An exact approach to calibrating infectious disease models to surveillance data: The case of HIV and HSV-2

David J. Gerberry; David J. Gerberry

doi:10.3934/mbe.2018007

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 1: 153-179. doi: 10.3934/mbe.2018007

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An exact approach to calibrating infectious disease models to surveillance data: The case of HIV and HSV-2

David J. Gerberry

Department of Mathematics, Xavier University, 3800 Victory Parkway, Cincinnati, OH 45207, USA

Received: 15 September 2016 Accepted: 02 March 2017 Published: 01 February 2018
MSC : Primary: 92D30; Secondary: 92D25, 37N25, 37N30, 92C60

When mathematical models of infectious diseases are used to inform health policy, an important first step is often to calibrate a model to disease surveillance data for a specific setting (or multiple settings). It is increasingly common to also perform sensitivity analyses to demonstrate the robustness, or lack thereof, of the modeling results. Doing so requires the modeler to find multiple parameter sets for which the model produces behavior that is consistent with the surveillance data. While frequently overlooked, the calibration process is nontrivial at best and can be inefficient, poorly communicated and a major hurdle to the overall reproducibility of modeling results. In this work, we describe a general approach to calibrating infectious disease models to surveillance data. The technique is able to match surveillance data to high accuracy in a very efficient manner as it is based on the Newton-Raphson method for solving nonlinear systems. To demonstrate its robustness, we use the calibration technique on multiple models for the interacting dynamics of HIV and HSV-2.
- Mathematical modeling,
- calibration,
- model-fitting,
- HIV,
- HSV-2,
- surveillance data
Citation: David J. Gerberry. An exact approach to calibrating infectious disease models to surveillance data: The case of HIV and HSV-2[J]. Mathematical Biosciences and Engineering, 2018, 15(1): 153-179. doi: 10.3934/mbe.2018007

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Abstract

When mathematical models of infectious diseases are used to inform health policy, an important first step is often to calibrate a model to disease surveillance data for a specific setting (or multiple settings). It is increasingly common to also perform sensitivity analyses to demonstrate the robustness, or lack thereof, of the modeling results. Doing so requires the modeler to find multiple parameter sets for which the model produces behavior that is consistent with the surveillance data. While frequently overlooked, the calibration process is nontrivial at best and can be inefficient, poorly communicated and a major hurdle to the overall reproducibility of modeling results. In this work, we describe a general approach to calibrating infectious disease models to surveillance data. The technique is able to match surveillance data to high accuracy in a very efficient manner as it is based on the Newton-Raphson method for solving nonlinear systems. To demonstrate its robustness, we use the calibration technique on multiple models for the interacting dynamics of HIV and HSV-2.

References

[1]	[ L. J. Abu-Raddad, A. S. Magaret, C. Celum, A. Wald, I. M. Longini, S. G. Self and L. Corey, Genital herpes has played a more important role than any other sexually transmitted infection in driving hiv prevalence in africa, PLoS ONE, 3 (2008), e2230.
[2]	[ B. Auvert,R. Ballard,C. Campbell,M. Caraël,M. Carton,G. Fehler,E. Gouws,C. MacPhail,D. Taljaard,J. V. Dam,B. Williams, Hiv infection among youth in a south african mining town is associated with herpes simplex virus-2 seropositivity and sexual behaviour, AIDS, 15 (2001): 885-898.
[3]	[ J. M. Baeten,D. Donnell,P. Ndase,N. R. Mugo,J. D. Campbell,J. Wangisi,J. W. Tappero,E. A. Bukusi,C. R. Cohen,E. Katabira,A. Ronald,E. Tumwesigye,E. Were,K. H. Fife,J. Kiarie,C. Farquhar,G. John-Stewart,A. Kakia,J. Odoyo,A. Mucunguzi,E. Nakku-Joloba,R. Twesigye,K. Ngure,C. Apaka,H. Tamooh,F. Gabona,A. Mujugira,D. Panteleeff,K. K. Thomas,L. Kidoguchi,M. Krows,J. Revall,S. Morrison,H. Haugen,M. Emmanuel-Ogier,L. Ondrejcek,R. W. Coombs,L. Frenkel,C. Hendrix,N. N. Bumpus,D. Bangsberg,J. E. Haberer,W. S. Stevens,J. R. Lingappa,C. Celum, Antiretroviral prophylaxis for HIV prevention in heterosexual men and women, N Engl J Med, 367 (2012): 399-410.
[4]	[ R. V. Barnabas,E. L. Webb,H. A. Weiss,J. N. Wasserheit, The role of coinfections in HIV epidemic trajectory and positive prevention, AIDS, 25 (2011): 1559-1573.
[5]	[ M.-C. Boily, R. F. Baggaley, L. Wang, B. Masse, R. G. White, R. J. Hayes and M. Alary, Heterosexual risk of hiv-1 infection per sexual act: Systematic review and meta-analysis of observational studies, Lancet Infect Dis, 9 (2009), 118–129, URL http://linkinghub.elsevier.com/retrieve/pii/S1473-3099(09)70021-0.
[6]	[ R. Burden and J. Faires, Numerical Analysis, Cengage Learning, 2010.
[7]	[ Cohen,Chen,McCauley,Gamble,Hosseinipour,Kumarasamy,Hakim,Kumwenda,Grinsztejn,Pilotto,Godbole,Mehendale,Chariyalertsak,Santos,Mayer,Hoffman,Eshleman,Piwowar-Manning,Wang,Makhema,Mills,de Bruyn,Sanne,Eron,Gallant,Havlir,Swindells,Ribaudo,Elharrar,Burns,Taha,Nielsen-Saines,Celentano,Essex,Fleming,HPTN 052 Study Team, Prevention of HIV-1 infection with early antiretroviral therapy., N Engl J Med, 365 (2011): 493-505.
[8]	[ M. Das, P. L. Chu, G. -M. Santos, S. Scheer, E. Vittinghoff, W. McFarland and G. N. Colfax, Decreases in community viral load are accompanied by reductions in new HIV infections in san francisco, PLoS ONE, 5 (2010), e11068.
[9]	[ E. E. Freeman,H. A. Weiss,J. R. Glynn,P. L. Cross,J. A. Whitworth,R. J. Hayes, Herpes simplex virus 2 infection increases hiv acquisition in men and women: Systematic review and meta-analysis of longitudinal studies, AIDS, 20 (2006): 73-83.
[10]	[ D. Gerberry,B. G. Wagner,J. G. García-Lerma,W. Heneine,S. Blower, Using geospatial modelling to optimize the rollout of antiretroviral-based pre-exposure HIV interventions in Sub-Saharan Africa, Nature Communications, 5 (2014): 1-15.
[11]	[ R. M. Granich,C. F. Gilks,C. Dye,K. M. De Cock,B. G. Williams, Universal voluntary HIV testing with immediate antiretroviral therapy as a strategy for elimination of HIV transmission: A mathematical model, Lancet, 373 (2009): 48-57.
[12]	[ R. H. Gray,M. J. Wawer,R. Brookmeyer,N. K. Sewankambo,D. Serwadda,F. Wabwire-Mangen,T. Lutalo,X. Li,T. vanCott,T. C. Quinn,R. P. Team, Probability of hiv-1 transmission per coital act in monogamous, heterosexual, hiv-1-discordant couples in rakai, uganda, Lancet, 357 (2001): 1149-1153.
[13]	[ R. J. Hayes,K. F. Schulz,F. A. Plummer, The cofactor effect of genital ulcers on the per-exposure risk of hiv transmission in sub-saharan africa, J Trop Med Hyg, 98 (1995): 1-8.
[14]	[ K. A. Powers,C. Poole,A. E. Pettifor,M. S. Cohen, Rethinking the heterosexual infectivity of hiv-1: A systematic review and meta-analysis, Lancet Infect Dis, 8 (2008): 553-563.
[15]	[ J. A. Røttingen,D. W. Cameron,G. P. Garnett, A systematic review of the epidemiologic interactions between classic sexually transmitted diseases and hiv: How much really is known?, Sex Transm Dis, 28 (2001): 579-597.
[16]	[ J. S. Smith,N. J. Robinson, Age-specific prevalence of infection with herpes simplex virus types 2 and 1: A global review, J Infect Dis, 186 (2002): 3-28.
[17]	[ R. J. Smith,S. M. Blower, Could disease-modifying HIV vaccines cause population-level perversity?, Lancet Infect Dis, 4 (2004): 636-639.
[18]	[ The World Bank, World development indicators, http://data.worldbank.org/data--catalog/world--development--indicators [Accessed: 25 Oct 2011], URL http://data.worldbank.org/data-catalog/world-development-indicators.
[19]	[ M. C. Thigpen,P. M. Kebaabetswe,L. A. Paxton,D. K. Smith,C. E. Rose,T. M. Segolodi,F. L. Henderson,S. R. Pathak,F. A. Soud,K. L. Chillag,R. Mutanhaurwa,L. I. Chirwa,M. Kasonde,D. Abebe,E. Buliva,R. J. Gvetadze,S. Johnson,T. Sukalac,V. T. Thomas,C. Hart,J. A. Johnson,C. K. Malotte,C. W. Hendrix,J. T. Brooks, Antiretroviral preexposure prophylaxis for heterosexual HIV transmission in botswana, N Engl J Med, 367 (2012): 423-434.
[20]	[ A. J. Vyse,N. J. Gay,M. J. Slomka,R. Gopal,T. Gibbs,P. Morgan-Capner,D. W. Brown, The burden of infection with HSV-1 and HSV-2 in England and Wales: Implications for the changing epidemiology of genital herpes., Sex Transm Infect, 76 (2000): 183-187.
[21]	[ A. Wald,K. Link, Risk of human immunodeficiency virus infection in herpes simplex virus type 2-seropositive persons: a meta-analysis, J Infect Dis, 185 (2002): 45-52.
[22]	[ H. Weiss, Epidemiology of herpes simplex virus type 2 infection in the developing world, Herpes, 11 (2004): 24A-35A.

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