×
Brouwer, Andrew F.; Meza, Rafael; Eisenberg, Marisa C.

Transmission heterogeneity and autoinoculation in a multisite infection model of HPV. (English) Zbl 1364.92040

Math. Biosci. 270, Part A, 115-125 (2015).
Summary: The human papillomavirus (HPV) is sexually transmitted and can infect oral, genital, and anal sites in the human epithelium. Here, we develop a multisite transmission model that includes autoinoculation to study HPV and other multisite diseases. Under a homogeneous-contacts assumption, we analyze the basic reproduction number \(R_{0}\), as well as type and target reproduction numbers, for a two-site model. In particular, we find that \(R_{0}\) occupies a space between taking the maximum of next generation matrix terms for same site transmission and taking the geometric average of cross-site transmission terms in such a way that heterogeneity in the same-site transmission rates increases \(R_{0}\) while heterogeneity in the cross-site transmission decreases it. Additionally, autoinoculation adds considerable complexity to the form of \(R_{0}\). We extend this analysis to a heterosexual population, which additionally yields dynamics analogous to those of vector-host models. We also examine how these issues of heterogeneity may affect disease control, using type and target reproduction numbers.

Cited in 2 Documents

MSC:

92D30 Epidemiology

Keywords:

basic reproduction number; HPV; multisite model; autoinoculation; heterogeneity; disease control

Software:

Matlab
Cite Review PDF
Full Text: DOI Link

References:

[1] Diekmann, O.; Heesterbeek, J. A.P.; Metz, J. A.J., On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations, J. Math.Biol., 28, 365-382 (1990) · Zbl 0726.92018
[2] Anderson, R. M.; May, R. M., Infectious Diseases of Humans: Dynamics and Control (1991), Oxford University Press: Oxford University Press New York
[3] Diekmann, O.; Heesterbeek, J., Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis, and Interpretation (2000), John Wiley: John Wiley New York/Chichester · Zbl 0997.92505
[4] van den Driessche, P.; Watmough, J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180, 29-48 (2002) · Zbl 1015.92036
[5] Roberts, M. G.; Heesterbeek, J. A.P., A new method for estimating the effort required to control an infectious disease, Proc. R.Soc. B Biol. Sci., 270, 1522, 1359-1364 (2003)
[6] Heesterbeek, J. A.P.; Roberts, M. G., The type-reproduction number T in models for infectious disease control, Math. Biosci., 206, 1, 3-10 (2007) · Zbl 1124.92043
[7] Shuai, Z.; Heesterbeek, J. A.P.; van den Driessche, P., Extending the type reproduction number to infectious disease control targeting contacts between types, J. Math. Biol., 67, 5, 1067-1082 (2013) · Zbl 1278.92031
[8] Goodman, M. T.; Shvetsov, Y. B.; McDuffie, K.; Wilkens, L. R.; Zhu, X.; Thompson, P. J.; Ning, L.; Killeen, J.; Kamemoto, L.; Hernandez, B. Y., Sequential acquisition of human papillomavirus (HPV) infection of the anus and cervix: the Hawaii HPV cohort study, J. Infect. Dis., 201, 9, 1331-1339 (2010)
[9] Edelstein, Z. R.; Schwartz, S. M.; Hawes, S.; Hughes, J. P.; Feng, Q.; Stern, M. E.; O’Reilly, S.; Lee, S.-K.; Fu Xi, L.; Koutsky, L. A., Rates and determinants of oral human papillomavirus infection in young men, Sex. Transm. Dis., 39, 11, 860-867 (2012)
[10] Steinau, M.; Hariri, S.; Gillison, M. L.; Broutian, T. R.; Dunne, E. F.; Tong, Z.-y.; Markowitz, L. E.; Unger, E. R., Prevalence of cervical and oral human papillomavirus infections among US women, J. Infect. Dis., 209, 11, 1739-1743 (2014)
[11] Ribes, J. A.; Steele, A. D.; Seabolt, J. P.; Baker, D. J., Six-year study of the incidence of herpes in genital and nongenital cultures in a Central Kentucky Medical Center patient population, J. Clin. Microbiol., 39, 9, 3321-3325 (2001)
[12] Beauman, J. G., Genital herpes infection: a review, Am. Fam. Phys., 72, 8, 1527-1534 (2005)
[13] Fatahzadeh, M.; Schwartz, R. A., Human herpes simplex virus infections: epidemiology, pathogenesis, symptomatology, diagnosis, and management, J. Am. Acad. Dermatol., 57, 5, 737-763 (2007)
[14] Jones, R. B.; Rabinovitch, R.a.; Katz, B. P.; Batteiger, B. E.; Quinn, T. S.; Terho, P.; Lapworth, M.a., Chlamydia trachomatis in the pharynx and rectum of heterosexual patients at risk for genital infection, Ann. Intern. Med., 102, 6, 757-762 (1985)
[15] Stenberg, K.; Må rdh, P. A., Genital infection with Chlamydia trachomatis in patients with chlamydial conjunctivitis: unexplained results, Sex. Transm. Dis., 18, 1, 1-4 (1991)
[16] Rank, R. G.; Yeruva, L., Hidden in plain sight: Chlamydial gastrointestinal infection and its relevance to persistence in human genital infection, Infect. Immun., 82, 4, 1362-1371 (2014)
[17] Calderone, R. A.; Fonzi, W. A., Virulence factors of Candida albicans., Trends Microbiol., 9, 7, 327-335 (2001)
[18] Stulberg, D. L.; Hutchinson, A. G., Molluscum contagiosum and warts, Am. Fam. Phys., 67, 6, 1233-1240 (2003)
[19] May, R. M.; Anderson, R. M., Transmission dynamics of HIV infection, Nature, 326, 137-142 (1987)
[20] Adler, F. R., The effects of averaging on the basic reproductive ratio, Math. Biosci., 111, 1, 89-98 (1992) · Zbl 0781.92026
[21] Neri, F. M.; Bates, A.; Füchtbauer, W. S.; Pérez-Reche, F. J.; Taraskin, S. N.; Otten, W.; Bailey, D. J.; Gilligan, C. A., The effect of heterogeneity on invasion in spatial epidemics: from theory to experimental evidence in a model system., PLoS Comput. Biol., 7, 9, e1002174 (2011)
[22] Robertson, S. L.; Eisenberg, M. C.; Tien, J. H., Heterogeneity in multiple transmission pathways: modelling the spread of cholera and other waterborne disease in networks with a common water source., J. Biol. Dyn., 7, 1, 254-275 (2013) · Zbl 1448.92333
[24] Molano, M.; van den Brule, A.; Plummer, M.; Weiderpass, E.; Posso, H.; Arslan, A.; Meijer, C. J.; Muñoz, N.; Franceschi, S., Determinants of clearance of human papillomavirus infections in colombian women with normal cytology: a population-based, 5-year follow-up study, Am.J. Epidemiol., 158, 5, 486-494 (2003)
[25] Franco, E. L.; Villa, L. L.; Sobrinho, J. P.; Prado, J. M.; Rousseau, M.-C.; Désy, M.; Rohan, T. E., Epidemiology of acquisition and clearance of cervical human papillomavirus infection in women from a high-risk area for cervical cancer, J. Infect. Dis., 180, 5, 1415-1423 (1999)
[26] Hernandez, B. Y.; Shvetsov, Y. B.; Goodman, M. T.; Wilkens, L. R.; Thompson, P. J.; Zhu, X.; Tom, J.; Ning, L., Genital and extra-genital warts increase the risk of asymptomatic genital human papillomavirus infection in men, Sex. Transm. Infect., 87, 5, 391-395 (2011)
[27] Ho, G.; Bierman, R., Natural history of cervicovaginal papillomavirus infection in young women, N. Engl. J. Med., 338, 7, 423-428 (1998)
[28] Giuliano, A. R.; Lee, J.-H.; Fulp, W.; Villa, L. L.; Lazcano, E.; Papenfuss, M. R.; Abrahamsen, M.; Salmeron, J.; Anic, G. M.; Rollison, D. E.; Smith, D., Incidence and clearance of genital human papillomavirus infection in men (HIM): a cohort study., Lancet, 377, 9769, 932-940 (2011)
[29] Kreimer, A. R.; Campbell, C. M.P.; Lin, H.-Y.; Fulp, W.; Papenfuss, M. R.; Abrahamsen, M.; Hildesheim, A.; Villa, L. L.; Salmerón, J. J.; Lazcano-Ponce, E.; Giuliano, A. R., Incidence and clearance of oral human papillomavirus infection in men: the HIM cohort study, Lancet, 6736, 13, 1-11 (2013)
[30] Dushoff, J.; Levin, S., The effects of population heterogeneity on disease invasion, Math. Biosci., 128, 1-2, 25-40 (1995) · Zbl 0832.92019
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.