African Journal of
Mathematics and Computer Science Research

  • Abbreviation: Afr. J. Math. Comput. Sci. Res.
  • Language: English
  • ISSN: 2006-9731
  • DOI: 10.5897/AJMCSR
  • Start Year: 2008
  • Published Articles: 262

Full Length Research Paper

A stage-structured two species competition model under the effect of disease

Manju Agarwal
  • Manju Agarwal
  • Department of Mathematics and Astronomy, University of Lucknow, Lucknow-226007, India.
  • Google Scholar
Vinay Verma
  • Vinay Verma
  • Department of Mathematics and Astronomy, University of Lucknow, Lucknow-226007, India.
  • Google Scholar


  •  Accepted: 22 January 2014
  •  Published: 12 February 2014

References

Anderson RM, May RM (1979). Population biology of infectious diseases. Part 1. Nature 280:361-367.
Crossref
 
Anderson RM, May RM (1986). The invasion, persistence and spread of infectious diseases with in animal and plant communities. Philos. Trans. R. Soc. London B 314:533.
Crossref
 
Bailey NTJ (1975). The Mathematical Theory of infectious Disease and its Application. Griffin, London.
 
Bailey NTJ (1982). The Biomathematics of Malaria. Giffin, London.
 
Begon M, Bowers MG (1995). Beyond host pathogen dynamics In: B.T. Grenfell, A.P. Dobson (Eds.), Ecology of Infectious Diseases in Natural Populations. Cambridge University, Cambridge. P. 478.
Crossref
 
d'Onofrio A (2002). Stability properties of pulse vaccination strategy in SEIR epidemic model. Math. Biosci. 179(1):57-72.
Crossref
 
Dutour AP (1982). Disease outbreak caused by drinking water. J. Water Pollut. Control Fed. 6:980-983.
 
Freedman HI, Gopalsamy K (1986). Global stability in time-delayed single-species dynamics. Bulletin of Mathematical Biology. 48(5-6): 485-492.
Crossref
 
Hethcote HW (1976). Qualitative analysis of communicable disease models. Bioscience 28:335-356.
Crossref
 
Hethcote HW (2000). The mathematics of infectious diseases. SIAM Review. 42(4):599-653.
Crossref
 
Hethcote HW, Stech HW, Vander DP (1981). Periodicity and stability in epidemic models In: S.N. Busenberg, K. Cooke (Eds.), A Survey in Differential Equations and Applications in Ecology, Epidemics and Population Problems. Academic Press, New York.
Crossref
 
Kuang Y (1993). Delay differential equations with application in population dynamics. New York, Academic Press.
 
Mena-Lorca J, Hethcote HW (1992). Dynamic models of infectious diseases as regulators of population size. J. Math. Biol. 30:693-716.
Pubmed
 
Roberts MG, Kao RR (2002). The dynamics of an infectious disease in a population with birth pulse. Math. Biol. 149:23-36.
 
Venturino E (2001). The effects of disease on competing species. Math. Biosci. 174:111-131.
Crossref
 
Waltman P (1974). Deterministic Threshold Models in the Theory of Epidemic In: Lecture notes in Biomathematics.  Springer Verlag, New York. P. 1
Crossref