Abstract
This paper presents a number of deterministic models for theoretically assessing the potential impact of an imperfect prophylactic HIV-1 vaccine that has five biological modes of action, namely “take,” “degree,” “duration,” “infectiousness,” and “progression,” and can lead to increased risky behavior. The models, which are of the form of systems of nonlinear differential equations, are constructed via a progressive refinement of a basic model to incorporate more realistic features of HIV pathogenesis and epidemiology such as staged progression, differential infectivity, and HIV transmission by AIDS patients. The models are analyzed to gain insights into the qualitative features of the associated equilibria. This allows the determination of important epidemiological thresholds such as the basic reproduction numbers and a measure for vaccine impact or efficacy. The key findings of the study include the following (i) if the vaccinated reproduction number is greater than unity, each of the models considered has a locally unstable disease-free equilibrium and a unique endemic equilibrium; (ii) owing to the vaccine-induced backward bifurcation in these models, the classical epidemiological requirement of vaccinated reproduction number being less than unity does not guarantee disease elimination in these models; (iii) an imperfect vaccine will reduce HIV prevalence and mortality if the reproduction number for a wholly vaccinated population is less than the corresponding reproduction number in the absence of vaccination; (iv) the expressions for the vaccine characteristics of the refined models take the same general structure as those of the basic model.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Anderson, R.M., May, R.M., 1991. Infectious Diseases of Humans: Dynamics and control, Oxford University Press, Oxford.
Anderson, R.M., Garnett, G.P., 1996. Low-efficacy HIV vaccines: Potential for community-based intervention programmes. Lancet 348, 1010–1013.
Anderson, R.M., Hanson, M., 2005. Potential public health impact of imperfect HIV type 1 vaccines. J. Infect. Dis. 191(Suppl. 1), S85–S96.
Arino, J., McCluskey, C.C., van den Driessche, P., 2003. Global results for an epidemic model with vaccination that exhibits backward bifurcation. SIAM J. Appl. Math. 64, 260–276.
Berzofsky, J., Ahlers, A., Janik, J., Morris, J., Sangkon, O., et al., 2004. Progress on new vaccine strategies against chronic viral infections. J. Clin. Invest. 114, 450–462.
Blower, S., McLean, A., 1994. Prophylactic vaccines, risk behavior change, and the probability of eradicating HIV in San Francisco. Science 265, 1451–1454.
Blower, S., McLean, A., 1995. AIDS: Modeling epidemic control. Science 267, 1250–1253.
Blower, S., Koelle, K., Mills, J., 2002. Health policy modeling: Epidemic control, HIV vaccines, and risky behavior. In: Kaplan and Brookmeyer (Eds.), Quantitative Evaluation of HIV Prevention Programs. Yale University Press, pp. 260–289.
Chang, M.L., Vitek, C., Esparza, J., 2003. Public health considerations for the use of a first generation HIV vaccine. Report from a WHO-UNAIDS-CDC consultation, Geneva, 20–21 November 2002. AIDS 17, W1–W10.
Chesney, M., Chambers, D., Kahn, J., 1997. Risk behavior for HIV infection in participants in preventive HIV vaccine trials: A cautionary note. J. Acquir. Immune. Defic. Syndr. Hum. Retrovirol. 16, 266–271.
Calarota, S., Weiner, D., 2003. Present status of human HIV vaccine development. AIDS 17(Suppl. 4), S73–S84.
Clements, C.J., Abdool-Karim, Q., Chang, M.L., Nkowane, B., Esparza, J., 2004. Breaking new ground—are changes in immunization services needed for the introduction of future HIV/AIDS vaccines and other new vaccines targeted at adolescents? Vaccine 22, 2822–2826.
Corbett, B.D., Moghadas, S.M., Gumel, A.B., 2003. Subthreshold domain of bistable equilibria for a model of HIV epidemiology. IJMMS 58, 3679–3698.
Diekmann, O., Heesterbeek, J.A.P., Metz, J.A.J., 1990. On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28, 503–522.
Dixon, S., McDonald, S., Roberts, J., 2002. The impact of HIV and AIDS on Africa's economic development. BMJ 324, 232–234.
Esparza, J., Osmanov, S., 2003. HIV vaccines: A global perspective. Curr. Mol. Med. 3, 183–193.
Fauci, A.S., Pantaleo, G., Stanley, S., Weissman, D., 1996. Immunopathogenic mechanisms of HIV infection. Ann. Intern. Med. 124, 654–663.
Fleck, F., 2004. Developing economies shrink as AIDS reduces workforce. BMJ 329, 129.
Gray, R., Wawer, M., Brookmeyer, R., Sewankambo, N., et al., for the Rakai Project Study Group, 2001. Probability of HIV-1 transmission per coital act in monogamous, heterosexual, HIV-discordant couples in Rakai, Uganda. Lancet 357, 1149–1153.
Gray, R., Li, X., Wawer, M., Gange, S., Serwadda, D., et al. (2003). Stochastic simulation of the impact of antiretroviral therapy and HIV vaccines on HIV transmission; Rakai, Uganda. AIDS 17, 1941–1951.
Gumel, A.B., Moghadas, S.M., Mickens, R.E., 2004. Effect of a preventive vaccine on the dynamics of HIV transmission. Commun. Nonlinear Sci. Numer. Simul. 9, 649–659.
Hethcote, H.W., 2000. The mathematics of infectious diseases. SIAM Rev. 42, 599–653.
Hethcote, H.W., Van Ark, J., 1992. Modeling HIV transmission and AIDS in the United States. Lecture Notes in Biomathematics vol. 95. Springer-Verlag, New York.
Hyman, J.M., Li, J., Stanley, E.A., 1999. The differential infectivity and staged progression models for the transmission of HIV. Math. Biosci. 208, 227–249.
Hyman, J.M., Li, J., Stanley, E.A., 2001. The initialization and sensitivity of multigroup models for the transmission of HIV. J. Theor. Biol. 155, 77–109.
Kribs-Zaleta, C., Velasco-Hernández, J., 2000. A simple vaccination model with multiple endemic states. Math. Biosci. 164, 183–201.
Lansky, A., Nakashima, A., Jones, J., 2000. Risk behaviors related to heterosexual transmission from HIV-infected persons. Sex. Transm. Dis. 27, 483–489.
Lee, D., Graham, B., Chiu, Y.-L., Gilbert, P., McElrath, M., et al., 2004. Breakthrough infections during phase 1 and 2 prime-boos HIV-1 vaccine trials with canarypox vectors (ALVAC) and booster dose of recombinant gp120 or gp160. J. Infect. Dis. 190, 903–907.
Longini, I., Clark, W., Byers, R., 1989. Statistical analysis of the stages of HIV infections using a Markov model. Stat. Med. 8, 831–843.
Massad, E., Coutinho, F., Burattini, M., Lopez, L., Struchiner, C.J., 2001. Modeling the impact of imperfect HIV vaccines on the incidence of the infection. Math. Comput. Model. 34, 345–351.
McCluskey, C., 2003. A model of HIV/AIDS with staged progression and amelioration. Math. Biosci. 181, 1–16.
McLean, A., Blower, S., 1993. Imperfect vaccines and herd immunity to HIV. Proc. R. Soc. Lond. B 253, 9–13.
Mellors, J., Munoz, A., Giorgi, J., Margolick, J., Tassoni, C., et al., 1997. Plasma viral load and CD4+ lymphocytes as prognostic markers of HIV-1 infection. Ann. Intern. Med. 126, 946–954.
Newman, P., Duan, N., Rudy, E., Johnston-Roberts, K., 2004. HIV risk and prevention in a post-vaccine context. Vaccine 22, 1954–1963.
Nicolosi, A., Musicco, M., Saracco, A., Lazzarin, A., 1994. Risk factors for woman-to-man sexual transmission of the human immunodeficiency virus. J. Acquir. Immune. Defic. Syndr. 7, 296–300.
O'Brien, T., Busch, M., Donegan, E., Ward, J., Wong, L., et al., 1994. Heterosexual transmission of human immunodeficiency virus type 1 from transfusion recipients to their sex partners. J. Acquir. Immune. Defic. Syndr. 7, 705–710.
Perko, L., 1996. Differential equations and dynamical systems. Springer-Verlag, New York.
Perelson, A., Nelson, P., 1999. Mathematical analysis of HIV-1 dynamics in vivo. SIAM Rev. 41, 3–44.
Porco, T., Blower, S., 1998. Designing HIV vaccination policies: Subtypes and cross-immunity. Interfaces 28, 167–190.
Porco, T., Blower, S., 2000. HIV vaccines: The effect of the mode of action on the coexistence of HIV subtypes. Math. Popul. Stud. 8, 205–229.
Quinn, T.C., Wawer, M.J., Sewankambo, N., et al., for the Rakai Project Study Group, 2000. Viral load and heterosexual transmission of human immunodeficiency virus. N. Engl. J. Med. 342, 921–929.
Royce, R., Sena, A., Cates, W., Cohen, M., 1997. Sexual transmission of HIV. N. Engl. J. Med. 336, 1072–1078.
Santra, S., Barouch, D., Korioth-Schmitz, B., Lord, C., Beddall, M., et al., 2004. Recombinant pox virus boosting of DNA-primed rhesus monkeys augments peak but not memory T lymphocyte responses Proc. Natl. Acad. Sci. 101, 11088–11093.
Shiver, J., Fu, T.-M., Chen, L., Casimiro, D., Davies, M.-A., et al., 2002. Replication-incompetent adenoviral vaccine vector elicits effective anti-immunodeficiency-virus immunity. Nature 415, 331–335.
Shiver, J., Emini, E., 2004. Recent advances in the development of HIV-1 vaccines using replication-incompetent adenovirus vectors. Ann. Rev. Med. 55, 355–372.
Takayama, A., 1993. Analytical Methods in Economics. University of Michigan Press, Ann Arbor.
United Nations Department of Economic and Social Affairs/Population Division, 2004. The Impact of AIDS. United Nations, New York.
van den Driessche, P., Watmough, J., 2002. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180, 29–48.
van Griensven, F., Keawkungwal, J., Tappero, J., Sangkum, U., Pitisuttithum, P., et al., 2004. Lack of increased HIV risk behavior among injection drug users participating in the AIDSVAX B/E HIV vaccine trial in Bangkok, Thailand. AIDS 18, 295–301.
Varian, H., 1992. Microeconomic Analysis, 3rd edn, W.W. Norton, New York.
World Bank, 1997. Confronting AIDS: Public Priorities in a Global Epidemic. Oxford University Press, Oxford.
WHO, 2004. The World Health Report: Changing History. World Health Organization, 1211 Geneva 27, Switzerland.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Elbasha, E.H., Gumel, A.B. Theoretical Assessment of Public Health Impact of Imperfect Prophylactic HIV-1 Vaccines with Therapeutic Benefits. Bull. Math. Biol. 68, 577–614 (2006). https://doi.org/10.1007/s11538-005-9057-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11538-005-9057-5