Modelling effects of public health educational campaigns on HIV/AIDS transmission dynamics. (English) Zbl 1205.34092
Summary: HIV/AIDS model for sexual transmission with explicit incubation period is proposed as a system of discrete time delay differential equations. The threshold and equilibrium for the model are determined and stabilities are examined. Qualitative analysis of the model is also presented. We use the model to study the effects of public health educational campaigns on the spread of HIV/AIDS as a single-strategy approach in HIV prevention. The education-induced basic reproductive for the model is compared with the basic reproductive number for the HIV/AIDS in the absence of any intervention to assess the possible community benefits of public health educational campaigns. We conclude from the study that in settings where public health educational campaigns of HIV/AIDS are effective and with reasonable average numbers of HIV-infected partners, public health educational campaigns can slow down the epidemic and are more effective when given to both sexually immature (pre- and early adolescence) and sexually mature individuals (adults) concurrently.
Keywords:
HIV/AIDS model; educational campaigns; basic reproductive number; incubation period; stabilityReferences:
| [1] | May, R. M.; Anderson, R. M., The transmission dynamics of Human Immunodeficiency Virus (HIV), Philos. Trans. Roy. Soc. B, 565-607 (1998) |
| [2] | Report on the Global HIV/AIDS Epidemic, UNAIDS and WHO, 1998.; Report on the Global HIV/AIDS Epidemic, UNAIDS and WHO, 1998. |
| [3] | J.X. Velasco-Hernández, H.B. Gershengorn, S.M. Blower, Could Widespread Use of Combination Antiretroviral Therapy Eradicate HIV Epidemics, The Lancet, Infectious Diseases, vol. 2, 2002, <http://infection.thelancet.com>; J.X. Velasco-Hernández, H.B. Gershengorn, S.M. Blower, Could Widespread Use of Combination Antiretroviral Therapy Eradicate HIV Epidemics, The Lancet, Infectious Diseases, vol. 2, 2002, <http://infection.thelancet.com> |
| [4] | Blower, S. M.; Gershengorn, H. B.; Grant, R. M., A tale of two futures: HIV and antiretroviral therapy in San Franscisco, Science, 287, 650-654 (2000) |
| [5] | Blower, S. M.; Aschenbach, A. N.; Gershengorn, H. B.; Kahn, J. O., Predicting the unpredictable: transmission of drug-resistant HIV, Nat. Med., 7, 1016-1020 (2001) |
| [6] | Hsu Schmitz, S. F., Effects of treatment or/and vaccination on HIV transmission in homosexuals with genetic heterogeneity, Math. Biosci., 167, 1-18 (2000) · Zbl 0979.92023 |
| [7] | Hsu Schmitz, S. F., Effects of genetic heterogeneity on HIV transmission in homosexual populations, (Castillo-Chavez, C.; Blower, S.; van den Driessche, P.; Kirschner, D.; Yakubu, A.-A., Mathematical Approaches for Emerging and Reemerging Infectious Diseases: Models, Methods and Theory (2002), Springer-Verlag), 245-260 · Zbl 1023.92029 |
| [8] | Anderson, R. M.; Gupta, S.; May, R. M., Potential of community-wide chemotherapy or immunotherapy to control the spread of HIV-1, Nature, 350-356 (1991) |
| [9] | Mclean, A.; Blower, S., Imperfect vaccines and herd immunity to HIV, Proc. Roy. Soc. Lond. B, 253, 9-13 (1993) |
| [10] | Blower, S. M.; Mclean, A. R., Prophylactic vaccines, risk behaviour change, and the probability of eradicating HIV in San Francisco, Science, 265, 1451-1454 (1994) |
| [11] | Mclean, A. R.; Blower, S. M., Modelling vaccination, Trends Microbiol., 3, 458-463 (1995) |
| [12] | Del Valle, S.; Evangelista, A. M.; Velasco, M. C.; Kribs-Zaleta, C. M.; Hsu Schmitz, S. F., Effects of education, vaccination and treatment on HIV transmission in homosexuals with genetic heterogeneity, Math. Biosci., 187, 111-133 (2004) · Zbl 1047.92042 |
| [13] | Blower, S. M.; Bodine, E. N.; Grovit-Ferbas, K., Predicting the Potential Public Health Impact of Disease-modifying HIV Vaccines in South Africa: The Problem Subtype. Predicting the Potential Public Health Impact of Disease-modifying HIV Vaccines in South Africa: The Problem Subtype, Current Drug Targets - Infectious Disorders (2005), Bentham Science Publishers Ltd |
| [14] | Hsieh, Y. H.; Velasco-Hernández, J. X., Community treatment of HIV-1: initial stage and asymptotic dynamics, Biosystems, 35, 75-81 (1995) |
| [15] | Velasco-Hernández, J. X.; Hsieh, Y. H., Modeling the effect of treatment and behavioral change in HIV transmission dynamics, J. Math. Biol., 32, 233-249 (1994) · Zbl 0792.92023 |
| [16] | Anderson, R. M.; Garnett, G. P., Low-efficacy HIV vaccines: potential for community-based intervention programmes, Lancet, 348, 1010-1013 (1996) |
| [17] | Gumel, A. B.; Moghadas, S. M.; Mickens, R. E., Effect of a preventative vaccine on the dynamics of HIV transmission, Commun. Nonlinear Sci. Numer. Simul., 9, 649-659 (2004) · Zbl 1051.92038 |
| [18] | Kgosimore, M.; Lungu, E. M., The effects of vaccination and treatment on the spread of HIV/AIDS, J. Biol. Syst., 12, 399-417 (2004) · Zbl 1074.92030 |
| [19] | Baggaley, R. F.; Ferguson, N. M.; Garnett, G. P., The epidemiological impact of antiretroviral use predicted by mathematical models: a review, Emerg. Themes Epidemiol., 2, 9 (2005) |
| [20] | Elbasha, E. H.; Gumel, A. B., Theoretical assessment of public health impact of imperfect prophylactic HIV vaccines with therapeutic benefits, Bull. Math. Biol., 68, 577-614 (2006) · Zbl 1334.91060 |
| [21] | Cooke, K. L.; van den, Driessche, Analysis of an SEIRS epidemic model with two delays, J. Math. Biol., 35, 240-260 (1996) · Zbl 0865.92019 |
| [22] | Mukandavire, Z.; Garira, W., HIV/AIDS model for assessing the effects of prophylactic sterilizing vaccines, condoms and treatment with amelioration, J. Biol. Syst., 14, 3, 323-355 (2006) · Zbl 1116.92042 |
| [23] | Mukandavire, Z.; Chiyaka, C.; Garira, W., Asymptotic properties of an HIV/AIDS model with a time delay, J. Math. Anal. Appl., 330, 2, 916-933 (2007) · Zbl 1110.92043 |
| [24] | Hsu Schmitz, S. F., A mathematical model of HIV transmission in homosexuals with genetic heterogeneity, J. Theor. Med., 2, 285-296 (2000) · Zbl 0962.92035 |
| [25] | Hyman, J. M.; Stanley, E. A., Using mathematical models to understand the AIDS epidemic, Math. Biosci., 90, 415-473 (1998) · Zbl 0727.92025 |
| [26] | Birkhoff, G.; Rota, G. C., Ordinary Differential Equations (1982), Ginn · Zbl 0183.35601 |
| [27] | Nagumo, M., Uber die Lage der Integralkurven gewonlicher Differentialgleichungen, Proc. Phys. Math. Soc. Jpn., 24, 551-559 (1942) · Zbl 0061.17204 |
| [28] | LaSalle, J. P., The Stability of Dynamical Systems, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 25 (1976), SIAM: SIAM Philadelphia · Zbl 0364.93002 |
| [29] | Diekmann, O.; Heesterbeek, J. A.P.; Metz, J. A.P., On the definition and computation of the basic reproduction ratio \(R_0\) in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28, 365-382 (1990) · Zbl 0726.92018 |
| [30] | van den Driessche, P.; Watmough, J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180, 29-48 (2002) · Zbl 1015.92036 |
| [31] | Ross, R., The Prevention of Malaria (1911), John Murray: John Murray London |
| [32] | Kermack, W. O.; McKendrick, A. G., Contributions to the mathematical theory of epidemics-I, Proc. Roy. Soc., 115A, 700-721 (1927), (reprint in Bull. Math. Biol. 53(1/2) (1991) 33-55) · JFM 53.0517.01 |
| [33] | Arino, J.; Cooke, K. L.; van den Driessche, P.; Velasco-Hernández, J., An epidemiology model that includes a leaky vaccine with general waning function, Discrete Contin. Dyn. Syst., 4, 479-495 (2004) · Zbl 1040.92035 |
| [34] | Kribs-Zaleta, C. M.; Velasco-Hernández, J. X., A simple vaccination model with multiple endemic states, Math. Biosci., 164, 183-201 (2000) · Zbl 0954.92023 |
| [35] | Dushoff, J.; Huang, W.; Castillo-Chavez, C., Backwards bifurcations and catastrophe in simple models of fatal diseases, J. Math. Biol., 36, 227-248 (1998) · Zbl 0917.92022 |
| [36] | Alexander, M. E.; Bowman, C.; Moghadas, S. M.; Summers, R.; Gumel, A. B.; Sahai, B. M., A vaccination model for transmission dynamics of influenza, SIAM J. Appl. Dyn. Syst., 3, 4, 503-524 (2004) · Zbl 1067.92051 |
| [37] | Korobeinikov, A.; Maini, P. K., A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence, Math. Biosci. Eng., 1, 1, 57-60 (2004) · Zbl 1062.92061 |
| [38] | Barbalat, I., Système d’équation différentielle d’Oscillation Nonlinéaires, Rev. Roum. Math. Pure. Appl., 4, 267-270 (1959) · Zbl 0090.06601 |
| [39] | Hofbauer, J.; So, J. W.H., Uniform persistence and repellors for maps, Proc. Am. Math. Soc., 107, 1137-1142 (1989) · Zbl 0678.58024 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
