# American Institute of Mathematical Sciences

March  2014, 19(2): 447-466. doi: 10.3934/dcdsb.2014.19.447

## Cost-effectiveness evaluation of gender-based vaccination programs against sexually transmitted infections

 1 Mprime Centre for Disease Modelling, York Institute of Health Research, Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada, Canada 2 Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China 3 Medical advisor, Direction des risques biologiques et de la santé au travail, Institut national de santé publique du Québec, Montréal, Canada

Received  April 2013 Revised  October 2013 Published  February 2014

The ultimate goal of a vaccination program is to interrupt pathogen transmission so as to eradicate the disease from the population in the future, and/or to decrease morbidity and mortality due to the disease in the short term. For sexually transmitted infections (STI) the determination of an optimal vaccination program is not straightforward since (1) the transmission probabilities between two different sexes are normally unequal (weighted to a greater probability from males to females than vice versa), (2) demographic parameters between the two sexes are unequal, (3) the prevalence of disease in one sex may have a greater impact on the morbidity and mortality of the next generation (transmission to the neonate) and, (4) the existence of pathogens closely related to the STI in question (i.e. herpes - HSV-1 vs. HSV-2, different strains of Chlamydia trachomatis, different strains of Neisseria which cause Gonorrhea, and others) may induce immunity in individuals that render a vaccine ineffective.
We have developed two models of sexually transmitted infections (with and without age structure) to evaluate the cost-efficacy of gender-based vaccination programs in the context of STI control. The first model ignores age structure for qualitative analysis of points (1-3), while the second refined one incorporates the age structure, reflecting the effects of immunity gained from infection of closely related strains (point 4), which is important for HSV-2 vaccination strategies. For both models, we find that the stability of the system and ultimate eradication of the disease depends explicitly on the corresponding reproduction number. We also find that vaccinating females is more cost-effective, providing a greater reduction in disease prevalence in the population and number of infected females of childbearing age. This result is counter-intuitive since vaccinating super-transmitters (males) over sub-transmitters (females) usually has the greatest impact on disease prevalence. Sensitivity analysis is implemented to investigate how the parameters affect the control reproduction numbers and infectious population sizes.
Citation: Jane M. Heffernan, Yijun Lou, Marc Steben, Jianhong Wu. Cost-effectiveness evaluation of gender-based vaccination programs against sexually transmitted infections. Discrete & Continuous Dynamical Systems - B, 2014, 19 (2) : 447-466. doi: 10.3934/dcdsb.2014.19.447
##### References:
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Infect. Dis., 167 (1993), 942. doi: 10.1093/infdis/167.4.942. Google Scholar [6] Centers for Disease Control and Prevention, Tracing the hidden epidemics: Trends in STIs in the United States,, 2000., (). Google Scholar [7] M. S. Cohen, Sexually transmitted diseases enhance HIV transmission: No longer a hypothesis,, Lancet, 351 (1998), 5. doi: 10.1016/S0140-6736(98)90002-2. Google Scholar [8] R. Cohen, S. Havlin and D. ben-Avraham, Efficient immunization strategies for computer networks and populations,, Phys. Rev. Lett., 91 (2003). doi: 10.1103/PhysRevLett.91.247901. Google Scholar [9] M. E. Craft and D. Caillaud, Network Models: An Underutilized Tool in Wildlife Epidemiology,, Interdiscip. Perspect. Infect. Dis., 2011 (2011). doi: 10.1155/2011/676949. Google Scholar [10] O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio $R_0$ in models for infectious diseases,, J. Math. Biol., 28 (1990), 365. doi: 10.1007/BF00178324. Google Scholar [11] E. H. Elbasha and A. B. Gumel, Theoretical assessment of public health impact of imperfect prophylactic HIV-1 vaccines with therapeutic benefits,, Bull. Math. Biol., 68 (2006), 577. doi: 10.1007/s11538-005-9057-5. Google Scholar [12] D. T. Fleming, G. M. McQuillan, R. E. Johnson, A. J. Nahmias, S. O. Aral, F. K. Lee and M. E. St. Louis, Herpes Simplex Virus Type 2 in the United States, 1976 to 1994,, New. Engl. J. Med., 53 (1998), 134. doi: 10.1097/00006254-199803000-00003. Google Scholar [13] G. P. Garnett, G. Dubin and M. Slaoui, The potential epidemiological impact of a genital herpes vaccine for women,, Sex. Transm. Infect., 80 (2004), 24. doi: 10.1136/sti.2002.003848. Google Scholar [14] J. M. Heffernan, R. J. Smith and L. M. Wahl, Perspectives on the basic reproductive ratio,, J. R. Soc. Interface, 2 (2005), 281. doi: 10.1098/rsif.2005.0042. Google Scholar [15] J. P. Hughes, G. P. Garnett and L. Koutsky, The theoretical population-level impact of a prophylactic human papilloma virus vaccine,, Epidemiology, 13 (2002), 631. doi: 10.1097/00001648-200211000-00006. Google Scholar [16] [17] [18] [19] M. Lipsitch, T. H. Bacon, J. J. Leary, R. Antia and B. R. Levin, Effects of antiviral usage on transmission dynamics of herpes simplex virus type 1 and on antiviral resistance: predictions of mathematical models,, Antimicrob Agents Chemother, 44 (2000), 2824. doi: 10.1128/AAC.44.10.2824-2835.2000. Google Scholar [20] M. Llamazares and R. J. Smith?, Evaluating human papillomavirus vaccination programs in Canada: Should provincial healthcare pay for voluntary adult vaccination?, BMC Public Health, 8 (2008). doi: 10.1186/1471-2458-8-114. Google Scholar [21] Y. Lou, R. Qesmi, Q. Wang, M. Steben, J. Wu and J. Heffernan, Epidemiological Impact of a Genital Herpes Type 2 Vaccine for Young Females,, PLoS ONE, 7 (2012). doi: 10.1371/journal.pone.0046027. Google Scholar [22] M. V. Maciosek, A. B. Coffield, N. M. Edwards, T. J. Flottemesch, M. J. Goodman and L. I. Solberg, Priorities among effective clinical preventive services: results of a systematic review and analysis,, Am. J. Prev. Med., 31 (2006), 52. Google Scholar [23] S. Marino, I. B. Hogue, C. J. Ray and D. E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology,, J. Theor. Biol., 254 (2008), 178. doi: 10.1016/j.jtbi.2008.04.011. Google Scholar [24] P. Mayaud, S. Hawkes and D. Mabey, Advances in control of sexually transmitted diseases in developing countries,, Lancet, 351 (1998), 29. doi: 10.1016/S0140-6736(98)90009-5. Google Scholar [25] G. J. Mertz, J. Benedetti, R. Ashley, S. A. Selke and L. Corey, Risk factors for the sexual transmission of genital herpes,, Ann. Intern. Med., 116 (1992), 197. doi: 10.7326/0003-4819-116-3-197. Google Scholar [26] A. J. Nahmias, F. K. Lee and S. Beckman-Nahmias, Sero-epidemiological and sociological patterns of herpes simplex virus infection in the world,, Scand. J. Infect. Dis. Suppl., 69 (1990), 19. Google Scholar [27] D. M. Patrick, M. Dawar, D. A. Cook, M. Krajden, H. C. Ng and M. L. Rekart, Antenatal seroprevalence of herpes simplex virus type 2 (HSV-2) in Canadian Women: HSV-2 Prevalence increases throughout the reproductive years,, Sex. Transm. Dis., 28 (2001), 424. doi: 10.1097/00007435-200107000-00011. Google Scholar [28] C. N. Podder and A. B. Gumel, Qualitative dynamics of a vaccination model for HSV-2,, IMA J. Appl. Math., 75 (2010), 75. doi: 10.1093/imamat/hxp030. Google Scholar [29] C. Podder and A. B. Gumel, Transmission dynamics of a two-sex model for herpes simplex virus Type II,, Can. Appl. Math. Q., 17 (2009), 339. Google Scholar [30] Public Health Agency of Canada, Genital herpes simplex virus (HSV) infections,, January 2008., (2008). Google Scholar [31] N. R. Roan and M. N. Starnbach, Conquering sexually transmitted diseases,, Nat. Rev. Immunol., 8 (2008), 313. Google Scholar [32] E. J. Schwartz and S. Blower, Predicting the potential individual- and population-level effects of imperfect herpes simplex virus type 2 vaccines,, J. Infect. Dis., 191 (2005), 1734. doi: 10.1086/429299. Google Scholar [33] D. Siegel, E. Golden, A. E. Washington, S. A. Morse, M. T. Fullilove, J. A. Catania, B. Marin and S. B. Hulley, Prevalence and correlates of herpes simplex infections: the population-based AIDs in multiethnic neighborhood study,, JAMA, 268 (1992), 1702. doi: 10.1001/jama.1992.03490130090036. Google Scholar [34] L. R. Stanberry, S. L. Spruance, A. L. Cunningham, D. I. Bernstein, A. Mindel, S. Sacks, S. Tyring, F. Y. Aoki, M. Slaoui, M. Denis, P. Vandepapeliere and G. Dubin, Glycoprotein-Dadjuvant vaccine to prevent genital herpes,, New. Engl. J. Med., 347 (2002), 1652. Google Scholar [35] H. R. Thieme, Convergence results and a Poincare-Bendixson trichotomy for asymptotically autonomous differential equations,, J. Math. Biol., 30 (1992), 755. doi: 10.1007/BF00173267. Google Scholar [36] P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,, Math. Biosci., 180 (2002), 29. doi: 10.1016/S0025-5564(02)00108-6. Google Scholar [37] R. J. Whitley and J. W. Gnann, The epidemiology and clinical manifestations of herpes simplex virus infections,, In The Human Herpesviruses, (1993). Google Scholar [38] F. Xu, M. R. Sternberg, B. J. Kottiri, G. M. McQuillan, F. K. Lee, A. J. Nahmias, S. M. Berman and L. E. Markowitz, Trends in herpes simplex virus type 1 and type 2 seroprevalence in the United States,, J. Am. Med. Assoc., 296 (2006), 964. doi: 10.1001/jama.296.8.964. Google Scholar [39] X.-Q. Zhao, Dynamical Systems in Population Biology,, Springer-Verlag, (2003). Google Scholar [40] X.-Q. Zhao and Z. Jing, lobal asymptotic behavior in some cooperative systems of functional-differential equations,, Can. Appl. Math. Q., 4 (1996), 421. Google Scholar

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##### References:
 [1] American Social Health Association, Oral Herpes,, Available at , (). Google Scholar [2] R. M. Anderson, J. Swinton and G. P. Garnett, Potential impact of low efficacy HIV-1 vaccines in populations with high rates of infection,, Proc. R. Soc. Lond. B, 261 (1995), 147. doi: 10.1098/rspb.1995.0129. Google Scholar [3] S. M. Blower and H. Dowlatabadi, Sensitivity and uncertainty analysis of complex models of disease transmission: An HIV model as an example,, Int. Stat. Rev., 2 (1994), 229. doi: 10.2307/1403510. Google Scholar [4] V. L. Brown and K. A. J. White, The role of optimal control in assessing the most cost-effective implementation of a vaccination strategy: HPV as a case study,, Math. Biosci., 231 (2011), 126. doi: 10.1016/j.mbs.2011.02.009. Google Scholar [5] Y. Bryson, M. Dillon, D. I. Bernstein, J. Radolf, P. Zakowski and E. Garratty, Risk of acquisition of genital herpes simplex virus type 2 in sex partners of persons with genital herpes: A prospective couple study,, J. Infect. Dis., 167 (1993), 942. doi: 10.1093/infdis/167.4.942. Google Scholar [6] Centers for Disease Control and Prevention, Tracing the hidden epidemics: Trends in STIs in the United States,, 2000., (). Google Scholar [7] M. S. Cohen, Sexually transmitted diseases enhance HIV transmission: No longer a hypothesis,, Lancet, 351 (1998), 5. doi: 10.1016/S0140-6736(98)90002-2. Google Scholar [8] R. Cohen, S. Havlin and D. ben-Avraham, Efficient immunization strategies for computer networks and populations,, Phys. Rev. Lett., 91 (2003). doi: 10.1103/PhysRevLett.91.247901. Google Scholar [9] M. E. Craft and D. Caillaud, Network Models: An Underutilized Tool in Wildlife Epidemiology,, Interdiscip. Perspect. Infect. Dis., 2011 (2011). doi: 10.1155/2011/676949. Google Scholar [10] O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio $R_0$ in models for infectious diseases,, J. Math. Biol., 28 (1990), 365. doi: 10.1007/BF00178324. Google Scholar [11] E. H. Elbasha and A. B. Gumel, Theoretical assessment of public health impact of imperfect prophylactic HIV-1 vaccines with therapeutic benefits,, Bull. Math. Biol., 68 (2006), 577. doi: 10.1007/s11538-005-9057-5. Google Scholar [12] D. T. Fleming, G. M. McQuillan, R. E. Johnson, A. J. Nahmias, S. O. Aral, F. K. Lee and M. E. St. Louis, Herpes Simplex Virus Type 2 in the United States, 1976 to 1994,, New. Engl. J. Med., 53 (1998), 134. doi: 10.1097/00006254-199803000-00003. Google Scholar [13] G. P. Garnett, G. Dubin and M. Slaoui, The potential epidemiological impact of a genital herpes vaccine for women,, Sex. Transm. Infect., 80 (2004), 24. doi: 10.1136/sti.2002.003848. Google Scholar [14] J. M. Heffernan, R. J. Smith and L. M. Wahl, Perspectives on the basic reproductive ratio,, J. R. Soc. Interface, 2 (2005), 281. doi: 10.1098/rsif.2005.0042. Google Scholar [15] J. P. Hughes, G. P. Garnett and L. Koutsky, The theoretical population-level impact of a prophylactic human papilloma virus vaccine,, Epidemiology, 13 (2002), 631. doi: 10.1097/00001648-200211000-00006. Google Scholar [16] [17] [18] [19] M. Lipsitch, T. H. Bacon, J. J. Leary, R. Antia and B. R. Levin, Effects of antiviral usage on transmission dynamics of herpes simplex virus type 1 and on antiviral resistance: predictions of mathematical models,, Antimicrob Agents Chemother, 44 (2000), 2824. doi: 10.1128/AAC.44.10.2824-2835.2000. Google Scholar [20] M. Llamazares and R. J. Smith?, Evaluating human papillomavirus vaccination programs in Canada: Should provincial healthcare pay for voluntary adult vaccination?, BMC Public Health, 8 (2008). doi: 10.1186/1471-2458-8-114. Google Scholar [21] Y. Lou, R. Qesmi, Q. Wang, M. Steben, J. Wu and J. Heffernan, Epidemiological Impact of a Genital Herpes Type 2 Vaccine for Young Females,, PLoS ONE, 7 (2012). doi: 10.1371/journal.pone.0046027. Google Scholar [22] M. V. Maciosek, A. B. Coffield, N. M. Edwards, T. J. Flottemesch, M. J. Goodman and L. I. Solberg, Priorities among effective clinical preventive services: results of a systematic review and analysis,, Am. J. Prev. Med., 31 (2006), 52. Google Scholar [23] S. Marino, I. B. Hogue, C. J. Ray and D. E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology,, J. Theor. Biol., 254 (2008), 178. doi: 10.1016/j.jtbi.2008.04.011. Google Scholar [24] P. Mayaud, S. Hawkes and D. Mabey, Advances in control of sexually transmitted diseases in developing countries,, Lancet, 351 (1998), 29. doi: 10.1016/S0140-6736(98)90009-5. Google Scholar [25] G. J. Mertz, J. Benedetti, R. Ashley, S. A. Selke and L. Corey, Risk factors for the sexual transmission of genital herpes,, Ann. Intern. Med., 116 (1992), 197. doi: 10.7326/0003-4819-116-3-197. Google Scholar [26] A. J. Nahmias, F. K. Lee and S. Beckman-Nahmias, Sero-epidemiological and sociological patterns of herpes simplex virus infection in the world,, Scand. J. Infect. Dis. Suppl., 69 (1990), 19. Google Scholar [27] D. M. Patrick, M. Dawar, D. A. Cook, M. Krajden, H. C. Ng and M. L. Rekart, Antenatal seroprevalence of herpes simplex virus type 2 (HSV-2) in Canadian Women: HSV-2 Prevalence increases throughout the reproductive years,, Sex. Transm. Dis., 28 (2001), 424. doi: 10.1097/00007435-200107000-00011. Google Scholar [28] C. N. Podder and A. B. Gumel, Qualitative dynamics of a vaccination model for HSV-2,, IMA J. Appl. Math., 75 (2010), 75. doi: 10.1093/imamat/hxp030. Google Scholar [29] C. Podder and A. B. Gumel, Transmission dynamics of a two-sex model for herpes simplex virus Type II,, Can. Appl. Math. Q., 17 (2009), 339. Google Scholar [30] Public Health Agency of Canada, Genital herpes simplex virus (HSV) infections,, January 2008., (2008). Google Scholar [31] N. R. Roan and M. N. Starnbach, Conquering sexually transmitted diseases,, Nat. Rev. Immunol., 8 (2008), 313. Google Scholar [32] E. J. Schwartz and S. Blower, Predicting the potential individual- and population-level effects of imperfect herpes simplex virus type 2 vaccines,, J. Infect. Dis., 191 (2005), 1734. doi: 10.1086/429299. Google Scholar [33] D. Siegel, E. Golden, A. E. Washington, S. A. Morse, M. T. Fullilove, J. A. Catania, B. Marin and S. B. Hulley, Prevalence and correlates of herpes simplex infections: the population-based AIDs in multiethnic neighborhood study,, JAMA, 268 (1992), 1702. doi: 10.1001/jama.1992.03490130090036. Google Scholar [34] L. R. Stanberry, S. L. Spruance, A. L. Cunningham, D. I. Bernstein, A. Mindel, S. Sacks, S. Tyring, F. Y. Aoki, M. Slaoui, M. Denis, P. Vandepapeliere and G. Dubin, Glycoprotein-Dadjuvant vaccine to prevent genital herpes,, New. Engl. J. Med., 347 (2002), 1652. Google Scholar [35] H. R. Thieme, Convergence results and a Poincare-Bendixson trichotomy for asymptotically autonomous differential equations,, J. Math. Biol., 30 (1992), 755. doi: 10.1007/BF00173267. Google Scholar [36] P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,, Math. Biosci., 180 (2002), 29. doi: 10.1016/S0025-5564(02)00108-6. Google Scholar [37] R. J. Whitley and J. W. Gnann, The epidemiology and clinical manifestations of herpes simplex virus infections,, In The Human Herpesviruses, (1993). Google Scholar [38] F. Xu, M. R. Sternberg, B. J. Kottiri, G. M. McQuillan, F. K. Lee, A. J. Nahmias, S. M. Berman and L. E. Markowitz, Trends in herpes simplex virus type 1 and type 2 seroprevalence in the United States,, J. Am. Med. Assoc., 296 (2006), 964. doi: 10.1001/jama.296.8.964. Google Scholar [39] X.-Q. Zhao, Dynamical Systems in Population Biology,, Springer-Verlag, (2003). Google Scholar [40] X.-Q. Zhao and Z. Jing, lobal asymptotic behavior in some cooperative systems of functional-differential equations,, Can. Appl. Math. Q., 4 (1996), 421. Google Scholar
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