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Research Article | DOI: https://doi.org/ISSRR-RA-25-018

Analysis and Control of a Gonorrhea Dynamic Model

Lakshmi. N. Sridhar *

Chemical Engineering Department University of Puerto Rico Mayaguez,United States of America

*Corresponding Author: Lakshmi. N. Sridhar, Chemical Engineering Department University of Puerto Rico Mayaguez,United States of America

Citation: Lakshmi. N. Sridhar (2025). Analysis and control of a Dynamic Model Involving Students Anxiety towards Mathematics, J International Social Science Research and Review. 2 (3), DOI: ISSRR-RA-25-018.

Copyright: Lakshmi. N. Sridhar, et al © (2025). This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Received: 01 August 2025 | Accepted: 15 August 2025 | Published: 28 August 2025

Keywords: gonorrhea; optimization; bifurcation; control

Abstract

Gonorrhea is a serious global health problem with more than 80 million new cases in 2020.  It is possible for infants born to infected mothers to acquire the infection during the birthing process. In infants, it is not uncommon for gonorrhoea to affect the eyes.   It is necessary to understand the dynamics and develop strategies to be able to control the spread of this disease. In this work, bifurcation analysis and multiobjective nonlinear model predictive control (MNLMPC) calculations are performed on a gonorrhea transmission model. Bifurcation analysis is a powerful mathematical tool used to deal with the nonlinear dynamics of any process. The MATLAB program MATCONT was used to perform the bifurcation analysis. Several factors must be considered, and multiple objectives must be met simultaneously.  The MNLMPC calculations were performed using the optimization language PYOMO   in conjunction with the state-of-the-art global optimization solvers IPOPT and BARON. The bifurcation analysis revealed the existence of branch points in the model. The branch points were beneficial because they enabled the multiobjective nonlinear model predictive control calculations to converge to the Utopia point in both problems, which is the most beneficial solution.

References

  1. Lajmanovich, A. J.A. Yorke, A deterministic model for gonorrhea in a nonhomogeneous population, Math. Biosci. 28 (3–4) (1976) 221–236.
    View at Publisher | View at Google Scholar
  2. Hooper, R., G. Reynolds, O. Jones, A. Zaidi, P. Wiesner, K. Latimer, A. Lester, A. Campbell, W. Harrison, W. Karney, et al., Cohort study of venereal disease. I: the risk of gonorrhea transmission from infected women to men, Am. J. Epidemiol. 108 (2) (1978) 136–144.
    View at Publisher | View at Google Scholar
  3. Kretzschmar, M., Y.T. van Duynhoven, A.J. Severijnen, Modeling prevention strategies for gonorrhea and Chlamydia using stochastic network simulations, Am. J. Epidemiol. 144 (3) (1996) 306–317.
    View at Publisher | View at Google Scholar
  4. Garnett, G.P. , K.J. Mertz, L. Finelli, W.C. Levine, M.E. St Louis, The transmission dynamics of gonorrhoea: modelling the reported behaviour of infected patients from Newark, New Jersey, Philos. Trans. R. Soc. Lond. B, Biol. Sci. 354 (1384) (1999) 787–797.
    View at Publisher | View at Google Scholar
  5. Mushayabasa, S., J.M. Tchuenche, C.P. Bhunu, E. Ngarakana-Gwasira, Modeling gonorrhea and HIV co-interaction, Biosystems 103 (1) (2011) 27–37.
    View at Publisher | View at Google Scholar
  6. Hethcote, H. W., J.A. Yorke, Gonorrhea Transmission Dynamics and Control, vol. 56, Springer, 2014.
    View at Publisher | View at Google Scholar
  7. Chan, P. A., A. Robinette, M. Montgomery, A. Almonte, S. Cu-Uvin, J.R. Lonks, K.C. Chapin, E.M. Kojic, E.J. Hardy, Extragenital infections caused by Chlamydia trachomatis and Neisseria gonorrhoeae: a review of the literature, Infect. Dis. Obstet. Gynecol. 2016 (2016) 5758387.
    View at Publisher | View at Google Scholar
  8. Grad, Y.H. , E. Goldstein, M. Lipsitch, P.J. White, Improving control of antibiotic-resistant gonorrhea by integrating research agendas across disciplines: key questions arising from mathematical modeling, J. Infect. Dis. 213 (6) (2016) 883–890.
    View at Publisher | View at Google Scholar
  9. Oyeniyi, R. , E. Are, M. Ibraheem, Mathematical modelling of syphilis in a heterogeneous setting with complications, J. Niger. Math. Soc. 36 (3) (2017) 479–490.
    View at Publisher | View at Google Scholar
  10. Adamu, I.I. , S. Usman, et al., Mathematical model for the dynamics of Neisseria gonorrhea disease with natural immunity and treatment effects, J. Math. Res. 10 (2018) 151–165.
    View at Publisher | View at Google Scholar
  11. Gumel, A.B., J.M.-S. Lubuma, O. Sharomi, Y.A. Terefe, Mathematics of a sex-structured model for syphilis transmission dynamics, Math. Methods Appl. Sci. 41 (18) (2018) 8488–8513.
    View at Publisher | View at Google Scholar
  12. Bonyah, E., M. Khan, K. Okosun, J. Gómez-Aguilar, Modelling the effects of heavy alcohol consumption on the transmission dynamics of gonorrhea with optimal control, Math. Biosci. 309 (2019) 1–11.
    View at Publisher | View at Google Scholar
  13. Adediipo, A.D., J.O. Akanni, O.M. Shangodare, Bifurcation and stability analysis of the dynamics of gonorrhea disease in the population, World Sci. News 143 (2020) 139–154.
    View at Publisher | View at Google Scholar
  14. David, J.F., V.D. Lima, J. Zhu, F. Brauer, A co-interaction model of HIV and syphilis infection among gay, bisexual and other men who have sex with men, Infect. Dis. Model. 5 (2020) 855–870
    View at Publisher | View at Google Scholar
  15. Newman, L.M., M. Kankam, A. Nakamura, T. Conrad, J. Mueller, J. O’Donnell, B.L. Osborn, K. Gu, G.A. Saviolakis, Thorough QT study to evaluate the effect of zoliflodacin, a novel therapeutic for gonorrhea, on cardiac repolarization in healthy adults, Antimicrob. Agents Chemother. 65 (12) (2021) e0129221.
    View at Publisher | View at Google Scholar
  16. Asamoah, J.K.K., G.Q. Sun, Fractional Caputo and sensitivity heat map for a gonorrhea transmission model in a sex structured population, Chaos Solitons Fractals 175 (2023) 114026.
    View at Publisher | View at Google Scholar
  17. Asamoah, J.K.K. Beilawu Safianu, Emmanuel Afrifa, Benjamin Obeng, Baba Seidu, Fredrick Asenso Wireko, Gui-Quan Sun,Optimal control dynamics of Gonorrhea in a structured population, Heliyon,Volume 9, Issue 10, 2023, e20531,ISSN 2405-8440. https://doi.org/10.1016/j.heliyon.2023.e20531.
    View at Publisher | View at Google Scholar
  18. Dhooge, A., Govearts, W., and Kuznetsov, A. Y., MATCONT: “A Matlab package for numerical bifurcation analysis of ODEs”, ACM transactions on Mathematical software 29(2) pp. 141-164, 2003.
    View at Publisher | View at Google Scholar
  19. Dhooge, A.,W. Govaerts; Y. A. Kuznetsov, W. Mestrom, and A. M. Riet , “CL_MATCONT”; A continuation toolbox in Matlab, 2004.
    View at Publisher | View at Google Scholar
  20. Kuznetsov,Y.A. “Elements of applied bifurcation theory” .Springer,NY, 1998.
    View at Publisher | View at Google Scholar
  21. Kuznetsov,Y.A.(2009).”Five lectures on numerical bifurcation analysis” ,Utrecht University,NL., 2009.
    View at Publisher | View at Google Scholar
  22. Govaerts, w. J. F., “Numerical Methods for Bifurcations of Dynamical Equilibria”, SIAM, 2000.
    View at Publisher | View at Google Scholar
  23. Flores-Tlacuahuac, A. Pilar Morales and Martin Riveral Toledo; “Multiobjective Nonlinear model predictive control of a class of chemical reactors” . I & EC research; 5891-5899, 2012.
    View at Publisher | View at Google Scholar
  24. Hart, William E., Carl D. Laird, Jean-Paul Watson, David L. Woodruff, Gabriel A. Hackebeil, Bethany L. Nicholson, and John D. Siirola. “Pyomo – Optimization Modeling in Python” Second Edition. Vol. 67.
    View at Publisher | View at Google Scholar
  25. Wächter, A., Biegler, L. “On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming”. Math. Program. 106, 25–57 (2006). https://doi.org/10.1007/s10107-004-0559-y
    View at Publisher | View at Google Scholar
  26. Tawarmalani, M. and N. V. Sahinidis, “A polyhedral branch-and-cut approach to global optimization”, Mathematical Programming, 103(2), 225-249, 2005
    View at Publisher | View at Google Scholar
  27. Sridhar LN. (2024)Coupling Bifurcation Analysis and Multiobjective Nonlinear Model Predictive Control. Austin Chem Eng. 2024; 10(3): 1107.
    View at Publisher | View at Google Scholar
  28. Upreti, Simant Ranjan(2013); Optimal control for chemical engineers. Taylor and Francis.
    View at Publisher | View at Google Scholar
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