Epidemics in two competing species

Nonlinear Analysis: Real World Applications

Volumn 10, Issue 2, 2009, Pages 723-744

  Han, Litao ^a   Pugliese, Andrea ^b  

^a RENMIN UNIVERSITY OF CHINA   (China)

^b UNIVERSITY OF TRENTO   (Italy)

Author keywords

Epidemic model; Hopf bifurcation; Multihost infection; Periodic solutions; Species extinction; Uniform persistence

Indexed keywords

ASYMPTOTIC STABILITY; BIFURCATION (MATHEMATICS); COMPETITION; SWITCHING CIRCUITS; SYSTEM STABILITY;

EPIDEMIC MODEL; MULTIHOST INFECTION; PERIODIC SOLUTIONS; SPECIES EXTINCTION; UNIFORM PERSISTENCE;

HOPF BIFURCATION;

EID: 56549097208     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2007.11.005     Document Type: Article

References (27)

1. Begon M., Bowers R.G., Kadianakis N., and Hodgkinson D.E. Disease and community structure: The importance of host self-regulation in a host-host-pathogen model. Am. Nat. 139 (1992) 1131-1150
2. Greenman J.V., and Hudson P.J. Infected coexistence instability with and without density-dependent regulation. J. Theoret. Biol. 185 (1997) 345-356
3. Saenz R.A., and Hethcote H.W. Competing species models with an infectious disease. Math. Biosci. Eng. 3 (2006) 219-235
4. Begon M., Hazel S.M., Baxby D., Bown K., Cavanagh R., Chantrey J., Jones T., and Bennett M. Transmission dynamics of a zoonotic pathogen within and between wildlife host species. Proc. R. Soc. Lond. B 266 (1999) 1939-1945
5. Tompkins D.M., White A.R., and Boots M. Ecological replacement of native red squirrels by invasive greys driven by disease. Ecology Lett. 6 (2003) 189-196
6. Begon M., Hazel S.M., Telfer S., Bown K., Carslake D., Cavanagh R., Chantrey J., Jones T., and Bennett M. Rodents, cowpox virus and islands: Densities, numbers and thresholds. J. Animal Ecology 2 (2003) 343-355
7. Holt R.D., and Pickering J. Infectious disease and species coexistence: A model of Lotka-Volterra form. Am. Nat. 126 (1985) 196-211
8. Begon M., and Bowers R.G. Beyond host-pathogen dynamics. In: Grenfell B.T., and Dobson A.P. (Eds). Ecology of Disease in Natural Populations (1995), Cambridge University Press, Cambridge 479-509
9. Hethcote H.W., Wang W., and Li Y. Species coexistence and periodicity in host-host-pathogen models. J. Math. Biol. 51 (2005) 629-660
10. Anderson R.M., and May R.M. The invasion, persistence, and spread of infectious diseases within animal and plant communites. Philos. Trans. R. Soc. Lond. B 314 (1986) 533-570
11. Bowers R.G., and Turner J. Community structure and the interplay between interspecific infection and competition. J. Theoret. Biol. 187 (1997) 95-109
12. Venturino E. The effects of diseases on competing species. Math. Biosci. 174 (2001) 111-131
13. Han L., Ma Z., and Shi T. An SIRS epidemic model of two competitive species. Math. Comput. Modelling 37 (2003) 87-108
14. van den Driessche P., and Zeeman M.L. Disease induced oscillations between two competing species. SIAM J. Appl. Dyn. Syst. 3 (2004) 601-619
15. Thieme H.R. Persistence under relaxed point-dissipativity (with application to an endemic model). SIAM J. Math. Anal. 24 (1993) 407-435
16. Gao L.Q., and Hethcote H.W. Disease transmission models with density-dependent demographics. J. Math. Biol. 30 (1992) 717-731
17. Zhou J., and Hethcote H.W. Population size dependent incidence in models for diseases without immunity. J. Math. Biol. 32 (1994) 809-834
18. 0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28 (1990) 365-382
19. Pugliese A. Population models for disease with no recovery. J. Math. Biol. 28 (1990) 65-82
20. Diekmann O., and Heesterbeek J.A.P. Mathematical Epidemiology of Infectious Diseases (2000), Wiley, New York
21. Rosà R., and Pugliese A. Effects of tick population dynamics and host densities on the persistence of tick-borne infections. Math. Biosci. 208 (2007) 216-240
22. Thieme H.R. Mathematics in Population Biology (2003), Princeton Univ. Press, Princeton
23. Magal P., and Zhao X. Global attractors and steady states for uniformly persistent dynamical systems. SIAM J. Math. Anal. 37 (2005) 251-275
24. Hofbauer J., and Sigmund K. The Theory of Evolution and Dynamical Systems (1988), Cambridge University Press, Cambridge
25. Shen J., and Jing Z. A new detecting method for conditions of existence of Hopf bifurcation. Acta Math. Appl. Sin. 11 (1995) 79-93
26. MATCONT. http://www.matcont.ugent.be
27. Thieme H.R. Epidemic and demographic interaction in the spread of potentially fatal diseases in growing population. Math. Biosci. 111 (1992) 99-130