: 173-201.
45. Wesley CL, Allen LJ (2008) The basic reproduction number in some discrete-time epidemic models. J Differ Equ Appl 14: 1127-1147.
46. Yang X, Pal N, Ackleh AS, Carter J (2011) A case study of green tree frog population size estimation by repeated capture-mark-recapture method with individual tagging. J Stat Comput Simul 81: 1879-1895.
47. Zhao X-Q (2003) Dynamical systems in population biology, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 16. Springer, New York.