Journal of Mathematical Biology

, Volume 53, Issue 2, pp 253–272 | Cite as

A Susceptible-infected Epidemic Model with Voluntary Vaccinations



An susceptible-infected epidemic model with endogenous behavioral changes is presented to analyze the impact of a prophylactic vaccine on disease prevalence. It is shown that, with voluntary vaccination, whether an endemic equilibrium exists or not does not depend on vaccine efficacy or the distribution of agent-types. Although an endemic equilibrium is unique in the absence of a vaccine, the availability of a vaccine can lead to multiple endemic equilibria that differ in disease prevalence and vaccine coverage. Depending on the distribution of agent-types, the introduction of a vaccine or, if one is available, a subsidy for vaccination can increase disease prevalence by inducing more risky behavior.

Keywords or Phrases

Endemic equilibrium Reproductive number Dynamic programming STD Voluntary vaccination Mass vaccination 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ahituv A., Hotz V., Philipson T. (1996) The responsiveness of the demand for condoms to the local prevalence of AIDS. J Hum Resour 31, 869–897CrossRefGoogle Scholar
  2. 2.
    Blower S., McLean A. (1994) Prophylactic vaccines, risk behavior change, and the probability of eradicating HIV in San Francisco. Science 265, 1451–1454CrossRefGoogle Scholar
  3. 3.
    Chen F. (2004) Rational behavioral response and the transmission of STDs. Theor Popul Biol 66, 307–316MATHCrossRefGoogle Scholar
  4. 4.
    Davenport M., Ribeiro R., Chao D., Perelson A. (2004) Predicting the impact of a nonsterilizing vaccine against human immunodeficiency virus. J Virol 78, 11340–11351CrossRefGoogle Scholar
  5. 5.
    Esparza J. (2001) An HIV vaccine: How and when?. Bull World Health Organ 79, 1133–1137Google Scholar
  6. 6.
    Feinleib J., Michael R. (1998) Reported changes in sexual behavior in response to AIDS in the United States. Prev Med 27, 400–411CrossRefGoogle Scholar
  7. 7.
    Garber D., Silvestri G., Feinberg M. (2004) Prospects for an AIDS vaccine three big questions, no easy answers. Lancet Infect Dis 4, 397–413CrossRefGoogle Scholar
  8. 8.
    Geoffard P-Y, Philipson T. (1996) Rational epidemics and their public control. Int Econ Rev 37, 603–624MATHCrossRefGoogle Scholar
  9. 9.
    Gray R., Li X., Wawer M., Gange S., Serwadda D., Sewankambo N., Moore R., Wabwire-Mangen F., Lutalo T., Quinn T. (2003) Stochastic simulation of the impact of antiretroviral therapy and HIV vaccines on HIV transmission; Rakai, Uganda. AIDS 17, 1941–1951CrossRefGoogle Scholar
  10. 10.
    Hanke T. (2001) Prospect of a prophylactic vaccine for HIV Br Med Bull 58, 205–218Google Scholar
  11. 11.
    Johnston M., Flores J. (2001) Progress in HIV vaccine development. Curr Opin Pharmacol 1, 504–510CrossRefGoogle Scholar
  12. 12.
    Kremer M. (1996) Integrating behavioral choice into epidemiological models of AIDS. Q J Econ 111, 549–573MATHCrossRefGoogle Scholar
  13. 13.
    Letvin N. (2005) Progress toward an HIV vaccine. Annu Rev Med 56, 213–223CrossRefGoogle Scholar
  14. 14.
    Levy J. (2001) What can be achieved with an HIV vaccine. Lancet 357, 223–224CrossRefGoogle Scholar
  15. 15.
    Massad E., Coutinho F., Burattini M., Lopez L., Struchiner C. (2001) Modeling the impact of imperfect HIV vaccines on the incidence of the infection. Math Comput Model. 34, 345–351MATHCrossRefGoogle Scholar
  16. 16.
    McLean A., Blower S. (1993) Imperfect vaccines and herd immunity to HIV. Proc R Soc Lond B 253, 9–13CrossRefGoogle Scholar
  17. 17.
    Newman P., Duan N., Rudy E., Johnston-Roberts K. (2004) HIV risk and prevention in a post-vaccine context. Vaccine 22, 1954–1963CrossRefGoogle Scholar
  18. 18.
    Philipson T., Posner R. (1993) Private Choices and Public Health: The AIDS Epidemic in an Economic Perspective. Harvard University Press, CambridgeGoogle Scholar
  19. 19.
    Ross S. (1983) Introduction to Stochastic Dynamic Programming. Academic Press, New YorkMATHGoogle Scholar
  20. 20.
    Smith R., Blower S. (2004) Could disease-modifying HIV vaccines cause population-level perversity. Lancet Infect Dis 4, 636–639CrossRefGoogle Scholar
  21. 21.
    Spearman P. (2003) HIV vaccine development: lessons from the past and promise for the future. Curr HIV Res 1, 101–120CrossRefGoogle Scholar
  22. 22.
    Stoneburner R., Low-Beer D. (2004) Population-level HIV declines and behavioral risk avoidance in Uganda. Science 304, 714–718CrossRefGoogle Scholar
  23. 23.
    UNAIDS: AIDS Epidemic Update: 2004. UNAIDS, Geneva (2004a)Google Scholar
  24. 24.
    UNAIDS: 2004 Report on the Global HIV/AIDS Epidemic: 4th Global Report. UNAIDS, Geneva (2004b)Google Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of EconomicsWake Forest UniversityWinston-SalemUSA

Personalised recommendations