2015, 2015(special): 569-578. doi: 10.3934/proc.2015.0569

Modeling HIV: Determining the factors affecting the racial disparity in the prevalence of infected women

1. 

Department of Mathematics, Howard University, Washington, DC 20059, United States

2. 

Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, MD 21250, United States, United States

Received  September 2014 Revised  March 2015 Published  November 2015

We present a mathematical model of the transmission of HIV through sexual contact in a population stratified by sexual behavior and by race/ethnicity. We consider two theories for the disproportionate prevalence of HIV in the population of African American women and Hispanic/Latino women compared with U.S. women of other races/ethnicities. First, we consider that minority women are being adversely affected by incurable STDs due to the non-disclosure of risky homosexual activities of their male sex partners. Second, we consider the effect of sexual network factors, such as the racially homophilic networks through the use of a partnership mixing matrix. Both analytic and numerical results indicate that the effect of the down low population on the disproportionate spread of HIV in women is small compared to the effect of homophilic racial mixing.
Citation: K.F. Gurski, K.A. Hoffman, E.K. Thomas. Modeling HIV: Determining the factors affecting the racial disparity in the prevalence of infected women. Conference Publications, 2015, 2015 (special) : 569-578. doi: 10.3934/proc.2015.0569
References:
[1]

, CDC FAST STATS,, , (). Google Scholar

[2]

U.L. Abbas, R. Glaubius, A. Mubayi, G. Hood and J.W. Mellors., Antiretroviral therapy and pre-exposure prophylaxis: combined impact on HIV transmission and drug resistance in South Africa,, Journal of Infectious Diseases, 208 (2013), 224. Google Scholar

[3]

R. M. Anderson and R. M. May., Infectious Diseases of Humans,, Oxford Science Publications, (1991). Google Scholar

[4]

C. Castillo-Chávez., Mathematical and Statistical Approaches to AIDS Epidemiology,, Lecture Notes in Biomathematics, (1989). Google Scholar

[5]

D. D. Celentano, F. Sifakis, J. Hylton, L. V. Torian, V. Guillin and B. A. Koblin., Race/ethnic differences in HIV prevalence and risks among adolescent and young adult men who have sex with men,, Journal of Urban Health: Bulletin of the New York Academy of Medicine, 82 (2005), 610. Google Scholar

[6]

Centers for Disease Control and Prevention., HIV transmission among black college student and non-student men who have sex with men - North Carolina, 2003,, Morbidity Mortality Weekly Report, 53 (2004), 731. Google Scholar

[7]

Centers for Disease Control and Prevention., HIV/AIDS surveillance report, 2005,, Technical report, 17 (2007). Google Scholar

[8]

Centers for Disease Control and Prevention., HIV surveillance supplemental report, 2010,, Technical report, 17 (2012). Google Scholar

[9]

Centers for Disease Control and Prevention., HIV surveillance supplemental report, 2010,, Technical report, 18 (2013). Google Scholar

[10]

J. P. Gabriel, C. Lefevre and C. Picard., Stochastic Processes in Epidemic Theory,, Lecture Notes in Biomathematics, (1990). Google Scholar

[11]

G.P. Garnett and R.P. Anderson., Balancing sexual partners in an age and activity stratified model of HIV transmission in heterosexual populations,, IMA Journal of Mathematics Applied in Medicine and Biology, 11 (1994), 161. Google Scholar

[12]

J. M. Hyman, J. Li and E. A. Stanley., The differential infectivity and staged progression models for the transmission of HIV,, Mathematical Biosciences, 155 (1999), 77. Google Scholar

[13]

K.P. Hadeler and C. Castillo-Chávez., A core group model for disease transmission,, Mathematical Biosciences, 128 (1995), 41. Google Scholar

[14]

D.J. Malebranche., Bisexually active black men in the United States and HIV: Acknowledging more than the "Down Low",, Archives of Sexual Behavior, 37 (2008), 810. Google Scholar

[15]

M. May, M. Gompels, V. Delpech, K Porter, F Poct, M Johnson, D Dinn, A Palfreeman, R Gilson, B Gazzard, T Hill, J Walsh, M Fisher, C Orkin, J Ainsworth, L Bansi, A Phillips, C Leen, M Nelson, J Anderson and C Sabin., Impact of late diagnosis and treatment on life expectancy in people with HIV-1: UK Collaborative HIV Cohort (UK CHIC) Study,, BMJ, (2011), 343. Google Scholar

[16]

W.D. Mosher, A. Chandra and J. Jones., Sexual behavior and selected health measures: men and women 15-44 years of age, United States, 2002,, Adv. Data., 362 (2005), 1. Google Scholar

[17]

Z. Mukandavire and W. Garira., Age and sex structured model for assessing the demographic impact of mother-to-child transmission of HIV/AIDS,, Bulletin of Mathematical Biology, 69 (2007), 2061. Google Scholar

[18]

F. Nakagawa, R.K. Lodwick, C.J. Smith, R. SSmith, V. Cambiano, J.D. Lundgren, V. Delpech and A.N. Phillips., Projected life expectancy of people with HIV according to timing of diagnosis,, AIDS, 26 (2012), 335. Google Scholar

[19]

M.E. Newcomb and B Mustanski., Racial differences in same-race partnering and the effects of sexual partnership characteristics on HIV risk in MSM: A prospective sexual diary study,, Acquir Immune Defic Syndr., 62 (2013), 329. Google Scholar

[20]

P.L. Patel, C.B. Borkowf, A Lasry, A. Lansky and J. Mermin., Estimating per-act HIV transmission risk: a systematic review,, AIDS, 10 (2014), 1509. Google Scholar

[21]

S.D. Pinkerton and P.R. Abramson., Effectiveness of condoms in preventing HIV transmission,, Soc Sci Med., 44 (1997), 1303. Google Scholar

[22]

B. Rapatski and J. Yorke., Modeling HIV outbreaks: the male to female prevalence ratio in the core population,, Mathematical Biosciences and Engineering, 6 (2009), 135. Google Scholar

[23]

T.G.M Sandfort and B. Dodge., ...And then there was the down low: Introduction to Black and Latino male bisexualities,, Archives of Sexual Behavior, 37 (2008), 675. Google Scholar

[24]

Z. Shuai, J.A.P. Heesterbeek and P. van den Driessche., Erratum to: "Extending the type reproduction number to infectious disease control targeting contacts between types'',, Journal of Mathematical Biology, 71 (2015), 255. Google Scholar

[25]

Z. Shuai, J.A.P. Heesterbeek and P. van den Driessche., Extending the type reproduction number to infectious disease control targeting contacts between types,, Journal of Mathematical Biology, 67 (2013), 1067. Google Scholar

[26]

E.K. Thomas, K.F. Gurski and K.A. Hoffman., Analysis of SI Models with multiple interacting populations using subpopulations,, Mathematical Biosciences and Engineering, 12 (2015), 135. Google Scholar

[27]

C.O. Uche and R. M. Anderson., Mixing matrices: Necessary constraints in populations of finite size,, IMA Journal of Mathematics Applied in Medicine and Biology, 13 (1996), 23. Google Scholar

[28]

U.S. Census Bureau., 2000 census of population and housing, summary file 1,, Technical report (2001)., (2001). Google Scholar

[29]

U.S. Census Bureau., 2010 census of population and housing, summary file 1,, Technical report, (2011). Google Scholar

[30]

A. Van Sighem, L. Gras, P. Reiss, K. Brinkman, F. de Wolf and ATHENA national observational cohort study., Life expectancy of recently diagnosed asymptomatic HIV-infected patients approaches that of uninfected individuals,, AIDS, 24 (2010), 1527. Google Scholar

show all references

References:
[1]

, CDC FAST STATS,, , (). Google Scholar

[2]

U.L. Abbas, R. Glaubius, A. Mubayi, G. Hood and J.W. Mellors., Antiretroviral therapy and pre-exposure prophylaxis: combined impact on HIV transmission and drug resistance in South Africa,, Journal of Infectious Diseases, 208 (2013), 224. Google Scholar

[3]

R. M. Anderson and R. M. May., Infectious Diseases of Humans,, Oxford Science Publications, (1991). Google Scholar

[4]

C. Castillo-Chávez., Mathematical and Statistical Approaches to AIDS Epidemiology,, Lecture Notes in Biomathematics, (1989). Google Scholar

[5]

D. D. Celentano, F. Sifakis, J. Hylton, L. V. Torian, V. Guillin and B. A. Koblin., Race/ethnic differences in HIV prevalence and risks among adolescent and young adult men who have sex with men,, Journal of Urban Health: Bulletin of the New York Academy of Medicine, 82 (2005), 610. Google Scholar

[6]

Centers for Disease Control and Prevention., HIV transmission among black college student and non-student men who have sex with men - North Carolina, 2003,, Morbidity Mortality Weekly Report, 53 (2004), 731. Google Scholar

[7]

Centers for Disease Control and Prevention., HIV/AIDS surveillance report, 2005,, Technical report, 17 (2007). Google Scholar

[8]

Centers for Disease Control and Prevention., HIV surveillance supplemental report, 2010,, Technical report, 17 (2012). Google Scholar

[9]

Centers for Disease Control and Prevention., HIV surveillance supplemental report, 2010,, Technical report, 18 (2013). Google Scholar

[10]

J. P. Gabriel, C. Lefevre and C. Picard., Stochastic Processes in Epidemic Theory,, Lecture Notes in Biomathematics, (1990). Google Scholar

[11]

G.P. Garnett and R.P. Anderson., Balancing sexual partners in an age and activity stratified model of HIV transmission in heterosexual populations,, IMA Journal of Mathematics Applied in Medicine and Biology, 11 (1994), 161. Google Scholar

[12]

J. M. Hyman, J. Li and E. A. Stanley., The differential infectivity and staged progression models for the transmission of HIV,, Mathematical Biosciences, 155 (1999), 77. Google Scholar

[13]

K.P. Hadeler and C. Castillo-Chávez., A core group model for disease transmission,, Mathematical Biosciences, 128 (1995), 41. Google Scholar

[14]

D.J. Malebranche., Bisexually active black men in the United States and HIV: Acknowledging more than the "Down Low",, Archives of Sexual Behavior, 37 (2008), 810. Google Scholar

[15]

M. May, M. Gompels, V. Delpech, K Porter, F Poct, M Johnson, D Dinn, A Palfreeman, R Gilson, B Gazzard, T Hill, J Walsh, M Fisher, C Orkin, J Ainsworth, L Bansi, A Phillips, C Leen, M Nelson, J Anderson and C Sabin., Impact of late diagnosis and treatment on life expectancy in people with HIV-1: UK Collaborative HIV Cohort (UK CHIC) Study,, BMJ, (2011), 343. Google Scholar

[16]

W.D. Mosher, A. Chandra and J. Jones., Sexual behavior and selected health measures: men and women 15-44 years of age, United States, 2002,, Adv. Data., 362 (2005), 1. Google Scholar

[17]

Z. Mukandavire and W. Garira., Age and sex structured model for assessing the demographic impact of mother-to-child transmission of HIV/AIDS,, Bulletin of Mathematical Biology, 69 (2007), 2061. Google Scholar

[18]

F. Nakagawa, R.K. Lodwick, C.J. Smith, R. SSmith, V. Cambiano, J.D. Lundgren, V. Delpech and A.N. Phillips., Projected life expectancy of people with HIV according to timing of diagnosis,, AIDS, 26 (2012), 335. Google Scholar

[19]

M.E. Newcomb and B Mustanski., Racial differences in same-race partnering and the effects of sexual partnership characteristics on HIV risk in MSM: A prospective sexual diary study,, Acquir Immune Defic Syndr., 62 (2013), 329. Google Scholar

[20]

P.L. Patel, C.B. Borkowf, A Lasry, A. Lansky and J. Mermin., Estimating per-act HIV transmission risk: a systematic review,, AIDS, 10 (2014), 1509. Google Scholar

[21]

S.D. Pinkerton and P.R. Abramson., Effectiveness of condoms in preventing HIV transmission,, Soc Sci Med., 44 (1997), 1303. Google Scholar

[22]

B. Rapatski and J. Yorke., Modeling HIV outbreaks: the male to female prevalence ratio in the core population,, Mathematical Biosciences and Engineering, 6 (2009), 135. Google Scholar

[23]

T.G.M Sandfort and B. Dodge., ...And then there was the down low: Introduction to Black and Latino male bisexualities,, Archives of Sexual Behavior, 37 (2008), 675. Google Scholar

[24]

Z. Shuai, J.A.P. Heesterbeek and P. van den Driessche., Erratum to: "Extending the type reproduction number to infectious disease control targeting contacts between types'',, Journal of Mathematical Biology, 71 (2015), 255. Google Scholar

[25]

Z. Shuai, J.A.P. Heesterbeek and P. van den Driessche., Extending the type reproduction number to infectious disease control targeting contacts between types,, Journal of Mathematical Biology, 67 (2013), 1067. Google Scholar

[26]

E.K. Thomas, K.F. Gurski and K.A. Hoffman., Analysis of SI Models with multiple interacting populations using subpopulations,, Mathematical Biosciences and Engineering, 12 (2015), 135. Google Scholar

[27]

C.O. Uche and R. M. Anderson., Mixing matrices: Necessary constraints in populations of finite size,, IMA Journal of Mathematics Applied in Medicine and Biology, 13 (1996), 23. Google Scholar

[28]

U.S. Census Bureau., 2000 census of population and housing, summary file 1,, Technical report (2001)., (2001). Google Scholar

[29]

U.S. Census Bureau., 2010 census of population and housing, summary file 1,, Technical report, (2011). Google Scholar

[30]

A. Van Sighem, L. Gras, P. Reiss, K. Brinkman, F. de Wolf and ATHENA national observational cohort study., Life expectancy of recently diagnosed asymptomatic HIV-infected patients approaches that of uninfected individuals,, AIDS, 24 (2010), 1527. Google Scholar

[1]

Nicolas Bacaër, Xamxinur Abdurahman, Jianli Ye, Pierre Auger. On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China. Mathematical Biosciences & Engineering, 2007, 4 (4) : 595-607. doi: 10.3934/mbe.2007.4.595

[2]

Helen Moore, Weiqing Gu. A mathematical model for treatment-resistant mutations of HIV. Mathematical Biosciences & Engineering, 2005, 2 (2) : 363-380. doi: 10.3934/mbe.2005.2.363

[3]

Zindoga Mukandavire, Abba B. Gumel, Winston Garira, Jean Michel Tchuenche. Mathematical analysis of a model for HIV-malaria co-infection. Mathematical Biosciences & Engineering, 2009, 6 (2) : 333-362. doi: 10.3934/mbe.2009.6.333

[4]

Xinyue Fan, Claude-Michel Brauner, Linda Wittkop. Mathematical analysis of a HIV model with quadratic logistic growth term. Discrete & Continuous Dynamical Systems - B, 2012, 17 (7) : 2359-2385. doi: 10.3934/dcdsb.2012.17.2359

[5]

Shingo Iwami, Shinji Nakaoka, Yasuhiro Takeuchi. Mathematical analysis of a HIV model with frequency dependence and viral diversity. Mathematical Biosciences & Engineering, 2008, 5 (3) : 457-476. doi: 10.3934/mbe.2008.5.457

[6]

Tyson Loudon, Stephen Pankavich. Mathematical analysis and dynamic active subspaces for a long term model of HIV. Mathematical Biosciences & Engineering, 2017, 14 (3) : 709-733. doi: 10.3934/mbe.2017040

[7]

Victor Fabian Morales-Delgado, José Francisco Gómez-Aguilar, Marco Antonio Taneco-Hernández. Mathematical modeling approach to the fractional Bergman's model. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 805-821. doi: 10.3934/dcdss.2020046

[8]

Arni S. R. Srinivasa Rao, Kurien Thomas, Kurapati Sudhakar, Philip K. Maini. HIV/AIDS epidemic in India and predicting the impact of the national response: Mathematical modeling and analysis. Mathematical Biosciences & Engineering, 2009, 6 (4) : 779-813. doi: 10.3934/mbe.2009.6.779

[9]

Tom Burr, Gerardo Chowell. The reproduction number $R_t$ in structured and nonstructured populations. Mathematical Biosciences & Engineering, 2009, 6 (2) : 239-259. doi: 10.3934/mbe.2009.6.239

[10]

Hui Cao, Yicang Zhou. The basic reproduction number of discrete SIR and SEIS models with periodic parameters. Discrete & Continuous Dynamical Systems - B, 2013, 18 (1) : 37-56. doi: 10.3934/dcdsb.2013.18.37

[11]

Svend Christensen, Preben Klarskov Hansen, Guozheng Qi, Jihuai Wang. The mathematical method of studying the reproduction structure of weeds and its application to Bromus sterilis. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 777-788. doi: 10.3934/dcdsb.2004.4.777

[12]

Nirav Dalal, David Greenhalgh, Xuerong Mao. Mathematical modelling of internal HIV dynamics. Discrete & Continuous Dynamical Systems - B, 2009, 12 (2) : 305-321. doi: 10.3934/dcdsb.2009.12.305

[13]

Tinevimbo Shiri, Winston Garira, Senelani D. Musekwa. A two-strain HIV-1 mathematical model to assess the effects of chemotherapy on disease parameters. Mathematical Biosciences & Engineering, 2005, 2 (4) : 811-832. doi: 10.3934/mbe.2005.2.811

[14]

Hee-Dae Kwon, Jeehyun Lee, Myoungho Yoon. An age-structured model with immune response of HIV infection: Modeling and optimal control approach. Discrete & Continuous Dynamical Systems - B, 2014, 19 (1) : 153-172. doi: 10.3934/dcdsb.2014.19.153

[15]

Ling Xue, Caterina Scoglio. Network-level reproduction number and extinction threshold for vector-borne diseases. Mathematical Biosciences & Engineering, 2015, 12 (3) : 565-584. doi: 10.3934/mbe.2015.12.565

[16]

Gerardo Chowell, Catherine E. Ammon, Nicolas W. Hengartner, James M. Hyman. Estimating the reproduction number from the initial phase of the Spanish flu pandemic waves in Geneva, Switzerland. Mathematical Biosciences & Engineering, 2007, 4 (3) : 457-470. doi: 10.3934/mbe.2007.4.457

[17]

Avner Friedman, Wenrui Hao. Mathematical modeling of liver fibrosis. Mathematical Biosciences & Engineering, 2017, 14 (1) : 143-164. doi: 10.3934/mbe.2017010

[18]

Lih-Ing W. Roeger, Z. Feng, Carlos Castillo-Chávez. Modeling TB and HIV co-infections. Mathematical Biosciences & Engineering, 2009, 6 (4) : 815-837. doi: 10.3934/mbe.2009.6.815

[19]

H. T. Banks, Robert Baraldi, Karissa Cross, Kevin Flores, Christina McChesney, Laura Poag, Emma Thorpe. Uncertainty quantification in modeling HIV viral mechanics. Mathematical Biosciences & Engineering, 2015, 12 (5) : 937-964. doi: 10.3934/mbe.2015.12.937

[20]

Hem Joshi, Suzanne Lenhart, Kendra Albright, Kevin Gipson. Modeling the effect of information campaigns on the HIV epidemic in Uganda. Mathematical Biosciences & Engineering, 2008, 5 (4) : 757-770. doi: 10.3934/mbe.2008.5.757

 Impact Factor: 

Metrics

  • PDF downloads (11)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]