Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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STABILITY OF A TWO-STRAIN EPIDEMIC MODEL WITH AN AGE STRUCTURE AND MUTATION

  • Wang, Xiaoyan (Department of Applied Mathematics, Yuncheng University) ;
  • Yang, Junyuan (Department of Applied Mathematics, Yuncheng University) ;
  • Zhang, Fengqin (Department of Applied Mathematics, Yuncheng University)
  • Received : 2011.04.04
  • Accepted : 2011.06.30
  • Published : 2012.01.30
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Abstract

A two-strain epidemic model with an age structure mutation and varying population is studied. By means of the spectrum theory of bounded linear operator in functional analysis, the reproductive numbers according to the strains, which associates with the growth rate ${\lambda}^*$ of total population size are obtained. The asymptotic stability of the steady states are obtained under some sufficient conditions.

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References

  1. C. Castillo-Chavez, W. Huang, J. Li, Competitive exclusion and coexistence of multiple strains in an SIS STD model, SIAM J. Appl. Math., 59 (1999), 1790-1800. https://doi.org/10.1137/S0036139997325862
  2. G.F. Webb, Theory of Nonlinear Age-Dependent Population Dynamics, Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, 1985.
  3. Z. Feng, M. Iannelli, F. Milner, A two-strain tuberculosis model with age of infection, SIAM J. Appl. Math. 62(2002), 1634-1641. https://doi.org/10.1137/S003613990038205X
  4. R. May, M. Nowak, Superinfection, metapopulation dynamics, and the evolution of diversity, J. Theor. Biol. 170(1994), 95-114. https://doi.org/10.1006/jtbi.1994.1171
  5. M. Nowak, R. May, Superinfection and the evolution of parasite virulence, Proc. Roy. Soc. London B. 255(1994), 81-106. https://doi.org/10.1098/rspb.1994.0012
  6. R. May, M. Nowak, Coinfection and the evolution of parasite virulence, Proc. Roy. Soc. London B 261(1995), 209-221. https://doi.org/10.1098/rspb.1995.0138
  7. V. Andreasen, J. Lin, S. Levin, The dynamics of cocirculating influenza strains conferring partial cross-immunity, J. Math. Biol. 35(1997), 825-836. https://doi.org/10.1007/s002850050079
  8. V. Andreasen, A. Pugliese, Pathogen coexistence induced by density dependent host mortality, J. Theor. Biol. 177(1995),159-166.
  9. S. Bonhoeffer, M. Nowak, Mutation and the evolution of virulence, Proc. Roy. Soc. London B 258(1994), 133-146. https://doi.org/10.1098/rspb.1994.0153
  10. M. Iannelli, M. Martcheva, Homogeneous dynamical systems and the age-structure SIR model with proportionate mixing incidence. in Evolution Equations: Application to Physics, Industry, Life Science, and Economics, Eds. G. Lumer, M. Iannelli, Birkhauser, Basel, 2003.
  11. A. Ackleh, L. Allen, Competitive exclusion and coexistence for pathogens in an epidemic model with variable population size, J. Math. Biol. 47(2003), 153-165. https://doi.org/10.1007/s00285-003-0207-9
  12. M. Lipsitch and J. J. OHagan, Patterns of antigenic diversity and the mechanisms that maintain them, J. R. Soc. Interface, 4 (2007), 787-802. https://doi.org/10.1098/rsif.2007.0229
  13. H. Inaba, Mathematical analysis of an age-structured SIR epidemic model with vertical transmission, Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), 69-96.
  14. M. Martcheva, B. M. Bolker and R. D. Holt, Vaccine-induced pathogen strain replacement: what are the mechanisms?, J. R. Soc. Interface, 5 (2008), 3-13. https://doi.org/10.1098/rsif.2007.0236
  15. H. R. Thieme, Pathogen competition and coexistence and the evolution of virulence, in "Math-ematics for Life Sciences and Medicine," Biol. Med. Phys. Biomed. Eng., Springer, Berlin, 2007, pp. 123-153.
  16. G.F. Webb, Population models structured by age, size, and spatial position, in Structured Population Models in Biology and Epidemiology, P. Magal and S. Ruan, eds., Lecture Notes in Math. 1936, Springer-Verlag, Berlin, New York, 2008, pp. 1-49.
  17. X.L. Li and J.X. Liu,An age-structure two-strain epidemic model with super-infection, Math. Biosci. Engin. 7 (2010), 123-147. https://doi.org/10.3934/mbe.2010.7.123