Abstract
Syphilis, an infection transmitted through sexual contact and attributed to the bacterium Treponema pallidum, remains a great public health challenge worldwide. We present a syphilis model with multi-phase treatments to study their impacts on the syphilis infection spread and control. The threshold which determines the spread and eradication of the syphilis is calculated. It is established that the syphilis-free equilibrium and endemic state for a special case are globally asymptotically stable when the reproduction numbers \(R_{o} < 1\) and \(\overline{R}_{o} > 1\) respectively. Furthermore, the sensitivity analysis conducted highlights the significance of the contact rate and rates of treating people with primary and secondary syphilis, indicating their pivotal role in influencing the transmission and management of the disease. The simulations are carried out using the ODE45 solver in MATLAB and results demonstrate that with the non-existence of treatment in the primary phase of the infection, treating those with secondary syphilis effectively reduces the disease burden. However, simultaneous treatment of people with secondary and primary syphilis and increasing the rates of treating them proves to be highly effective in diminishing the overall syphilis-infected population. Conclusively, the best strategy for alleviating the disease burden entails reducing contact rates and augmenting the rates of treating people with secondary and primary syphilis.
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References
Andrawus J, Eguda FY (2017) Mathematical analysis of a model for syphilis endemicity. Int J Sci Eng Appl Sci 3(8):48–72
Bandekar SR, Ghosh M (2022) Mathematical modeling of COVID-19 in India and its states with optimal control. Model Earth Syst Environ 8. https://doi.org/10.1007/s40808-021-01202-8
Bhadauria AS, Devi S, Gupta N (2022) Modelling and analysis of a SEIQR model on COVID-19 pandemic with delay. Model Earth Syst Environ 8:3201–3214. https://doi.org/10.1007/s40808-021-01279-1
Bonyah E, Chukwu CW, Juga ML, Fatmawati (2021) Modeling fractional order dynamics of Syphilis via Mittag-Leffler law. AIMS Mathematics 6(8):8367–8389
Castillo-Chavez C, Feng Z, Huang W (2002) On the computation of Ro and its role on global stability. In: Castillo-Chavez C, van den Driessche P, Kirschner D, Yakubu A-A (eds) Mathematical Approaches for Emerging and Re-emerging Infectious Diseases: An Introduction. Springer-Verlag, Berlin, pp 229–250
Centers for Disease Control and Prevention (CDC) (2021) National Overview of STDs https://www.cdc.gov/std/statistics/2021/overview.htm#Syphilis. Accessed 3 August 2023.
Centers for Disease Control and Prevention (CDC) (2022) Syphilis – CDC Fact Sheet. www.cdc.gov/std/syphilis/stdfact-syphilis.htm. Accessed 2 August 2023.
Centers for Disease Control and Prevention (CDC) (2023) Syphilis-Detailed Facts Sheet. https://www.cdc.gov/std/syphilis/stdfact-syphilis-detailed.htm. Accessed 7 August 2023.
Farman M, Shehzad A, Akgül A, Hincal E, Baleanu D (2023) El Din SM (2023) A fractal-fractional sex structured syphilis model with three stages of infection and loss of immunity with analysis and modeling. Results Phys 54:107098
Farman M, Nisar KS, Shehzad A, Baleanu D, Amjad A, Sultan F (2024) Computational analysis and chaos control of the fractional order syphilis disease model through modeling. Ain Shams Eng J. https://doi.org/10.1016/j.asej.2024.102743. (In press)
Feldman J, Mishra S (2019) What could re-infection tell us about R0? A modeling case-study of syphilis transmission. Infect Dis Model 4:257–264. https://doi.org/10.1016/j.idm.2019.09.002
Garnett GP, Aral SO, Hoyle DV, Cates W, Anderson RM (1997) The natural history of syphilis: implications for the transition dynamics and control of infection. Sex Transm Dis 24(4):185–200
Grassly C, Fraser C, Garnett GP (2005) Host immunity and synchronized epidemics of syphilis across the United States. Nature 433:417–421
Gulersen M, Lenchner E, Eliner Y, Grunebaum A, Johnson L, Chervenak FA, Bornstein E (2023) Risk factors and adverse outcomes associated with syphilis infection during pregnancy. Am J Obstet Gynecol MFM 5(6):100957. https://doi.org/10.1016/j.ajogmf.2023.100957
Iboi E, Okuonghae D (2016) Population dynamics of a mathematical model for syphilis. Appl Math Model 40:3573–3590
Jing W, Ma N, Liu W, Zhao Y (2021) The effect of public health awareness and behaviors on the transmission dynamics of syphilis in Northwest China, 2006–2018, based on a multiple-stages mathematical model. Infect Dis Model 6:1092–1109. https://doi.org/10.1016/j.idm.2021.08.009
LaSalle JP (1976) The stability of dynamical systems, CBMS-NSF Regional conference series in applied mathematics, SIAM, Philadelphia. https://doi.org/10.1137/1.9781611970432
Lorenz Z, Rybolt L, Ghanem KG, Shiroky-Kochavi J (2023) A patient with secondary syphilis following incomplete treatment of primary infection. Lancet Infect Dis 23(11):e497–e504. https://doi.org/10.1016/S1473-3099(23)00211-6
Masoumnezhad M, Rajabi M, Chapnevis A, Dorofeev A, Shateyi S, Kargar NS, Nik HS (2020) An approach for the global stability of mathematical model of an infectious disease. Symmetry 12(11):1778. https://doi.org/10.3390/sym12111778
Mbachu HI (2020) Mathematical modeling of the transmission dynamics of syphilis disease using differential transformation method. Math Model Appl 5(2):47–54. https://doi.org/10.11648/j.mma.20200502.11
Milner F, Zhao R (2010) A new mathematical model of syphilis. Math Model Nat Phenom 5(6):96–108. https://doi.org/10.1051/mmnp/20105605
Momoh AA, Bala Y, Washachi DJ (2021) Déthié D (2021) Mathematical analysis and optimal control interventions for sex structured syphilis model with three stages of infection and loss of immunity. Adv Differ Equ 1:1–26
Mwanga GG (2022) Mathematical modelling of syphilis transmission dynamics: impacts of mass media report, risky sexual behavior and treatment. Tanzania J Sci 48(1):196–211
Okuonghae D, Gumel AB, Ikhimwin BO, Iboi E (2018) Mathematical assessment of the role of early latent infections and targeted control strategies on syphilis transmission dynamics. Acta Biotheor 69(1):47–84
Oliveira GL, Ferreira AJ, Teles CA, Paixao ES, Fiaccone R, Lana R, Aquino R, Cardoso AM, Soares MA, Santos IO, Pereira M, Barreto ML, Ichihara MY (2023) Estimating the real burden of gestational syphilis in Brazil, 2007–2018: a Bayesian modeling study. Lancet Reg Health–Am 25:100564
Peeling RW, Mabey D, Chen X, Garcia PJ (2023) Syphilis. The Lancet 402(10398):336–346. https://doi.org/10.1016/S0140-6736(22)02348-0
Saad-Roy CM, Shuai Z, Van den Driessche P (2016) A mathematical model of syphilis transmission in an MSM population. Math Biosci 227:59–70
Spicknall IH, Kreisel KM, Weinstock HS (2021) Estimates of the prevalence and incidence of syphilis in the United States, 2018. Sex Transm Dis 48(4):247–325. https://doi.org/10.1097/OLQ.0000000000001364
Tudor ME, Al Aboud AM, Leslie SW, Gossman W (2023) Syphilis. In: StatPearl. Treasure Island (FL) StatPearls Publishing. https://www.ncbi.nlm.nih.gov/books/NBK534780/. Accessed 9 May 2024
Tuite AR, Testa C, Rönn M, Bellerose M, Gift T, Fridge J, Molotnikov L, Desmarais C, Berruti A, Menzies N, Malyuta Y, Hsu K, Salomon JA (2020) Exploring how epidemic context influences syphilis screening impact: a mathematical modeling study. Sex Transm Dis 47(12):798–810. https://doi.org/10.1097/OLQ.0000000000001249
Van den Driessche P, Watmough J (2002) Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci 180:29–48
Wong NS, Powers KA, Tucker JD, Lee SS, Goh BT, Zhao P, Chen L, Wang C, Yang LG (2020) Modelling the impact of a sex work crackdown on syphilis transmission among female sex workers and their clients in South China. Sex Transm Infect 0:1–7. https://doi.org/10.1136/sextrans-2020-054497
World Health Organization (2020) Syphilis Key facts. https://www.who.int/news-room/fact-sheets/detail/syphilis. Accessed 2 August 2023.
Zhang Y, Wang K, Zhu J, Wu J (2023) A network suspected infectious disease model for the development of syphilis transmission from 2015 to 2021 in Hubei province, China. J Appl Microbiol 134(12):lxad311. https://doi.org/10.1093/jambio/lxad311
Zhao T, Zhang Z, Jiao H, Liao Y (2023) Mathematical analysis of the transmission dynamics of syphilis in China. J Pure Appl Math 7(1):32–36
Zhu J, Takeh BT, David J, Sang J, Moore DM, Hull M, Grennan T, Wong J, Montaner JSG, Lima VD (2024) Impact of screening and doxycycline prevention on the syphilis epidemic among men who have sex with men in British Columbia: a mathematical modelling study. Lancet Reg Health Am 33:100725. https://doi.org/10.1016/j.lana.2024.100725
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Olopade, I., Ajao, S., Akinwumi, T. et al. Mathematical modelling of the impacts of syphilis multi-stage treatments. Model. Earth Syst. Environ. 10, 5489–5502 (2024). https://doi.org/10.1007/s40808-024-02075-3
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DOI: https://doi.org/10.1007/s40808-024-02075-3