A Nonlinear Delay Mathematical Model for Predicting Chlamydia Dynamics and Intervention Effects - Zeb, Shah; Mohd Yatim, Siti Ainor; Kamran, Ayesha; Zulfiqar, Sabahat; Rafiq, Muhammad; Mohamad Noor, Nursyazwani (Communication in Biomathematical Sciences, 2025)
Chlamydia is a widespread sexually transmitted infection in Europe, often leading to complications such as rectal discomfort, throat inflammation, and reactive arthritis. This study presents a novel nonlinear delay differential equation model that enhances the classical SEIAISR framework to more accurately represent Chlamydia transmission dynamics. The model integrates biologically justified exponential time delays to reflect incubation periods and the delayed impact of interventions like condom use, routine screening, partner reduction, and microbiome health. We establish the existence and uniqueness of solutions using the Banach fixed point theorem and analyze the model’s dynamics by computing the basic reproduction number and studying equilibria and their stability via Lyapunov functions and Routh-Hurwitz criteria. A sensitivity analysis identifies key epidemiological drivers. For numerical simulation, we employ Euler’s method, the Runge-Kutta 4th order (RK4) method, and a specially developed non-standard finite difference (NSFD) scheme. The NSFD approach preserves critical properties such as positivity and stability, making it suitable for realistic long-term predictions. Results highlight the importance of timely interventions and show the superiority of structurepreserving numerical methods. The findings support the development of more targeted and effective strategies to reduce chlamydia transmission and complications among high-risk groups, reinforcing evidence-based decisionmaking within the healthcare system.