Table : Model Summary Year Population Subpopulation Composition Intervention Method Partnership Formation Outcome of Interest Validity 200014 Heterosexual No real world data Commercial sex workers, unpartnered males (bridge population), non-core group females and long-term unbreakable couples; HIV status: susceptible and infective. No programs, program only for core group, only available for bridge group Ordinary differential equations(ODE); Analytical solution and numerical examples All unpartnered males could only form the sexual partnership with CSW or get married. No concurrent partnership. HIV prevalence under different intervention scenarios; mathematical equilibrium Strength: assess the effects of intervention on different target subgroups; sensitivity analysis Limitation: all single males were assumed to only have sexual contacts with FSW, no specific intervention proposed 20011 Homosexual San Francisco, USA Risk level which is distinguished by the risk of getting disease (sexual activity and safe sex); HIV status: susceptible, infective Condom Integro-differential equations analytical and numerical solution Proportionate AIDS/HIV incidence S: Performed sensitivity analysis L: proportionate mixing assumption, when assortative mixing is a more realistic assumption 20039 Heterosexual Odessa, Ukraine Male IDUs, female IDUs, male general population and female general population. (considered some IDUs be FSWs); HIV status: susceptible and infective No Proposing the calculation of R0 but not in detail equations has been constructed Proportionate R0 S: assessed the attribution of bridging population, locally unique L: No sensitivity analysis, no intervention implementation, did not specify HIV stages 200310 Homosexual Amsterdam, Netherlands The population is divided into singles and pairs. Paired partners could be both negative, both positive(with the same stage or different stage) and discordant HIV status: susceptible, infected stage 1(more infective) and infected stage2 (less infective); Uncertainty analysis of HAART ODE; solve numerically Proportionate but the nature of the partnership is defined as casual or steady. Men in the steady partnership will have less casual partnerships. Concurrency is not allowed. HIV incidence contributed by steady or casual relationship S: Performed uncertainty analysis L:Neglect types of partnership in between 200411 Early HAART treatment HIV incidence due to early treatment
Table 5 Continued Article Population Structure Intervention Method Partnership Formation Outcome of interest Validity 20063 Heterosexual Uganda, urban Kenya, Zimbabwe and urban Haiti 5 sexual activity groups, gender, age structure HIV status: 5 different disease stages: susceptible, acute infection, latent infection, pre-AIDS and full blown AIDS. No Partial differential equations, with parameters estimated from data; Runge-Kutta Assortative to proportionate HIV prevalence S: Fit the model with different assumptions; L: Not counting on concurrent relationship; No sensitivity analysis (at least not mentioned) 20074 Zimbabwe 1) Reduce mixing. 2) Changes in age at first sex. 3) Changes in condom use HIV prevalence under different intervention scenarios; Lifetime probability of getting HIV 20078 Heterosexual Sub-Saharan Africa Gender, age, sexual activity level, PrEP status, and HIV-1 drug resistance. HIV status: recent, chronic, AIDS. PrEP ODEs, numerical solution Assortative to Proportionate Cumulative HIV incidence averted because of PrEP Effectiveness of intervention/PrEP S:Sensitivity analysis, Considered drug resistant mutation L: did not quantify the accuracy of model prediction; No impact of mixing pattern on PrEP 200718 Heterosexual Yunnan, China Sexual activity level which are, males who never have sexual contacts with FSWs (low) and males who have sexual contacts with FSWs; HIV status: susceptible and infective No equations; Analytical solutions based on parameters estimated from data Proportionate R0 S: Include some uncertainty analysis L: one infective stage; Unrealistic assumption; size of sex workers assumed to be static; 200812 Heterosexual No Real World Data By gender by population patches, individual could move between patches on certain rate (Each patch might keep constant population size; with varying population size; or constant mobility.) HIV status: Susceptible, Infected or AIDS Generic control problem. No specific intervention strategies have been applied but consider how to distribute a fixed budget over time. ODES, numerical solution, using cross entropy technique (Monte Carlo method) Contact from one patch to another depending on the HIV prevalence within each patch The control function which represents the amount of budget spent in each population per time unit S: Fitted with different parameters and control strategies, uncertainty analysis. Useful in decision-making L: Not validated by real world data.
Table 5 Continued Year Population Structure Intervention Method Partnership Formation Outcome of Interest Validity 20095 Heterosexual Zimbabwe 3 sexual activity group, gender; HIV status: 5 different disease stages susceptible, acute infection, latent infection, pre-AIDS and full-blown AIDS. Prefixed intervention from the survey: condom use rate, partnership turnover rate. Not testing new intervention strategies Partial differential equations, with parameters, estimated from data Partnerships formed from the two higher risk groups are classified as casual; Others are regular. The mixing pattern is either random or assortative. HIV Strength: Sensitivity analysis, uses the model to see whether behavior existed given the observational prevalence. Limitation: Not considering the duration of relationship and concurrency 200915 Heterosexual Manicaland, Zimbabwe Marital status, age group, sexual activity group (sex worker, casual sex or spousal sex); HIV status: susceptible, primary, incubating, pre-AIDS, full-blown AIDS. Reducing the number of sexual partnerships involving widows. ODEs numerical solution using Runge-Kutta algorithm; Widows prefer or random; widows date within their age groups VS. Older male widows prefer younger women compared to non-widows Predicted case averted (the percentage fewer cases in the intervention compared to baseline) Strength: Locally appropriate, unique target population. Targeted intervention Limitation: No sensitivity analysis, data only available for three years follow-up 200916 Homosexual Shanghai, China Sex-role preference (only top, only bottom or versatile), money boy(male sex workers); HIV status: susceptible and infective HAART; Vaccine ODEs analytical analysis; Disassortative HIV prevalence Strength: Considered vaccine effectiveness Limitation: Did not consider the impact of different HIV stages 201013 Heterosexual Amsterdam, Netherlands By ethnic groups: Africans, Caribbean (countries with high HIV prevalence) and general Dutch people; By gender. 6 subpopulations in total. HIV status: susceptible, acute, chronic, and pre-AIDS. HAART ODE numerical solutions Assortative, proportionate and disassortative are all considered as mixing patterns. Partnerships are formed as the main partnership (steady and long-term) and secondary partnership (casual or concurrent steady partnership). HIV prevalence under different mixing pattern simulation Strength: Model could apply to different countries Limitation: Only considered immigrants and local people in the mixing, neglect the other common characteristics such as age,
Table 5 Continued Year Population Structure Intervention Method Partnership Formation Outcome of Interest Validity 20117 Heterosexual Uganda Population is divided by sexual activity level, defined as the partner turnover rate and age mixing ; HIV state of the population: susceptible, 4 stages HIV without ART; 3 HIV stages with ART and one AIDS state Behavioral (migration, partner turnover, dating) ODEs; Numerical solution Partner mixing could be random, assortative and cross-generational mixing is also considered HIV prevalence contributed by natural disease dynamic Strength: Performed sensitivity analysis Limitation: Only two age groups and fitting only account women dating within or older than 25 years old. 20146 ART and behavioral changes (increasing partner turnover rate as a result of ART introduction) HIV prevalence under intervention 201417 Homosexual Bangalore, India Sex-role preference predominantly top, versatile and predominantly bottom; HIV status: susceptible acute, chronic and pre-AIDS PrEP ODE, numerical solution Maximum assortative, setting plausible (DD maximum assortative while other groups disassortative), proportionate, and disassortative R0/ HIV prevalence Strength: Different types of mixing patterns and targeted intervention were considered Limitation: Did not consider the behavior intervention due to PrEP 20152 Homosexual United Kingdoms Population are divided into 2 age groups (15-34and 35-64) and 2 sexual activity groups: high activity, low activity(¡=1 partners per year); HIV status: HIV progression is divided into 5 stages including ART use stage (by CD4 count) HAART ODEs Monte Carlo filtering method Sexual partnership types: one-off or repeat sexual partnership; assortative, disassortative, proportionate are all assessed in the model; proportionate mixing by disease stages Percentages of each subpopulation contributing to HIV prevalence Strength: Sensitivity analysis was performed Limitation: Uncertain parameterization (the limited availability of data) Highlighted articles were included in addition to the 2011 and 2012 reviews.
25. Anderson RM. Mathematical and statistical studies of the epidemiology of HIV. AIDS. 1989;3(6):333-346. 26. Anderson RM, Medley GF, May RM, Johnson AM. A preliminary study of the transmission dynamics of the human immunodeficiency virus (HIV), the causative agent of AIDS. IMA J Math Appl Med Biol. 1986;3(4):229-263. 27. Bansal S, Grenfell BT, Meyers LA. When individual behaviour matters: homogeneous and network models in epidemiology. J R Soc Interface. 2007;4(16):879-891. 28. Hethcote HW, Van Ark JW. Epidemiological models for heterogeneous populations: proportionate mixing, parameter estimation, and immunization programs. Mathematical Biosciences. 1987;84(1):85-118. 29. Brauer F. Compartmental models in epidemiology. Mathematical epidemiology: Springer; 2008:19-79. 30. Kermack WO, McKendrick AG. A Contribution to the Mathematical Theory of Epidemics. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. 1927;115(772):700-721. 31. Srinivas MN, xe, teille A, xe. 212. Networks in Indian Social Structure. Man. 32. Punyacharoensin N, Edmunds WJ, De Angelis D, White RG. Mathematical models for the study of HIV spread and control amongst men who have sex with men. European Journal of Epidemiology. 2011;26(9):695-709. 33. Mishra S, Steen R, Gerbase A, Lo YR, Boily MC. Impact of High-Risk Sex and Focused Interventions in Heterosexual HIV Epidemics: A Systematic Review of Mathematical Models. PLoS ONE. 2012;7(11).
34. Edwards R, Kim S, van den Driessche P. A multigroup model for a heterosexually transmitted disease. Math Biosci. 2010;224(2):87-94. 35. Lubin G. There Are 42 Million Prostitutes In The World, And Here's Where They Live. Business Insider. 01/17/2012, 2012. 36. Quinn TC, Wawer MJ, Sewankambo N, et al. Viral load and heterosexual transmission of human immunodeficiency virus type 1. Rakai Project Study Group. N Engl J Med. 2000;342(13):921-929. 37. Cohen MS, Chen YQ, McCauley M, et al. Prevention of HIV-1 infection with early antiretroviral therapy. N Engl J Med. 2011;365(6):493-505. 38. Lubega M, Nakyaanjo N, Nansubuga S, et al. Understanding the socio-structural context of high HIV transmission in kasensero fishing community, South Western Uganda. BMC Public Health. 2015;15:1033.