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A Multi-risk Model for Understanding the Spread of Chlamydia

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Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases

Abstract

Chlamydia trachomatis, CT, infection is the most frequently reported sexually transmitted infection in the United States. To better understand the recent increase in disease prevalence, and help guide in mitigation efforts, we created and analyzed a multi-risk model for the spread of chlamydia in the heterosexual community. The model incorporates the heterogeneous mixing between men and women with different number of partners and the parameters are defined to approximate the disease transmission in the 15–25 year-old New Orleans African American community. We use sensitivity analysis to assess the relative impact of different levels of screening interventions and behavior changes on the basic reproduction number. Our results quantify, and validate, the impact that reducing the probability of transmission per sexual contact, such as using prophylactic condoms, can have on CT prevalence.

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Notes

  1. 1.

    Let K be a hermitian matrix. We define \(e^+(K)\) as the number of positive eigenvalues, \(e^-(K)\) as the number of negative eigenvalues, and \(e^0(K)\) as the number of zero eigenvalues. Inertia of K is a tuple \((e^+(K), e^-(K)), e^0(K)\). If A is an invertible matrix then Sylvester inertia theorem states: \(inertia(K)=inertia(A^{-1}KA)\).

References

  1. Althaus, C.L., Heijne, J., Roellin, A., Low, N.: Transmission dynamics of chlamydia trachomatis affect the impact of screening programmes. Epidemics 2(3), 123–131 (2010)

    Article  Google Scholar 

  2. Arriola, L., Hyman, J.M.: Sensitivity analysis for uncertainty quantification in mathematical models. In: Mathematical and Statistical Estimation Approaches in Epidemiology, pp. 195–247. Springer, New York (2009)

    Google Scholar 

  3. Arriola, L.M., Hyman, J.M.: Being sensitive to uncertainty. Comput. Sci. Eng. 9(2), 10–20 (2007)

    Article  Google Scholar 

  4. Busenberg, S., Castillo-Chavez, C.: A general solution of the problem of mixing of subpopulations and its application to risk-and age-structured epidemic models for the spread of aids. Math. Med. Biol. 8(1), 1–29 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chitnis, N., Hyman, J.M., Cushing, J.M.: Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model. Bull. Math. Biol. 70(5), 1272–1296 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Clarke, J., White, K.A., Turner, K.: Exploring short-term responses to changes in the control strategy for chlamydia trachomatis. Comput. Math. Methods Med. 11(4), 353–368 (2012)

    MATH  Google Scholar 

  7. Cohen, M.S.: Sexually transmitted diseases enhance HIV transmission: no longer a hypothesis. Lancet 351, S5–S7 (1998)

    Article  Google Scholar 

  8. Datta, S.D., Torrone, E., Kruszon-Moran, D., Berman, S., Johnson, R., Satterwhite, C.L., Papp, J., Weinstock, H.: Chlamydia trachomatis trends in the united states among persons 14 to 39 years of age, 1999–2008. Sex. Transm. Dis. 39(2), 92–96 (2012)

    Article  Google Scholar 

  9. Del Valle, S., Hethcote, H., Hyman, J.M., Castillo-Chavez, C.: Effects of behavioral changes in a smallpox attack model. Math. Biosci. 195(2), 228–251 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  10. Del Valle, S.Y., Hyman, J.M., Chitnis, N.: Mathematical models of contact patterns between age groups for predicting the spread of infectious diseases. Math. Biosci. Eng. MBE 10, 1475 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  11. Del Valle, S.Y., Hyman, J.M., Hethcote, H.W., Eubank, S.G.: Mixing patterns between age groups in social networks. Soc. Netw. 29(4), 539–554 (2007)

    Article  Google Scholar 

  12. Eaton, D.K., Kann, L., Kinchen, S., Shanklin, S., Ross, J., Hawkins, J., Harris, W.A., Lowry, R., McManus, T., Chyen, D., et al.: Youth risk behavior surveillance-united states, 2009. Morb. Mortal. Wkly. Rep. Surveill. Summ. (Washington, DC: 2002), 59(5), 1–142 (2010)

    Google Scholar 

  13. Golden, M.R., Hogben, M., Handsfield, H.H., St Lawrence, J.S., Potterat, J.J., Holmes, K.K.: Partner notification for HIV and STD in the united states: low coverage for gonorrhea, chlamydial infection, and HIV. Sex. Transm. Dis. 30(6), 490–496 (2003)

    Article  Google Scholar 

  14. Gottlieb, S.L., Brunham, R.C., Byrne, G.I., Martin, D.H., Xu, F., Berman, S.M.: Introduction: the natural history and immunobiology of chlamydia trachomatis genital infection and implications for chlamydia control. J. Infect. Dis. 201(Supplement 2), S85–S87 (2010)

    Article  Google Scholar 

  15. Gottlieb, L.S., Martin, D.H., Xu, F., Byrne, G.I., Brunham, R.C.: Summary: the natural history and immunobiology of chlamydia trachomatis genital infection and implications for chlamydia control. J. Infect. Dis. 201(Supplement 2), S190–S204 (2010)

    Article  Google Scholar 

  16. Heffernan, J.M., Smith, R.J., Wahl, L.M.: Perspectives on the basic reproductive ratio. J. R. Soc. Interface 2(4), 281–293 (2005)

    Article  Google Scholar 

  17. Hillis, S.D., Wasserheit, J.N.: Screening for chlamydia: a key to the prevention of pelvic inflammatory disease. N. Engl. J. Med. 334(21), 1399–1401 (1996)

    Article  Google Scholar 

  18. Hyman, J.M., Li, J.: Behavior changes in SIS STD models with selective mixing. SIAM J. Appl. Math. 57(4), 1082–1094 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  19. Hyman, J.M., Li, J.: Disease transmission models with biased partnership selection. Appl. Numer. Math. 24(2), 379–392 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  20. Hyman, J.M., Li, J., Stanley, E.A.: The differential infectivity and staged progression models for the transmission of HIV. Math. Biosci. 155(2), 77–109 (1999)

    Article  MATH  Google Scholar 

  21. Hyman, J.M., Li, J., Stanley, E.A.: The initialization and sensitivity of multigroup models for the transmission of HIV. J. Theor. Biol. 208(2), 227–249 (2001)

    Article  Google Scholar 

  22. Hyman, J.M., Li, J., Stanley, E.A.: Modeling the impact of random screening and contact tracing in reducing the spread of HIV. Math. Biosci. 181(1), 17–54 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  23. Hyman, J.M., Stanley, E.A.: Using mathematical models to understand the AIDS epidemic. Math. Biosci. 90(1), 415–473 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  24. Hyman, J.M., Stanley, E.A.: The effect of social mixing patterns on the spread of AIDS. In: Castillo-Chavez, C.C., Levin, S.A., Shoemaker, C.A. (eds.) Mathematical Approaches to Problems in Resource Management and Epidemiolog, pp. 190–219. Springer, Berlin (1989)

    Chapter  Google Scholar 

  25. Hyman, J.M., Stanley, E.A.: A risk-based heterosexual model for the AIDS epidemic with biased sexual partner selection. In: Kaplan, E.E., Brandeau, M. (eds.) Modeling the AIDS Epidemic, pp. 331–364. Raven Press, New York (1994)

    Google Scholar 

  26. Kretzschmar, M., van Duynhoven, Y.T.H.P., Severijnen, A.J.: Modeling prevention strategies for gonorrhea and chlamydia using stochastic network simulations. Am. J. Epidemiol. 144(3), 306–317 (1996)

    Article  Google Scholar 

  27. Kretzschmar, M., Welte, R., Van den Hoek, A., Postma, M.J.: Comparative model-based analysis of screening programs for chlamydia trachomatis infections. Am. J. Epidemiol. 153(1), 90–101 (2001)

    Article  Google Scholar 

  28. Lan, J., van den Brule, A.J., Hemrika, D.J., Risse, E.K., Walboomers, J.M., Schipper, M.E., Meijer, C.J.: Chlamydia trachomatis and ectopic pregnancy: retrospective analysis of salpingectomy specimens, endometrial biopsies, and cervical smears. J. Clin. Pathol. 48(9), 815–819 (1995)

    Article  Google Scholar 

  29. Low, N., McCarthy, A., Macleod, J., Salisbury, C., Campbell, R., Roberts, T.E., Horner, P., Skidmore, S., Sterne, J.A., Sanford, E., et al.: Epidemiological, social, diagnostic and economic evaluation of population screening for genital chlamydial infection. Health Technol. Assess. (Winchester, England), 11(8):iii–iv (2007)

    Google Scholar 

  30. Manore, C.A., Hickmann, K.S., Xu, S., Wearing, H.J., Hyman, J.M.: Comparing dengue and chikungunya emergence and endemic transmission in A. aegypti and A. albopictus. J. Theor. Biol. 356, 174–191 (2014)

    Article  MathSciNet  Google Scholar 

  31. Niccolai, L.M., Livingston, K.A., Laufer, A.S., Pettigrew, M.M.: Behavioural sources of repeat chlamydia trachomatis infections: importance of different sex partners. Sex. Transm. Infect. 87(3), 248–253 (2011)

    Article  Google Scholar 

  32. Pearlman, M.D., Mcneeley, S.G.: A review of the microbiology, immunology, and clinical implications of chlamydia trachomatis infections. Obstet. Gynecol. Surv. 47(7), 448–461 (1992)

    Article  Google Scholar 

  33. Schwebke, J.R., Rompalo, A., Taylor, S., Sena, A.C., Martin, D.H., Lopez, L.M., Lensing, S., Lee, J.Y.: Re-evaluating the treatment of nongonococcal urethritis: emphasizing emerging pathogens-a randomized clinical trial. Clin. Infect. Dis. 52(2), 163–170 (2011)

    Article  Google Scholar 

  34. Sylvester, J.J.: Xix. a demonstration of the theorem that every homogeneous quadratic polynomial is reducible by real orthogonal substitutions to the form of a sum of positive and negative squares. Lond. Edinb. Dublin Philos. Mag. J. Sci. 4(23), 138–142 (1852)

    Google Scholar 

  35. Torrone, E., Papp, J., Weinstock, H.: Prevalence of chlamydia trachomatis genital infection among persons aged 14–39 years-united states, 2007–2012. MMWR Morb. Mortal. Wkly. Rep. 63(38), 834–838 (2014)

    Google Scholar 

  36. Turner, K.M.E., Adams, E.J., LaMontagne, D.S., Emmett, L., Baster, K., Edmunds, W.J.: Modelling the effectiveness of chlamydia screening in England. Sex. Transm. Infect. 82(6), 496–502 (2006)

    Article  Google Scholar 

  37. Van den Driessche, P., Watmough, J.: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180(1), 29–48 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  38. Walker, J., Tabrizi, S.N., Fairley, C.K., Chen, M.Y., Bradshaw, C.S., Twin, J., Taylor, N., Donovan, B., Kaldor, J.M., McNamee, K., et al.: Chlamydia trachomatis incidence and re-infection among young women-behavioural and microbiological characteristics. PLoS One 7(5), e37778 (2012)

    Article  Google Scholar 

  39. Ward, H., Rönn, M.: The contribution of STIs to the sexual transmission of HIV. Curr. Opin. HIV AIDS 5(4), 305 (2010)

    Article  Google Scholar 

  40. Westrom, L.: Effect of pelvic inflammatory disease on fertility. Venereol. Off. Publ. Natl. Venereol. Counc. Aust. 8(4), 219–222 (1995)

    Google Scholar 

  41. Weström, L.V.: Sexually transmitted diseases and infertility. Sex. Transm. Dis. 21(2 Suppl), S32–S37 (1993)

    Google Scholar 

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Acknowledgments

We thank Patricia Kissinger for her insight and guidance in determining what factors need to be considered in modeling the spread of CT. We also thank Jeremy Dewar for his assistance with the sensitivity analysis and feedback on the manuscript. This work was supported by the endowment for the Evelyn and John G. Phillips Distinguished Chair in Mathematics at Tulane University, and National Institute of General Medical Sciences of the National Institutes of Health program for Models of Infectious Disease Agent Study (MIDAS) under Award Number U01GM097658. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

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Authors and Affiliations

  1. Department of Mathematics, Tulane University, New Orleans, LA, 70118, USA

    Asma Azizi, Ling Xue & James M. Hyman

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  1. Asma Azizi
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  2. Ling Xue
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  3. James M. Hyman
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Correspondence to James M. Hyman .

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Editors and Affiliations

  1. School of Public Health, Georgia State University, Atlanta, Georgia, USA

    Gerardo Chowell

  2. Department of Mathematics, Tulane University, New Orleans, Louisiana, USA

    James M. Hyman

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Azizi, A., Xue, L., Hyman, J.M. (2016). A Multi-risk Model for Understanding the Spread of Chlamydia. In: Chowell, G., Hyman, J. (eds) Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases. Springer, Cham. https://doi.org/10.1007/978-3-319-40413-4_15

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