Abstract
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.
Article PDF
Similar content being viewed by others
References
Ahituv A., Hotz V., Philipson T. (1996) The responsiveness of the demand for condoms to the local prevalence of AIDS. J Hum Resour 31, 869–897
Blower S., McLean A. (1994) Prophylactic vaccines, risk behavior change, and the probability of eradicating HIV in San Francisco. Science 265, 1451–1454
Chen F. (2004) Rational behavioral response and the transmission of STDs. Theor Popul Biol 66, 307–316
Davenport M., Ribeiro R., Chao D., Perelson A. (2004) Predicting the impact of a nonsterilizing vaccine against human immunodeficiency virus. J Virol 78, 11340–11351
Esparza J. (2001) An HIV vaccine: How and when?. Bull World Health Organ 79, 1133–1137
Feinleib J., Michael R. (1998) Reported changes in sexual behavior in response to AIDS in the United States. Prev Med 27, 400–411
Garber D., Silvestri G., Feinberg M. (2004) Prospects for an AIDS vaccine three big questions, no easy answers. Lancet Infect Dis 4, 397–413
Geoffard P-Y, Philipson T. (1996) Rational epidemics and their public control. Int Econ Rev 37, 603–624
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, 1941–1951
Hanke T. (2001) Prospect of a prophylactic vaccine for HIV Br Med Bull 58, 205–218
Johnston M., Flores J. (2001) Progress in HIV vaccine development. Curr Opin Pharmacol 1, 504–510
Kremer M. (1996) Integrating behavioral choice into epidemiological models of AIDS. Q J Econ 111, 549–573
Letvin N. (2005) Progress toward an HIV vaccine. Annu Rev Med 56, 213–223
Levy J. (2001) What can be achieved with an HIV vaccine. Lancet 357, 223–224
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, 345–351
McLean A., Blower S. (1993) Imperfect vaccines and herd immunity to HIV. Proc R Soc Lond B 253, 9–13
Newman P., Duan N., Rudy E., Johnston-Roberts K. (2004) HIV risk and prevention in a post-vaccine context. Vaccine 22, 1954–1963
Philipson T., Posner R. (1993) Private Choices and Public Health: The AIDS Epidemic in an Economic Perspective. Harvard University Press, Cambridge
Ross S. (1983) Introduction to Stochastic Dynamic Programming. Academic Press, New York
Smith R., Blower S. (2004) Could disease-modifying HIV vaccines cause population-level perversity. Lancet Infect Dis 4, 636–639
Spearman P. (2003) HIV vaccine development: lessons from the past and promise for the future. Curr HIV Res 1, 101–120
Stoneburner R., Low-Beer D. (2004) Population-level HIV declines and behavioral risk avoidance in Uganda. Science 304, 714–718
UNAIDS: AIDS Epidemic Update: 2004. UNAIDS, Geneva (2004a)
UNAIDS: 2004 Report on the Global HIV/AIDS Epidemic: 4th Global Report. UNAIDS, Geneva (2004b)
Author information
Authors and Affiliations
Corresponding author
Additional information
I would like to thank one of the editors of the journal, Alan Hastings, for his comments and suggestions.
Rights and permissions
About this article
Cite this article
Chen, F.H. A Susceptible-infected Epidemic Model with Voluntary Vaccinations. J. Math. Biol. 53, 253–272 (2006). https://doi.org/10.1007/s00285-006-0006-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00285-006-0006-1