Numerical Investigation of a Chlamydia Epidemic Model
DOI:
https://doi.org/10.11113/mjfas.v21n2.4085Keywords:
Chlamydia disease, mathematical model, reproductive number analysis, Euler, RK4, NSFD.Abstract
In this article, we analysed the numerical study of five compartmental epidemic model with Chlamydia infection. The population is divided into five classes: susceptible, exposed, infected in the asymptomatic phase, infected in the symptomatic phase and recovered (SEIAISR). This model was shown to have two equilibrium points: a disease-free equilibrium and an endemic equilibrium. The local stability was defined using the computed effective reproduction number R0, as well as the sensitivity of variables. When R0 < 1, the disease-free equilibrium ( ) is locally asymptotically stable, and if R0 > 1, the endemic equilibrium ( ) is locally asymptotically stable. This model is solved numerically using three numerical techniques: forward Euler, RK-4, and proposed non-standard finite difference (NSFD) techniques. The (NSFD) technique becomes a more efficient and reliable numerical technique than the forward Euler and RK-4 techniques. The NSFD technique retains all essential characteristics of a continuous (SEIAISR) chlamydia epidemic model, like positivity and stability of equilibria. In contrast, well-known forward Euler and RK-4 techniques cannot sustain these characteristics. Furthermore, the NSFD technique is independent of time step size, while forward Euler and RK-4 depend on the time step size. The numerical simulations with a numerical test were represented to validate all the results.
References
Sharma, S., & Samanta, G. P. (2014). Analysis of a Chlamydia epidemic model. Journal of Biological Systems, 22(4), 713–744.
Huai, P., Li, F., Chu, T., & et al. (2020). Prevalence of genital Chlamydia trachomatis infection in the general population: A meta-analysis. BMC Infectious Diseases, 20, 589.
Rönn, M. M., Wolf, E. E., Chesson, H., Menzies, N. A., Galer, K., Gorwitz, R., Gift, T., Hsu, K., & Salomon, J. A. (2017). The use of mathematical models of Chlamydia transmission to address public health policy questions: A systematic review. Sexually Transmitted Diseases, 44(5), 278–283.
Rodrigues, R., Silva, A. R., Sousa, C., & Vale, N. (2024). Addressing challenges in Chlamydia trachomatis detection: A comparative review of diagnostic methods. Medicina, 60(8), 1236.
Haque, M., McKimm, J., Sartelli, M., Dhingra, S., Labricciosa, F. M., Islam, S., Jahan, D., Nusrat, T., Chowdhury, T. S., Coccolini, F., Iskandar, K., Catena, F., & Charan, J. (2020). Strategies to prevent healthcare-associated infections: A narrative overview. Risk Management and Healthcare Policy, 13, 1765–1780.
Mangenah, C., Sibanda, E. L., Maringwa, G., Sithole, J., Gudukeya, S., Mugurungi, O., Hatzold, K., Terris-Prestholt, F., Maheswaran, H., Thirumurthy, H., & Cowan, F. M. (2024). Provider and female client economic costs of integrated sexual and reproductive health and HIV services in Zimbabwe. PLOS ONE, 19(2), e0291082.
Dukers-Muijrers, N. H. T. M., Evers, Y. J., Hoebe, C. J. P. A., et al. (2022). Controversies and evidence on Chlamydia testing and treatment in asymptomatic women and men who have sex with men: A narrative review. BMC Infectious Diseases, 22, 255.
Sahu, R. (2020). Immunogenicity and protective efficacy of chlamydial nano-encapsulated vaccine in mice. Alabama State University.
Abter, E. I., & Mahmud, M. A. (1996). Screening for chlamydia to prevent pelvic inflammatory disease. The New England Journal of Medicine, 335(20), 1531–1533.
McIntosh, E. D. G. (2020). Development of vaccines against the sexually transmitted infections gonorrhoea, syphilis, Chlamydia, herpes simplex virus, human immunodeficiency virus, and Zika virus. Therapeutic Advances in Vaccines and Immunotherapy, 8, 2515135520923887.
Zhu, J., Takeh, B. T., David, J., Sang, J., Moore, D. M., Hull, M., Grennan, T., Wong, J., Montaner, J. S. G., & Lima, V. D. (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. The Lancet Regional Health – Americas, 33, 100725.
Makhoul, M., Ayoub, H. H., Awad, S. F., Chemaitelly, H., & Abu-Raddad, L. J. (2024). Impact of a potential Chlamydia vaccine in the USA: Mathematical modelling analyses. BMJ Public Health, 2(1), e000345.
Ginters, E., Dumpis, U., Liñán, L. C., Eroles, M. A. P., Nazemi, K., Matvejevs, A., & Estrada, M. A. R. (2024). A paradigm for modeling infectious diseases: Assessing malware spread in early-stage outbreaks.
Poston, T. B. (2024). Advances in vaccine development for Chlamydia trachomatis. Pathogens and Disease, 82.
Shah, N. H., Vaghela, J. N., Pandya, P. M., & Shah, Y. N. (2022). Mathematical model for transmission of Chlamydia due to sexual activity and unhygienic environment. Exploration of Medicine, 375–385.
Smid, J., Althaus, C. L., & Low, N. (2019). Discrepancies between observed data and predictions from mathematical modelling of the impact of screening interventions on Chlamydia trachomatis prevalence. Scientific Reports, 9(1), 7547.
Wilson, D. P. (2004). Mathematical modelling of Chlamydia. ANZIAM Journal, 45, 201–214.
Adetunde, I. A., Koduah, M., Amporful, J. K., Dwummoh, A. S., Nyarko, P. K., Ennin, C. C., Appiah, S. T., & Oladejo, N. (2009). Epidemiology of Chlamydia bacteria infections — A review. Journal of American Science, 5(4), 55–64.
Mushayabasa, S. (2012). The epidemiological consequences of Chlamydia and gonorrhea coinfection: Insights from a mathematical model. International Journal of Applied Mathematics and Computation, 4(3), 295–306.
Xx Omori, R., Chemaitelly, H., Althaus, C. L., et al. (2019). Does infection with Chlamydia trachomatis induce long-lasting partial immunity? Insights from mathematical modelling. Sexually Transmitted Infections, 95(2), 115–121.
Althaus, C. L., Turner, K. M. E., Schmid, B. V., et al. (2012). Transmission of Chlamydia trachomatis through sexual partnerships: A comparison between three individual-based models and empirical data. Journal of the Royal Society Interface, 9(66), 136–146.
Guedri, K., Zarin, R., Makhdoum, B. M., Niyazi, H. A., & Khalifa, H. A. E.-W. (2025). Advanced mathematical modeling of syphilis transmission dynamics and disability outcomes in sex-structured populations. Modeling Earth Systems and Environment, 11(1). https://doi.org/10.1007/s40808-024-02218-6
Zeb, S., Mohd Yatim, S. A., Rafiq, M., Ahmad, W., Kamran, A., & Karim, M. F. (2024). Treatment and delay control strategy for a non-linear Rift Valley fever epidemic model. AIP Advances, 14(11).
Alsaadi, A., Raza, A., Riaz, M. B., & Shafique, U. (2025). Stability and computational analysis of Influenza-A epidemic model through double time delay. Alexandria Engineering Journal, 110, 64–76.
Shafique, U., Al-Shamiri, M. M., Raza, A., Fadhal, E., Rafiq, M., & Ahmed, N. (2024). Numerical analysis of bacterial meningitis stochastic delayed epidemic model through computational methods. Computer Modeling in Engineering & Sciences, 141(1), 311–329.
Shahid, N., Raza, A., Iqbal, S., et al. (2024). Stochastic delayed analysis of coronavirus model through efficient computational method. Scientific Reports, 14, 21170.
Butt, A. I. K., Rafiq, M., Ahmad, W., & Ahmad, N. (2023). Implementation of computationally efficient numerical approach to analyze a COVID-19 pandemic model. Alexandria Engineering Journal, 69, 341–362.
Raza, A., Awrejcewicz, J., Rafiq, M., & Mohsin, M. (2021). Breakdown of a nonlinear stochastic Nipah virus epidemic model through efficient numerical methods. Entropy, 23(12), 1588. https://doi.org/10.3390/e23121588
Raza, A., Arif, M. S., & Rafiq, M. (2019). A reliable numerical analysis for stochastic gonorrhea epidemic model with treatment effect. International Journal of Biomathematics, 12(6), 1950072. https://doi.org/10.1142/S1793524519500724
Raza, A., Arif, M. S., & Rafiq, M. (2019). A reliable numerical analysis for stochastic dengue epidemic model with incubation period of virus. Advances in Difference Equations, 2019(1), 32. https://doi.org/10.1186/s13662-019-1958-y
Metz, G., Thielmann, R. R., Roosjen, H., Stutterheim, S. E., & Crutzen, R. (2025). Systematic optimization and evaluation of a Dutch sexual health intervention: Role model stories for chlamydia prevention, testing, and treatment. Digital Health, 11. https://doi.org/10.1177/20552076241308447
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Copyright (c) 2025 Ayesha Kamran, Shah Zeb, Siti Ainor Mohd Yatim, Muhammad Rafiq
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