A co-infection model for human papillomavirus (HPV) and syphilis with cost-effectiveness optimal control analysis is developed and presented. The full co-infection model is shown to undergo the phenomenon of backward bifurcation when a certain condition is satisfied. The global asymptotic stability of the disease-free equilibrium of the full model is shown not to exist when the associated reproduction number is less than unity. The existence of endemic equilibrium of the syphilis-only sub-model is shown to exist and the global asymptotic stability of the disease-free and endemic equilibria of the syphilis-only sub-model was established, for a special case. Sensitivity analysis is also carried out on the parameters of the model. Using the syphilis associated reproduction number, $ℛ_{0 s}$ $ℛ_{0 s}$ , as the response function, it is observed that the five-ranked parameters that drive the dynamics of the co-infection model are the demographic parameter $μ$ $μ$ , the effective contact rate for syphilis transmission, $β_{s}$ $β_{s}$ , the progression rate to late stage of syphilis $σ_{2}$ $σ_{2}$ , and syphilis treatment rates: $τ_{1}$ $τ_{1}$ and $τ_{2}$ $τ_{2}$ for co-infected individuals in compartments $H_{i}$ $H_{i}$ and $H_{l}$ $H_{l}$ , respectively. Moreover, when the HPV associated reproduction number, $ℛ_{0 h}$ $ℛ_{0 h}$ , is used as the response function, the five most dominant parameters that drive the dynamics of the model are the demographic parameter $μ$ $μ$ , the effective contact rate for HPV transmission, $β_{h}$ $β_{h}$ , the fraction of HPV infected who develop persistent HPV $ρ_{1}$ $ρ_{1}$ , the fraction of individuals vaccinated against incident HPV infection $ϕ$ $ϕ$ and the HPV vaccine efficacy $π_{h}$ $π_{h}$ . Numerical simulations of the optimal control model showed that the optimal control strategy which implements syphilis treatment controls for singly infected individuals is the most cost-effective of all the control strategies in reducing the burden of HPV and syphilis co-infections.

Keywords:

AMSC: 92B05

Remember to check out the Most Cited Articles in IJB!

Check out new Biomathematics books in our Mathematics 2018 catalogue!
Featuring author Frederic Y M Wan and more!

References

1. D. Aadland, D. Finnoff and K. Huang , Syphilis cycles, J. Econ. Financ. 13(1) (2013) 297–348. Google Scholar
2. World Health Organization, Eliminating congenital syphilis (2019), www.who.int/reproductive-health/stis/syphilis.html (accessed on August 6, 2019). Google Scholar
3. S. M. Berman , Maternal syphilis: Pathophysiology and treatment, Bull. World Health Organ. 82(6) (2004) 433–438. Web of Science, Google Scholar
4. H. G. Ahmed, S. H. Bensumaidea and I. M. Ashankyty , Frequency of human papillomavirus (HPV) subtypes 31, 33, 35, 39 and 45 among Yemeni women with cervical cancer, Infect. Ag. Cancer 10(29) (2015) 1–6. Google Scholar
5. D. Saslow, D. Solomon and H. W. Lawson , American Cancer Society, American Society for Colposcopy and Cervical Pathology, and American Society for Clinical pathology screening guidelines for the prevention and early detection of cervical cancer, Am. J. Clin. Pathol. 137 (2012) 516–542. Crossref, Web of Science, Google Scholar
6. P. van Damme, P. Bonanni, X. Bosch, E. Joura, S. K. Kjaer, C. J. L. M. Meijer, K-U. Petry, B. Soubeyrand, T. Verstraeten and M. Stanley , Use of the nonavalent HPV vaccine in individuals previously fully or partially vaccinated with bivalent or quadrivalent HPV vaccines, Vaccine 34 (2016) 757–761. Crossref, Web of Science, Google Scholar
7. L. M. S. Souza, W. M. Miller, J. A. C. Nery, A. F. B. de Andrade and M. D. Asensi , A syphilis co-infection study in human papilloma virus patients attended in the sexually transmitted infection ambulatory clinic, Santa Casa de Misericrdia Hospital, Rio de Janeiro, Brazil, Braz. J. Infect. Dis. 13(3) (2009) 207–209. Crossref, Web of Science, Google Scholar
8. X. Zhang, J. Yu, M. Li, X. Sun, Q. Han, M. Li, F. Zhou, X. Li, Y. Yang, D. Xiao, Y. Ruan, Q. Jin and L. Gao , Prevalence and related risk behaviors of HIV, syphilis, and anal HPV infection among men who have sex with men from Beijing, China, AIDS Behav. 17 (2013) 1129–1136. Crossref, Web of Science, Google Scholar
9. H.-F. Tseng, H. Morgenstern, T. M. Mack and R. K. Peters , Risk factors for anal cancer: Results of a population-based case: Control study, Cancer Causes Control 14 (2003) 837–846. Crossref, Web of Science, Google Scholar
10. J. R. Daling, N. S. Weiss, L. L. Klopfenstein, L. E. Cochran, W. H. Chow and R. Daifuku , Correlates of homosexual behaviour and the incidence of anal cancer. JAMA 247 (1982) 1988–1990. Crossref, Web of Science, Google Scholar
11. R. da Motta, R. D. Sperhacke, Ad-G. Adami, B. Pharma, S. K. Kato, A. C. Vanni, M. P. Paganella, M. C. P. de Oliveira, S. P. Giozza, A. R. C. da Cunha, G. F. M. Pereira and A. S. Benzaken , Syphilis prevalence and risk factors among young men presenting to the Brazilian Army in 2016, Medicine 97 (2018) 47. Crossref, Web of Science, Google Scholar
12. A. E. Miranda, N. C. Figueiredo, V. M. Pinto, P. Kimberly and S. Talhari , Risk factors for syphilis in young women attending a family health program in Vitria, Brazil, An. Bras. Dermatol. 87(1) (2012) 76–83. Crossref, Google Scholar
13. D. Okuonghae and A. Omame , Analysis of a mathematical model for COVID-19 population dynamics in Lagos, Nigeria, Chaos Soliton. Fract. 139 (2020) 110032. Crossref, Web of Science, Google Scholar
14. R. A. Umana, A. Omame and S. C. Inyama , Deterministic and stochastic models of the dynamics of drug resistant tuberculosis, FUTO J. Ser. 2(2) (2016) 173–194. Google Scholar
15. J. I. Uwakwe, S. C. Inyama and A. Omame , Mathematical model and optimal control of new-castle disease (ND), Appl. Comput. Math. 9(3) (2020) 70–84, https://doi.org/10.11648/j.acm.20200903.14. Crossref, Google Scholar
16. A. Omame and S. C. Inyama , Stochastic model and simulation of the prevalence of measles, Int. J. Math. Sci. Eng. 8(1) (2014) 311–323. Google Scholar
17. A. Omame and D. Okuonghae , A co-infection model for oncogenic human papillomavirus and tuberculosis with optimal control and cost-effectiveness analysis, Optim. Contr. Appl. Meth. (2021), https://doi.org/10.1002/oca.2717. Crossref, Web of Science, Google Scholar
18. G. P. Garnett, S. O. Aral, D. V. Hoyle, W. Cates and R. M. Anderson , The natural history of syphilis: Implications for the transition dynamics and control of infection, Sex Transm. Dis. 24(4) (1997) 185–200. Crossref, Web of Science, Google Scholar
19. C. Grassly, C. Fraser and G. P. Garnett , Host immunity and synchronized epidemics of syphilis across the United States, Nature 433 (2005) 417–421. Crossref, Web of Science, Google Scholar
20. E. Iboi and D. Okuonghae , Population dynamics of a mathematical model for syphilis, Appl. Math. Model. 40 (2016) 3573–3590. Crossref, Web of Science, Google Scholar
21. C. M. Saad-Roy, Z. Shuai and P. van den Driessche , A mathematical model of syphilis transmission in an MSM population, Math Biosci. 277 (2016) 59–70. Crossref, Web of Science, Google Scholar
22. D. Okuonghae, A. B. Gumel, B. O. Ikhimwin and E. Iboi , Mathematical assessment of the role of early latent infections and targeted control strategies on syphilis transmission dynamics. Acta Biotheor. 67 (2019) 47–84, https://doi.org/10.1007/s10441-018-9336-9. Crossref, Web of Science, Google Scholar
23. A. A. Alsaleh and A. B. Gumel , Analysis of a risk-structured vaccination model for the dynamics of oncogenic and warts-causing HPV types, Bull. Math. Biol. 76 (2014) 1670–1726. Crossref, Web of Science, Google Scholar
24. M. T. Malik, J. Reimer, A. B. Gumel, E. H. Elbasha and S. M. Mahmud , The impact of an imperfect vaccine and pap cytology screening on the transmission of Human Papillomavirus and occurrence of associated cervical dysplasia and cancer, Math. Biosci. Eng. 10(4) (2013) 1173–1205. Crossref, Web of Science, Google Scholar
25. F. Saldana, A. Korobeinikov and I. Barradas , Optimal control against the human papillomavirus: protection versus eradication of the infection, Abstr. Appl. Anal. 2019 (2019) 4567825, https://doi.org/10.1155/2019/4567825. Crossref, Google Scholar
26. T. Malik, M. Imran and R. Jayaraman , Optimal control with multiple human papillomavirus vaccines, J. Theor. Biol. 393 (2016) 179–193. Crossref, Web of Science, Google Scholar
27. A. Omame, R. A. Umana, D. Okuonghae and S. C. Inyama , Mathematical analysis of a two-sex Human Papillomavirus (HPV) model, Int. J. Biomath. 11(7) (2018) 1850092. Link, Web of Science, Google Scholar
28. A. Omame, D. OkuonghaE, R. A. Umana and S. C. Inyama , Analysis of a co-infection model for HPV-TB, Appl. Math. Model. 77 (2020) 881–901. Crossref, Web of Science, Google Scholar
29. A. Nwankwo and D. Okuonghae , Mathematical analysis of the transmission dynamics of HIV syphilis Co-infection in the presence of treatment for syphilis, Bull. Math. Biol. 80(3) (2018) 437–492. Crossref, Web of Science, Google Scholar
30. F. B. Agusto and A. I. Adekunle , Optimal control of a two-strain tuberculosis-HIV/AIDS co-infection model, BioSystems 119 (2014) 20–24. Crossref, Web of Science, Google Scholar
31. J. Andrawus, A. Nwankwo and D. Okuonghae , Bifurcation analysis of a mathematical model for TB-dengue co-infection, Nig. Res. J. Eng. Environ. Sci. 2(2) (2017) 390–407. Google Scholar
32. J. Andrawus, A. Nwankwo and D. Okuonghae , Population dynamics of a mathematical model for TB-dengue co-infection, Trans. Nig. Ass. Math. Phys. 5 (2017) 285–292. Google Scholar
33. E. Bonyah, M. A. Khan, K. O. Okosun and J. F. Gmez-Aguilar , On the co-infection of dengue fever and Zika virus, Optim. Contr. Appl. Meth. 40(3) (2019) 394–421. Crossref, Web of Science, Google Scholar
34. E. O. Alzahrani, W. Ahmad, M. A. Khan and S. J. Malebary , Optimal control strategies of Zika virus model with mutant, Comm. Nonlinear Sci. Numer. Simul. 93 (2021) 105532, https://doi.org/10.1016/j.cnsns.2020.105532. Crossref, Web of Science, Google Scholar
35. E. Bonyah and S. K. Asiedu , Analysis of a lymphatic filariasis-schistosomiasis coinfection with public health dynamics: Model obtained through Mittag-Leffler function, Discr Cont. Dyn. Sys. Ser. S 13(3) (2020) 519–537. Web of Science, Google Scholar
36. K. U. Egeonu, A. Omame and S. C. Inyama , A co-infection model for two-strain malaria and cholera with optimal control, Int. J. Dyn. Cont. (2021), https://doi.org/10.1007/s40435-020-00748-2. Crossref, Google Scholar
37. K. O. Okosun, M. A. Khan, E. Bonyah and O. O. Okosun , Cholera-schistosomiasis coinfection dynamics. Optim. Contr. Appl. Meth. 40(4) (2019) 703–727. Crossref, Web of Science, Google Scholar
38. A. Omame, N. Sene, I. Nometa, C. I. Nwakanma, E. U. Nwafor, N. O. Iheonu and D. Okuonghae, Analysis of COVID-19 and comorbidity co-infection model with optimal control, medRxiv preprint (2019), https://doi.org/10.1101/2020.08.04.20168013. Google Scholar
39. A. Omame, C. U. Nnanna and S. C. Inyama , Optimal control and cost-effectiveness analysis of an HPV-chlamydia trachomatis co-infection model, Acta Biotheor. (2021), https://doi.org/10.1007/s10441-020-09401-z. Crossref, Web of Science, Google Scholar
40. P. van den Driessche and J. Watmough , Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (2002) 29–48. Crossref, Web of Science, Google Scholar
41. C. Castillo-Chavez, Z. Feng and W. Huang , On the computation of $R_{0}$ $R_{0}$ and its role on global stability, in Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction, The IMA Volumes in Mathematics and its Applications, Vol. 125 (Springer, New York, 1999), pp. 229–250. Google Scholar
42. C. Castillo-Chavez and B. Song , Dynamical models of tuberculosis and their applications, Math. Biosci. Eng. 2 (2004) 361–404. Crossref, Web of Science, Google Scholar
43. M. Ghosh, S. Olaniyi and O. S. Obabiyi , Mathematical analysis of reinfection and relapse in malaria dynamics, Appl. Math. Comput. 373 (2020) 1–18. Web of Science, Google Scholar
44. R. A. Adams , Calculus: A Complete Course (Pearson Addison Wesley, Toronto, 2006). Google Scholar
45. J. La Salle and S. Lefschetz , The Stability of Dynamical Systems (SIAM, Philadelphia, 1976). Crossref, Google Scholar
46. Brazil Demographics Profile (2018), http://www.indexmundi.com/brazil/ demographics_profile (accessed on December 31, 2018). Google Scholar
47. 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) 229–243. Crossref, Web of Science, Google Scholar
48. F. Milner and R. Zhao , A new mathematical model of syphilis, Math. Model. Nat. Phenom. 5(6) (2010) 96–108. Crossref, Web of Science, Google Scholar
49. CDC, CDC Vaccine Price List, Vaccines for Children Program (VFC) (2015), http://www.cdc.gov/vaccines/programs/vfc/awardees/vaccine-management/price-list/. Google Scholar
50. J. G. Kahn, A. Jiwani, G. B. Gomez, S. J. Hawkes and H. W. Chesson , The cost and cost-effectiveness of scaling up screening and treatment of syphilis in pregnancy: A model, PLoS ONE 9(1) (2014) e87510, https://doi.org/10.1371/journal.pone.0087510. Crossref, Web of Science, Google Scholar
51. S. Lenhart and J. T. Workman , Optimal Control Applied to Biological Models (Chapman & Hall, Boca Raton, 2007). Crossref, Google Scholar
52. A. Omame, D. Okuonghae and S. C. Inyama , A mathematical study of a model for HPV with two high-risk strains, in Mathematics Applied to Engineering, Modelling, and Social Issues, Studies in Systems, Decision and Control, eds. F. Smith, H. Dutta and J. N. Mordeson , Vol. 200 (Springer, Singapore, 2020) 107–149. Google Scholar
53. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko , The Mathematical Theory of Optimal Processes (Wiley, New York, 1962). Google Scholar
54. C. C. Soares, I. George, E. Lampe, L. Lewis and M. G. Morgado , HIV-1, HBV, HCV, HTLV, HPV-16/18, and Treponema pallidum infections in a sample of Brazilian men who have sex with men, PLoS ONE 9(8) (2014) e102676, https://doi.org/10.1371/journal.pone.0102676. Crossref, Web of Science, Google Scholar

Vol. 14, No. 07

Metrics

Downloaded 29 times

History

Received 13 March 2020

Accepted 4 March 2021

Published: 17 April 2021

Keywords

PDF download

System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

A co-infection model for HPV and syphilis with optimal control and cost-effectiveness analysis

Abstract

References

Mathematical analysis of a two-sex Human Papillomavirus (HPV) model

Optimal control application to the epidemiology of HBV and HCV co-infection

Stability analysis and optimal control of an epidemic model with vaccination

GLOBAL DYNAMICS, OPTIMAL CONTROL AND COST-EFFECTIVENESS ANALYSIS FOR ANTHRAX TRANSMISSION MODEL IN ANIMAL POPULATIONS WITH VACCINATION AND SANITATION

Optimal control of intervention strategies in malaria–tuberculosis co-infection with relapse

OPTIMAL CONTROL AND COST-EFFECTIVE ANALYSIS OF A SCABIES MODEL WITH DIRECT AND INDIRECT TRANSMISSIONS

DYNAMICS ANALYSIS OF A VACCINATION MODEL FOR HPV TRANSMISSION

Multiple control strategies against human papilloma virus spread: A mathematical model