Incubation periods under various anti-retroviral therapies in homogeneous mixing and age-structured dynamical models: a theoretical approach. (English) Zbl 1350.92027
Summary: With the launch of second line anti-retroviral therapy for HIV infected individuals, there has been an increased expectation of survival period for people with HIV. We consider previously well-known models in HIV epidemiology where the parameter for the incubation period is used as one of the important components to explain the dynamics of the variables. Such models are extended here to explain the dynamics with respect to a given therapy that prolongs the life of an HIV infected individual. A deconvolution method is demonstrated for estimation of parameters in the situations when no-therapy and multiple therapies are given to the infected population. The models and deconvolution method are extended in order to study the impact of therapy in age-structured populations. A generalization for a situation when \(n\)-types of therapies are available is given. Models are demonstrated using hypothetical data, and sensitivity of the parameters is also computed.
MSC:
| 92C50 | Medical applications (general) |
| 92C60 | Medical epidemiology |
| 44A35 | Convolution as an integral transform |
References:
| [1] | O.O. Aalen, V.T. Farewell, D. De Angelis, N.E. Day and O.N. Gill, New therapy explains the fall in AIDS incidence with a substantial rise in number of persons on treatment expected , AIDS 13 (1999), 103-108. |
| [2] | R.M. Anderson, The epidemiology of HIV infection : Variable incubation plus infectious periods and heterogeneity in sexual activity , J. Roy. Stat. Soc. 151 (1988), 66-98. · Zbl 1159.92313 · doi:10.2307/2982185 |
| [3] | R.M. Anderson and R.M. May, Infectious diseases of humans , Dyn. Contr., Oxford University Press, 1991. |
| [4] | M.A. Artzrouni, \((1992)\) Modeled time-varying density function for the incubation period of AIDS, J. Math. Biol. 31 (1992), 73-99. · Zbl 0759.92008 · doi:10.1007/BF00163843 |
| [5] | —-, Back-calculation and projection of the HIV/AIDS epidemic among homosexual/bisexual men in three European countries : Evalution of past projections and updates allowing for treatment effects , Europ. J Epidem. 19 (2004), 171-179. |
| [6] | N.G. Becker, J.J.C. Lewis, Z.F. Li, et al., Age-specific back-projection of HIV diagnosis data statistics in medicine , 22 (2003), 2177-2190. |
| [7] | J.T. Boerma, et al., Monitoring the scale-up of antiretroviral therapy programmes : Methods to estimate coverage , Bull. WHO 84 (2006), 145-150. |
| [8] | B.A. Boyle, R. Elion, C.J. Cohen, E. DeJesus, T. Hawkins and G.J. Moyle, Advances in HIV therapeutics : News from the \(4\)th International AIDS Society Conference , AIDS Read. 17 (2007), 484-490. |
| [9] | R. Brookmeyer and M.H. Gail, AIDS epidemiology, A quantitative approach , Oxford University Press, New York, 1994. |
| [10] | —-, A method for obtaining short-term projections and lower bounds on the size of the AIDS epidemic , J. Amer. Stat. Assoc. 83 (1988), 301-308. · Zbl 0644.62108 · doi:10.2307/2288844 |
| [11] | C. Castillo-Chavez, Mathematical and statistical approaches to AIDS epidemiology , C. Castillo-Chavez, ed., Lect. Notes Biomath. 83 , Springer-Verlag, Berlin, 1989. · Zbl 0682.00023 |
| [12] | C. Castillo-Chavez, K. Cooke, W. Huang and S.A. Levin, On the role of long incubation periods in the dynamics of acquired immunodeficiency syndrome (AIDS), I, Single population models , J. Math. Biol. 27 (1989), 373-398. · Zbl 0715.92029 · doi:10.1007/BF00290636 |
| [13] | M.S. Cohen, Y.Q. Chen, M. McCauley, et al., Prevention of HIV-\(1\) infection with early antiretroviral therapy , New Eng. J Med. 365 (2011), 493-505. |
| [14] | S. Conti, M. Masocco, P. Pezzotti, et al., Differential impact of combined antiretroviral therapy on the survival of Italian patients with specific AIDS-defining illnesses , J. Acquir. Immun. Defic. Synd. 25 (2000), 451-458. |
| [15] | B. Eng, K.P. Cain, K. Nong, V. Chhum, E. Sin, S. Roeun, S. Kim, S. Keo, T.A. Heller and J.K. Varma, Impact of a public antiretroviral program on TB/HIV mortality : Banteay Meanchey, Cambodia , Southeast Asian J. Trop Med Public Health 40 (2009), 89-92. |
| [16] | J.E. Golub, V. Saraceni, S.C. Cavalcante, A.G. Pacheco, L.H. Moulton, B.S. King, A. Efron, R.D. Moore, R.E. Chaisson and B. Durovni, The impact of antiretroviral therapy and isoniazid preventive therapy on tuberculosis incidence in HIV-infected patients in Rio de Janeiro , Brazil. AIDS. 21 (2007), 1441-1448. |
| [17] | R. Gray, V. Ssempiija, J. Shelton, D. Serwadda, F. Nalugoda, J. Kagaayi, G. Kigozi and MJ Wawer, The contribution of HIV-discordant relationships to new HIV infections in Rakai, Uganda , AIDS, 2/14/2011. |
| [18] | J. Griffiths, D. Lowrie and J. Williams, An age-structured model for the AIDS epidemic , Europ. J. Oper. Res. 124 (2000), 1-14. · Zbl 0955.92032 · doi:10.1016/S0377-2217(99)00288-X |
| [19] | T.B. Hallett, S. Gregson, S. Dube and G.P. Garnett, The impact of monitoring HIV patients prior to treatment in resource-poor settings : Insights from mathematical modelling , PLoS Med. 5 (2008), e53. |
| [20] | C.C. Hung, M.Y. Chen, C.F. Hsiao, S.M. Hsieh, W.H. Sheng and S.C. Chang, Improved outcomes of HIV-1- infected adults with tuberculosis in the era of highly active antiretroviral therapy , AIDS 17 (2003), 2615-2622. |
| [21] | N. Joglekar, R. Paranjape, R. Jain, et al., Barriers to ART adherence & follow ups among patients attending ART centres in Maharashtra, India , Indian J. Med. Res. 134 (2011), 954-959. |
| [22] | J.A. Johnson, J.F. Li, X. Wei, J. Lipscomb, D. Irlbeck, C. Craig, A. Smith, D.E. Bennett, M. Monsour, P. Sandstrom, E.R. Lanier and W. Heneine, 219 Minority HIV-1 drug resistance mutations are present in antiretroviral treatment-naïve populations and associate with reduced treatment efficacy , PLoS Med. 5 (2008), e158. |
| [23] | M. Kakehashi, A mathematical analysis of the spread of HIV/AIDS in Japan , IMA J. Math. Appl. Med. 15 (1998), 299-311. · Zbl 0912.92028 |
| [24] | B.A. Larson, M.P. Fox, S. Rosen, M. Bii, C. Sigei, D. Shaffer, F. Sawe, M. Wasunna and J.L. Simon, 251 early effects of antiretroviral therapy on work performance : Preliminary results from a cohort study of Kenyan agricultural workers , AIDS 22 (208), 421-425. |
| [25] | M. Mahy, J. Stover, K. Stanecki, R. Stoneburner and J.M. Tassie, Estimating the impact of antiretroviral therapy : Regional and global estimates of life-years gained among adults , Sex Trans. Infect. 86 (2010), Suppl 2:ii67-71. |
| [26] | R.M. May, R.M. Anderson and A.R. McLean, Possible demographic consequences of HIV/AIDS epidemics , I, Assuming HIV infection always leads to AIDS, Math. Biosci. 90 (1988), 475-505. · Zbl 0673.92008 · doi:10.1016/0025-5564(88)90079-X |
| [27] | Monitoring of Antiretroviral Therapy in Resource \textendash limited settings: Discussion , http://www.medscape.com/viewarticle/726673_4. |
| [28] | Y. Mouton, S. Alfandari, M. Valette, et al., Impact of protease inhibitors on AIDS-defining events and hospitalizations in \(10\) French AIDS reference centres , AIDS 11 (1997), F101-F105. |
| [29] | M.J. Mugavero, B.W. Pence, K. Whetten, J. Leserman, M. Swartz D. Stangl and N.M. Thielman, Predictors of AIDS-related morbidity and mortality in a southern U.S. cohort , AIDS Patient Care STDS 21 (2007), 681-690. |
| [30] | M.A. Nowak and R.M. May, Virus dynamics , Oxford University Press, Oxford, 2000. · Zbl 1101.92028 |
| [31] | M. Over, E. Marseille, K. Sudhakar, J. Gold, I. Gupta, A. Indrayan, S.K. Hira, N. Nagelkerke, A.S.R.S. Rao and P. Heywood, Antiretroviral therapy and HIV prevention in India : Modeling costs and consequences of policy options , Sex Trans. Dis. 33 (2006) (10 Suppl), S145-52. |
| [32] | A.S. Perelson and P.W. Nelson, Mathematical analysis of HIV-1 dynamics in vivo , SIAM Rev. 41 (1999), 3-44. · Zbl 1078.92502 · doi:10.1137/S0036144598335107 |
| [33] | Press Information Bureau, Ministry of Health and Family Welfare, government of India, http://pib.nic.in/newsite/ PrintRelease.aspx?relid=89785. |
| [34] | C. Pretorius, J. Stover, L. Bollinger, N. Bacaër, B. Williams, Evaluating the cost-effectiveness of pre-exposure prophylaxis \((\)PrEP\()\) and its impact on HIV-1 transmission in South Africa , PLoS One. 5 (2010):e13646. |
| [35] | N. Rajagopalan, J.B. Suchitra, A. Shet, Z.K. Khan, J. Martin-Garcia, M.R. Nonnemacher, J.M. Jacobson and B. Wigdahl, Mortality among HIV-Infected patients in resource limited settings : A case controlled analysis of inpatients at a community care center , Amer. J Infect. Dis. 5 (2009), 219-224. |
| [36] | A.S.R.S. Rao, S. Basu, A. Basu and J.K. Ghosh, Parametric models for incubation distribution in presence of left and right censoring , Indian J. Pure Appl. Math. 36 (2005), 371-384. · Zbl 1092.62120 |
| [37] | A.S.R.S. Rao and M. Kakehashi, A combination of differential equations and convolution in understanding the spread of an epidemic , Sadhana - Proc. Ind. Acad. Sci. Eng. 29 (2004), 305-313. · Zbl 1076.92019 · doi:10.1007/BF02703780 |
| [38] | —-, Incubation time distribution in back-calculation applied to HIV/AIDS data in India , Math. Biosci. Eng. 2 (2005), 263-277. · Zbl 1071.62108 · doi:10.3934/mbe.2005.2.263 |
| [39] | Arni S.R. Srinivasa Rao and S.K.I. Hira, Evidence of shorter incubation period of HIV-1 in Mumbai, India , Inter. J. STD AIDS 14 (2003), 499-503. |
| [40] | Arni S.R. Srinivasa Rao, Kurien Thomas, Kurapati Sudhakar and Ramesh Bhat, Improvement in survival of people living with HIV/AIDs and requirement for \(1\)st- and \(2\)nd-line ART in India : A mathematical model , Not. Amer. Math. Soc. 59 (2012), 560-562. · Zbl 1277.92026 |
| [41] | Arni S.R. Srinivasa Rao, Kurien Thomas, Kurapati Sudhakar and Philip K. Maini, HIV/AIDS epidemic in India and predicting the impact of the national response: mathematical modeling and analysis , Math. Biosci. Eng. 6 (2009), 779-813. · Zbl 1178.92048 · doi:10.3934/mbe.2009.6.779 |
| [42] | S.J. Reynolds, F. Makumbi, G. Nakigozi, J. Kagaayi, R.H. Gray, M. Wawer, T.C. Quinn and D. Serwadda, HIV-1 transmission among HIV-1 discordant couples before and after the introduction of antiretroviral therapy , AIDS 25 (2011), 473-477. |
| [43] | Libin Rong, Zhilan Feng and Alan S. Perelson, Emergence of HIV-\(1\) drug resistance during antiretroviral treatment , Bull. Math. Biol. 69 (2007), 2027-2060. · Zbl 1298.92053 · doi:10.1007/s11538-007-9203-3 |
| [44] | —-, Mathematical analysis of age-structured HIV-1 dynamics with combination antiretroviral therapy , SIAM J. Appl. Math. 67 (2007), 731-756. · Zbl 1121.92043 · doi:10.1137/060663945 |
| [45] | J.A. Salomon and D.R. Hogan, Evaluating the impact of antiretroviral therapy on HIV transmission , AIDS (2008), Suppl 1:S149-59. |
| [46] | L.A. Shafer, R.N. Nsubuga, R. White, B.N. Mayanja, R. Chapman, K. O’brien, L. Van der Paal, H. Grosskurth and D. Maher, Antiretroviral therapy and sexual behavior in Uganda : A cohort study , AIDS 25 (2011), 671-678. |
| [47] | M. Simcock, M. Blasko, U. Karrer, et al., Treatment and prognosis of AIDS-related lymphoma in the era of highly active antiretroviral therapy : Findings from the Swiss HIV cohort study , Antiv Ther. 12 (2007), 931-939. |
| [48] | P. Srikantiah, M. Ghidinelli, D. Bachani, et al., Scale-up of national antiretroviral therapy programs : Progress and challenges in the Asia Pacific region , AIDS 24 (2010), Supplement: S62-S71. |
| [49] | J. Stover, N. Walker, N.C. Grasslyand and M. Marston, Projecting the demographic impact of AIDS and the number of people in need of treatment : Updates to the Spectrum projection package , Sex Trans. Infect. 82 (2006), Suppl 3:iii45-50. |
| [50] | H. Thirumurthy, A. Jafri, G. Srinivas, V. Arumugam, R.M. Saravanan, S.K. Angappan, M. Ponnusamy, S. Raghavan, M. Merson and S. Kallolikar, Two-year impacts on employment and income among adults receiving antiretroviral therapy in Tamil Nadu, India : A cohort study , AIDS 25 (2011), 239-246. |
| [51] | United Nations, Department of Economic and Social Affairs, Population Division (2006), World population prospects : The \(2007\) revision s. |
| [52] | J. Weber, R. Tatoud and S. Fidler, Postexposure prophylaxis, preexposure prophylaxis or universal test and treat : The strategic use of antiretroviral drugs to prevent HIV acquisition and transmission , AIDS 24 (2010), Suppl 4:S27-39. |
| [53] | X.P. Wei, S.K. Ghosh, M.E. Taylor, et al., Viral dynamics in human-immunodeficiency-virus type-\(1\) infection , Nature 373 (1995), 117-122. |
| [54] | WHO, Antiretroviral therapy for HIV infection in adults and adolescents: recommendations for a public health approach , 2010 rev. |
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.
