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Assessing Syphilis transmission among MSM population incorporating low and high-risk infection: a modeling study

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Abstract

Globally, there is a high incidence of Syphilis among men who have sex with men (MSM). This is due to risk factors, such as having multiple partners, condomless sex, or substance abuse. In this paper, we present a mathematical model for Syphilis transmission dynamics among the MSM popion that incorporates high/low-risk transmission classes. The model equilibrium points and basic reproduction number (\(\mathcal {R}_{0}\)) are computed, and a bifurcation analysis is performed. Analytical results show that in the absence of infection-acquired immunity, the disease-free equilibrium is globally asymptotically stable when \(\mathcal {R}_{0}<1.\) Global sensitivity analysis was performed using the Latin-hypercube sampling technique to determine sensitive parameters. The results indicate that the most sensitive parameters are the high-risk transmission rate, progression rate from primary infection to secondary infection, human recruitment, and mortality rates. Results from numerical simulations suggest that increasing the Syphilis treatment rates and reducing high/low-risk infection rates is essential for controlling Syphilis spread in the MSM population. We envisage that our findings can serve as a tool for Syphilis risk assessment to help alleviate public health concerns associated with Syphilis transmission within the MSM population.

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Acknowledgements

The authors would like to thank our respective universities and the anonymous reviewers for their valuable comments, which helped strengthen our paper, and Dr. Binod Pant from Arizona State University for discussing and providing guidance on the model formulation.

Funding

This work is not supported by any funding.

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Authors and Affiliations

  1. Department of Mathematics, Wake Forest University, Winston-Salem, NC, 27109, USA

    Chidozie Williams Chukwu

  2. Department of Decision Sciences, College of Economic and Management Sciences, University of South Africa, Preller Street, Muckleneuk Ridge Pretoria, South Africa

    Zviiteyi Chazuka

  3. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, USA

    Salman Safdar

  4. Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok, 16424, Indonesia

    Iffatricia Haura Febriana & Dipo Aldila

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  1. Chidozie Williams Chukwu
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  4. Iffatricia Haura Febriana
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  5. Dipo Aldila
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Contributions

Conceptualization: CWC, modification: DA; formal analysis: DA, SS, and IHF; investigation: CWC and DA; writing—original draft: CWC, ZC, DA, and SS, numerical simulations: CWC, ZC, and DA, and editing: ZC, SS, and CWC. All authors agreed on the final version of the manuscript.

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Correspondence to Chidozie Williams Chukwu.

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Communicated by Carla M. A. Pinto.

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Appendices

Appendix A

The coefficients \(a_0,~ a_1,\) and \(a_2\) for the polynomial (13) are given below

$$\begin{aligned} a_0= & {} (1-\mathcal {R}_0) K {\xi }^{2} \left( \mu +\kappa \right) \left( \mu +\tau _{{3}} \right) \mu \, \left( \alpha +\mu \right) \left( \mu +\sigma +\tau _{{2}} \right) \left( \mu +\xi +\tau _{{1}} \right) \\{} & {} \left( \mu +\omega _{{1}}+\omega _{{2 }} \right) \left( \gamma +\mu \right) , \\ a_1= & {} -\xi ^{2} \left( \xi q_{1}+\mu +\sigma +\tau _{2}\right) \alpha \pi \beta _{l} \left( \mu +\kappa \right) \left( \mu +\tau _{3}\right) \left( \mu +\gamma \right) q_{2}-\xi \\{} & {} \left( \xi q_{1}+\mu +\sigma +\tau _{2}\right) \dots \\{} & {} \left[ \alpha \pi \left( \mu +\kappa \right) \left( \mu +\tau _{3}\right) \left( \tau _{2}+\mu +\sigma \right) \left( \mu +\gamma \right) \beta _{l} \dots \right. \\{} & {} -\mu \left( \left( \mu +\kappa \right) \left( \mu +\tau _{3}\right) \left( \tau _{2}+\mu +\sigma \right) \left( \tau _{1}+\mu +\xi \right) \left( \omega _{1}+\mu \right) \left( \mu +\gamma \right) \dots \right. \\{} & {} + \gamma \kappa \,\mu ^{2} \left( \omega _{1}+\tau _{1}+\tau _{2}+\tau _{3}+\mu +\sigma +\xi \right) + \gamma \kappa \mu \\{} & {} \left( \sigma \xi +\sigma \omega _{1}+\sigma \tau _{1}+\sigma \tau _{3}+\xi \omega _{1}+\xi \tau _{2}\right) \dots \\{} & {} + \gamma \kappa \mu \left( \xi \tau _{3}+\omega _{1} \tau _{2}+\omega _{1} \tau _{3}+\tau _{1} \tau _{2}+\tau _{1} \tau _{3}+\tau _{2} \tau _{3}\right) \dots \\{} & {} + \kappa \left( \left( \left( \xi +\sigma +\tau _{2}\right) \omega _{1}+\left( \sigma +\tau _{2}\right) \left( \xi +\tau _{1}\right) \right) \tau _{3}+\sigma \xi \omega _{1}\right) \gamma \dots \\{} & {} + \left. \left( \tau _{3}+\mu \right) \left( \tau _{2}+\mu +\sigma \right) \left( \tau _{1}+\mu +\xi \right) \left( \omega _{1}+\mu \right) \left( \gamma +\kappa +\mu \right) \right] .\\ a_2= & {} \beta _h(\mathcal {R}_0) \beta _l \mu (\xi q_1 + \mu + \sigma + \tau _2) (\xi q_2 + \mu + \sigma + \tau _2) \\{} & {} \left[ (\tau _3+\mu )(\tau _2+\mu +\sigma )((\alpha +\mu )(\alpha +\gamma +\mu )+\gamma \kappa )\tau _1 + (\mu +\xi )(\alpha +\mu )(\tau _3+\mu )\right. \\{} & {} \left. (\tau _2+\mu +\sigma )(\gamma +\mu ) \right. \\{} & {} + \kappa (\alpha +\mu )(\tau _3+\mu )(\tau _2+\mu +\sigma )(\gamma +\mu ) \\{} & {} +\left. \left. \xi (\tau _3+\mu )(\tau _2+\mu +\sigma )(\gamma +\mu ) + \xi \alpha ((\tau _3+\mu ) (\tau _2+\gamma +\mu +\sigma ) + \gamma \sigma )\right) \right] , \end{aligned}$$

with \(K = (\mu +\alpha ) (\mu +\xi +\tau _1)(\mu +\psi +\tau _2)\).

Appendix B

Table 3 Pairwise PRCC comparisons (unadjusted p values)
Full size table
Table 4 Pairwise PRCC comparisons (FDR-adjusted p values)
Full size table

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Chukwu, C.W., Chazuka, Z., Safdar, S. et al. Assessing Syphilis transmission among MSM population incorporating low and high-risk infection: a modeling study. Comp. Appl. Math. 43, 205 (2024). https://doi.org/10.1007/s40314-024-02669-8

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