A Framework for Network-Based Epidemiological Modeling of Tuberculosis Dynamics Using Synthetic Datasets

Abstract

We present a framework for discrete network-based modeling of TB epidemiology in US counties using publicly available synthetic datasets. We explore the dynamics of this modeling framework by simulating the hypothetical spread of disease over 2 years resulting from a single active infection in Washtenaw County, MI. We find that for sufficiently large transmission rates that active transmission outweighs reactivation, disease prevalence is sensitive to the contact weight assigned to transmissions between casual contacts (that is, contacts that do not share a household, workplace, school, or group quarter). Workplace and casual contacts contribute most to active disease transmission, while household, school, and group quarter contacts contribute relatively little. Stochastic features of the model result in significant uncertainty in the predicted number of infections over time, leading to challenges in model calibration and interpretation of model-based predictions. Finally, predicted infections were more localized by household location than would be expected if they were randomly distributed. This modeling framework can be refined in later work to study specific county and multi-county TB epidemics in the USA.

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References

  1. Abu-Raddad LJ, Sabatelli L, Achterberg JT, Sugimoto JD, Longini IM, Dye C, Halloran ME (2009) Epidemiological benefits of more-effective tuberculosis vaccines, drugs, and diagnostics. PNAS 106(33):13980–13985

    Article  Google Scholar 

  2. Aktogu S, Yorgancioglu A, Cirak K, Kose T, Dereli S (1996) Clinical spectrum of pulmonary and pleural tuberculosis: a report of 5,480 cases. Eur Resp J 9(10):2031–2035

    Article  Google Scholar 

  3. Bansal S, Grenfell BT, Meyers LA (2007) When individual behaviour matters: homogeneous and network models in epidemiology. J R Soc Interface 4(16):879–891. https://doi.org/10.1098/rsif.2007.1100

    Article  Google Scholar 

  4. Blower SM, Mclean AR, Porco TC, Small PM, Hopewell PC, Sanchez MA, Moss AR (1995) The intrinsic transmission dynamics of tuberculosis epidemics. Nat Med 1(8):815–821

    Article  Google Scholar 

  5. Castillo-Chavez C, Feng Z (1998) Global stability of an age-structure model for TB and its applications to optimal vaccination strategies. Math Biosci 151(2):135–154

    Article  Google Scholar 

  6. CDC (2019) Reported tuberculosis in the United States, 2018. US Department of Health and Human Services, Centers for Disease Control and Prevention, Atlanta

    Google Scholar 

  7. CDC, Division of Tuberculosis Elimination (2009) The report of a verified case of tuberculosis (RVCT) instructions and self-study modules. US Department of Health and Human Services, Centers for Disease Control and Prevention, Atlanta

    Google Scholar 

  8. CDC, Division of Tuberculosis Elimination (2011) TB elimination: the difference between latent TB infection and TB disease. US Department of Health and Human Services, Centers for Disease Control and Prevention, Atlanta

    Google Scholar 

  9. CIA (2020) The World Factbook 2020. Central Intelligence Agency, Washington, DC. https://www.cia.gov/library/publications/resources/the-world-factbook/index.html Accessed 21 May 2020

  10. Cooley P, Lee BY, Brown S, Cajka J, Chasteen B, Ganapathi L, Stark JH, Wheaton WD, Wagener DK, Burke DS (2010) Protecting health care workers: a pandemic simulation based on Allegheny county. Influenza Other Respir Viruses 4(2):61–72. https://doi.org/10.1111/j.1750-2659.2009.00122.x

    Article  Google Scholar 

  11. Del Valle S, Hyman J, Hethcote H, Eubank S (2007) Mixing patterns between age groups in social networks. Soc Netw 29(4):539–554. https://doi.org/10.1016/j.socnet.2007.04.005

    Article  Google Scholar 

  12. Dobler CC, Chidiac R, Williamson JP, Jelfs PJ (2016) Repeat exposure to active tuberculosis and risk of re-infection. Med J Austr 204(2):77–78. https://doi.org/10.5694/mja15.00749

    Article  Google Scholar 

  13. Dushoff J, Levin S (1995) The effects of population heterogeneity on disease invasion. Math Biosci 128(1):25–40. https://doi.org/10.1016/0025-5564(94)00065-8

    Article  MATH  Google Scholar 

  14. Everitt B (1998) Cambridge dictionary of statistics. Cambridge University Press, Cambridge

    Google Scholar 

  15. Gomez JE, McKinney JD (2004) M. tuberculosis persistence, latency, and drug tolerance. Tuberculosis 84(1):29–44. https://doi.org/10.1016/j.tube.2003.08.003

    Article  Google Scholar 

  16. Grefenstette JJ, Brown ST, Rosenfeld R, DePasse J, Stone NT, Cooley PC, Wheaton WD, Fyshe A, Galloway DD, Sriram A, Guclu H, Abraham T, Burke DS (2013) FRED (a framework for reconstructing epidemic dynamics): an open-source software system for modeling infectious diseases and control strategies using census-based populations. BMC Public Health 13(1):940. https://doi.org/10.1186/1471-2458-13-940

    Article  Google Scholar 

  17. Gupta S, Anderson RM, May RM (1989) Networks of sexual contacts: implications for the pattern of spread of HIV. AIDS 3(12):807–817

    Article  Google Scholar 

  18. Guzzetta G, Ajelli M, Yang Z, Merler S, Furlanello C, Kirschner D (2011) Modeling socio-demography to capture tuberculosis transmission dynamics in a low burden setting. J Theor Biol 289(1):197–205

    MathSciNet  Article  Google Scholar 

  19. Kao YH, Eisenberg MC (2018) Practical unidentifiability of a simple vector-borne disease model: implications for parameter estimation and intervention assessment. Epidemics 25:89–100. https://doi.org/10.1016/j.epidem.2018.05.010

    Article  Google Scholar 

  20. Kasaie P, Andrews JR, Kelton WD, Dowdy DW (2014) Timing of tuberculosis transmission and the impact of household contact tracing: an agent-based simulation model. Am J Respir Crit Care Med 189(7):845–852

    Article  Google Scholar 

  21. Keeling M (2005) The implications of network structure for epidemic dynamics. Theor Popul Biol 67(1):1–8. https://doi.org/10.1016/j.tpb.2004.08.002

    Article  MATH  Google Scholar 

  22. Keeling MJ, Eames KTD (2005) Networks and epidemic models. J R Soc Interface 2(4):295–307. https://doi.org/10.1098/rsif.2005.0051

    Article  Google Scholar 

  23. Knight GM, Griffiths UK, Sumner T, Laurence YV, Gheorghe A, Vassall A, Glaziou P, White RG (2014) Impact and cost-effectiveness of new tuberculosis vaccines in low- and middle-income countries. PNAS 111(43):15520–15525

    Article  Google Scholar 

  24. Lalor MK, Anderson LF, Hamblion EL, Burkitt A, Davidson JA, Maguire H, Abubakar I, Thomas HL (2017) Recent household transmission of tuberculosis in England, 2010–2012: retrospective national cohort study combining epidemiological and molecular strain typing data. BMC Med 15(1):105. https://doi.org/10.1186/s12916-017-0864-y

    Article  Google Scholar 

  25. Lee B, Brown S, Cooley P, Potter M, Wheaton W, Voorhees R, Stebbins S, Grefenstette J, Zimmer S, Zimmerman R, Assi T, Bailey R, Wagener D, Burke D (2010a) Simulating school closure strategies to mitigate an influenza epidemic. J Public Health Manag Pract 16(3):252–261. https://doi.org/10.1097/PHH.0b013e3181ce594e

    Article  Google Scholar 

  26. Lee BY, Brown ST, Cooley PC, Zimmerman RK, Wheaton WD, Zimmer SM, Grefenstette JJ, Assi TM, Furphy TJ, Wagener DK, Burke DS (2010b) A computer simulation of employee vaccination to mitigate an influenza epidemic. Am J Prev Med 38(3):247–257. https://doi.org/10.1016/j.amepre.2009.11.009

    Article  Google Scholar 

  27. Lee BY, Brown ST, Bailey RR, Zimmerman RK, Potter MA, McGlone SM, Cooley PC, Grefenstette JJ, Zimmer SM, Wheaton WD, Quinn SC, Voorhees RE, Burke DS (2011) The benefits to all of ensuring equal and timely access to influenza vaccines in poor communities. Health Affairs 30(6):1141–1150. https://doi.org/10.1377/hlthaff.2010.0778

    Article  Google Scholar 

  28. Lietman T, Blower SM (2000) Potential impact of tuberculosis vaccines as epidemic control agents. Clin Infect Dis 30(Supplement 3):S316–S322

    Article  Google Scholar 

  29. Macal CM, North MJ, Collier N, Dukic VM, Lauderdale DS, David MZ, Daum RS, Shumm P, Evans JA, Wilder JR, Wegener DT (2012) Modeling the spread of community-associated MRSA. In: Proceedings of the 2012 Winter simulation conference (WSC), pp 1–12. https://doi.org/10.1109/WSC.2012.6465271

  30. Macal CM, North MJ, Collier N, Dukic VM, Wegener DT, David MZ, Daum RS, Schumm P, Evans JA, Wilder JR, Miller LG, Eells SJ, Lauderdale DS (2014) Modeling the transmission of community- associated methicillin-resistant Staphylococcus aureus: a dynamic agent-based simulation. J Transl Med 12:124

    Article  Google Scholar 

  31. Mancuso JD, Diffenderfer JM, Ghassemieh BJ, Horne DJ, Kao TC (2016) The prevalence of latent tuberculosis infection in the United States. Am J Respir Crit Care Med 194(4):501–509

    Article  Google Scholar 

  32. Marino S, Hogue IB, Ray CJ, Kirschner DE (2008) A methodology for performing global uncertainty and sensitivity analysis in systems biology. J Theor Biol 254(1):178–196

    MathSciNet  Article  Google Scholar 

  33. McKay MD, Beckman RJ, Conover WJ (1979) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21(2):239–245

    MathSciNet  MATH  Google Scholar 

  34. Merler S, Ajelli M (2010) The role of population heterogeneity and human mobility in the spread of pandemic influenza. Proc R Soc B Biol Sci 277(1681):557–565. https://doi.org/10.1098/rspb.2009.1605

    Article  Google Scholar 

  35. Miramontes R, Hill AN, Yelk Woodruff RS, Lambert LA, Navin TR, Castro KG, LoBue PA (2015) Tuberculosis infection in the united states: prevalence estimates from the national health and nutrition examination survey, 2011–2012. PLoS ONE 10(11):1–17. https://doi.org/10.1371/journal.pone.0140881

    Article  Google Scholar 

  36. Mniszewski SM, Del Valle SY, Stroud PD, Riese JM, Sydoriak SJ (2008) EpiSimS simulation of a multi-component strategy for pandemic influenza. In: Proceedings of the 2008 spring simulation multiconference, society for computer simulation international, San Diego, CA, USA, SpringSim’08, pp 556–563

  37. Mossong J, Hens N, Jit M, Beutels P, Auranen K, Mikolajczyk R, Massari M, Salmaso S, Tomba GS, Wallinga J, Heijne J, Sadkowska-Todys M, Rosinska M, Edmunds WJ (2008) Social contacts and mixing patterns relevant to the spread of infectious diseases. PLoS Med 5(3):e74

    Article  Google Scholar 

  38. Prats C, Montanola-Sales CM, Gilabert-Navarro JF, Valls J, Casanovas-Garcia J, Vilaplana C, Cardona PJ, López D (2016) Individual-based modeling of tuberculosis in a user-friendly interface: understanding the epidemiological role of population heterogeneity in a city. Front Microbiol 6:1564

    Article  Google Scholar 

  39. Prem K, Cook AR, Jit M (2017) Projecting social contact matrices in 152 countries using contact surveys and demographic data. PLoS Comput Biol 13(9):e1005697

    Article  Google Scholar 

  40. Read JM, Eames KT, Edmunds WJ (2008) Dynamic social networks and the implications for the spread of infectious disease. J R Soc Interface 5(26):1001–1007. https://doi.org/10.1098/rsif.2008.0013

    Article  Google Scholar 

  41. Renardy M, Kirschner D (2019) Evaluating vaccination strategies for tuberculosis in endemic and non-endemic settings. J Theor Biol 469:1–11

    MathSciNet  Article  Google Scholar 

  42. Sepkowitz KA (1996) How contagious is tuberculosis? Clin Infect Dis 23(5):954–962. https://doi.org/10.1093/clinids/23.5.954

    Article  Google Scholar 

  43. Shea KM, Kammerer JS, Winston CA, Navin TR Jr, Horsburgh R (2014) Estimated rate of reactivation of latent tuberculosis infection in the United States, overall and by population subgroup. Am J Epidemiol 179(2):216–225

    Article  Google Scholar 

  44. Stewart R, Tsang C, Pratt R, Price S, Langer A (2018) Tuberculosis-United States, 2017. Morb Mortal Wkly Rep (MMWR) 67:317–323

    Article  Google Scholar 

  45. Tian Y, Osgood ND, Al-Azem A, Hoeppner VH (2013) Evaluating the effectiveness of contact tracing on tuberculosis outcomes in Saskatchewan using individual-based modeling. Health Educ Behav 40(1S):98S–110S

    Article  Google Scholar 

  46. US Census Bureau (2018) Quickfacts: Washtenaw county, Michigan. https://www.census.gov/quickfacts/washtenawcountymichigan. Accessed 11 Nov 2019

  47. van Rie A, Warren R, Richardson M, Victor TC, Gie RP, Enarson DA, Beyers N, van Helden PD (1999) Exogenous reinfection as a cause of recurrent tuberculosis after curative treatment. N Engl J Med 341(16):1174–1179. https://doi.org/10.1056/NEJM199910143411602

    Article  Google Scholar 

  48. Verver S, Warren RM, Munch Z, Richardson M, van der Spuy GD, Borgdorff MW, Behr MA, Beyers N, van Helden PD (2004) Proportion of tuberculosis transmission that takes place in households in a high-incidence area. Lancet 363(9404):212–214. https://doi.org/10.1016/S0140-6736(03)15332-9

    Article  Google Scholar 

  49. Vynnycky E, Fine PEM (1997) The natural history of tuberculosis: the implications of age-dependent risks of disease and the role of reinfection. Epidemiol Infect 119(2):183–201

    Article  Google Scholar 

  50. Washtenaw County Health Department (2019) Tuberculosis (TB) information. https://www.washtenaw.org/2617/Tuberculosis-TB-Information. Accessed 23 Sept 2019

  51. Weis SE, Slocum PC, Blais FX, King B, Nunn M, Matney GB, Gomez E, Foresman BH (1994) The effect of directly observed therapy on the rates of drug resistance and relapse in tuberculosis. N Engl J Med 330(17):1179–1184. https://doi.org/10.1056/NEJM199404283301702

    Article  Google Scholar 

  52. Wheaton W (2014) 2010 RTI U.S. Synthetic population Ver 1.0. Online database, RTI International. https://www.epimodels.org/midas/pubsyntdata1.do. Accessed 12 Dec 2018

  53. Wheaton WD, Cajka JC, Chasteen BM, Wagener DK, Cooley PC, Ganapathi L, Roberts DJ, Allpress JL (2009) Synthesized population databases: a US geospatial database for agent-based models. Methods Rep RTI Press 10:905

    Google Scholar 

  54. WHO (2019) Global tuberculosis report 2019. World Health Organization, Geneva

    Google Scholar 

  55. Wilkinson D, Pillay M, Crump J, Lombard C, Davies GR, Sturm AW (1997) Molecular epidemiology and transmission dynamics of Mycobacterium tuberculosis in rural Africa. Trop Med Int Health 2(8):747–753. https://doi.org/10.1046/j.1365-3156.1997.d01-386.x

    Article  Google Scholar 

  56. Yuen CM, Kammerer JS, Marks K, Navin TR, France AM (2016) Recent transmission of tuberculosis—United States, 2011–2014. PLoS ONE 11(4):e0153728

    Article  Google Scholar 

  57. Ziv E, Daley CL, Blower S (2004) Potential public health impact of new tuberculosis vaccines. Emerg Infect Dis 10(9):1529–1535

    Article  Google Scholar 

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Acknowledgements

This research was supported by NIH Grants R01AI123093 and U01 HL131072 awarded to DEK. The 2010 U.S. Synthetic Population database was created by RTI International, which is funded by the National Institutes of General Medical Sciences (NIGMS).

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Correspondence to Denise E. Kirschner.

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Renardy, M., Kirschner, D.E. A Framework for Network-Based Epidemiological Modeling of Tuberculosis Dynamics Using Synthetic Datasets. Bull Math Biol 82, 78 (2020). https://doi.org/10.1007/s11538-020-00752-9

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Keywords

  • Tuberculosis
  • Epidemiology
  • Network-based model
  • Synthetic population