Journal of Mathematical Biology

, Volume 28, Issue 1, pp 65–82 | Cite as

Population models for diseases with no recovery

  • A. Pugliese
Article

Abstract

An SI epidemic model with a general shape of density-dependent mortality and incidence rate is studied. The asymptotic behaviour is global convergence to an endemic equilibrium, above a threshold, and to a disease-free equilibrium, below the threshold. The effect of vaccination is then examined.

Key words

Epidemic models Nonlinear incidence rate Population regulation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Anderson, R. M.: Directly transmitted viral and bacterial infections of man. In: Anderson, R. M. (ed.) Population dynamics of infectious diseases, pp. 1–37. London: Chapman and Hall 1982Google Scholar
  2. 2.
    Anderson, R. M., Jackson, H. C., May, R. M., Smith, A. M.: Population dynamics of fox rabies in Europe. Nature 289, 765–771 (1981)Google Scholar
  3. 3.
    Anderson, R. M., May, R. M.: Regulation and stability of host-parasite population interactions. J. Anim. Ecol. 47, 219–247 (1978)Google Scholar
  4. 4.
    Anderson, R. M., May, R. M.: Population biology of infectious diseases, I. Nature 280, 361–367 (1979)Google Scholar
  5. 5.
    Andreasen, V.: Disease regulation of age-structured host populations. Theor. Popul. Biol., in press (1989)Google Scholar
  6. 6.
    Brauer, F.: Epidemic models in populations of varying size. In: Castillo-Chavez, C., Levin, S. A., Shoemaker C. (eds.) Mathematical approaches to ecological and environmental problem solving. (Lect. Notes. Biomath., in press) Berlin Heidelberg New York: Springer 1989Google Scholar
  7. 7.
    Bruaer, F.: Models for the spread of universally fatal diseases (manuscript)Google Scholar
  8. 8.
    Brauer, F.: Some infectious disease models with population dynamics and general contact rates (manuscript)Google Scholar
  9. 9.
    Busenberg, S., Cooke, K. L., Pozio, M. A.: Analysis of a model of a vertically transmitted disease. J. Math. Biol. 17, 305–329 (1983)Google Scholar
  10. 10.
    Castillo-Chavez, C., Cooke, K. L., Huang, W., Levin, S. A.: On the role of long incubation periods in the dynamics of acquired immunodeficiency syndrome (AIDS). Part 1: Single population models. J. Math. Biol. 27, 373–398 (1989)Google Scholar
  11. 11.
    Getz, W. M., Pickering, J.: Epidemic models: thresholds and population regulation. Am. Nat. 121, 892–898 (1983)Google Scholar
  12. 12.
    Hastings, A.: Global stability of two species systems. J. Math. Biol. 5, 399–403 (1978)Google Scholar
  13. 13.
    Liu, W. M., Hethcote, H. W., Levin, S. A.: Dynamical behavior of epidemiological models with nonlinear incidence rates. J. Math. Biol. 25, 359–380 (1987)Google Scholar
  14. 14.
    Liu, W. M., Levin, S. A., Iwasa, Y.: Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models. J. Math. Biol. 23, 187–204 (1986)Google Scholar
  15. 15.
    May, R. M., Anderson, R. M., McLean, A. R.: Possible demographic consequences of HIV/AIDS epidemics. Math. Biosci. 90, 475–505 (1988)Google Scholar
  16. 16.
    Ye, Yan-Qian: Theory of limit cycles. Providence: Am. Math. Soc. 1986Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • A. Pugliese
    • 1
  1. 1.Dipartimento di MatematicaUniversità di TrentoPovoItaly

Personalised recommendations