Mathematical Modeling and Sensitivity Analysis of Trachoma Transmission Dynamics using a Six-Compartment Model
DOI:
https://doi.org/10.62054/ijdm/0302.18Abstract
Trachoma, caused by Chlamydia trachomatis, remains a leading infectious cause of blindness in many developing regions. Mathematical modeling provides a framework to quantify transmission dynamics and evaluate control strategies. In this study, we formulated a six-compartment deterministic model comprising of susceptible , exposed , infectious , recovered , trichiasis , and healed compartments to investigate the epidemiology of trachoma. The model incorporates frequency-dependent transmission, treatment, recovery, and natural death. Analytical results include derivation of the basic reproduction number (R0) using the Next Generation Matrix approach, determination of disease-free and endemic equilibria, and assessment of local stability using the Routh–Hurwitz criterion. Global stability of the disease-free equilibrium was established via the Castro–Chavez method. Sensitivity analysis identified the transmission rate () as the most influential parameter driving , whereas the recovery rate () exerts the strongest negative effect. Numerical simulations using the fourth-order Runge–Kutta method demonstrate the temporal dynamics of the infectious population, confirming the analytical results. Graphical analyses, including contour and 3D surface plots of , illustrate the threshold behavior, highlighting the critical interplay between transmission and recovery. These findings emphasize that integrated interventions combining transmission reduction (facial cleanliness and environmental sanitation) and effective treatment are required to reduce below unity, thereby achieving sustainable control and elimination of trachoma. This study provides quantitative insights to guide public health policies in trachoma-endemic regions
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Copyright (c) 2026 Agada A. Andrew, Washachi D. Jacob, Aliyu G. Dzarma, Aliyu G. Dzarma, Adejoh B. Sunday (Author)
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