Work

Mathematical Modeling and Analysis of Trachoma Transmission Dynamics: Evaluating the Synergy of Mass Drug Administration and Adult‐Targeted Education

Year: 2026

Type: article

Abstract: Trachoma remains a leading cause of preventable blindness in many low‐resource settings, driven by persistent transmission within closely interacting age groups. In this study, we develop and analyze a nonlinear age‐structured compartmental model that captures the transmission dynamics of trachoma between children and adults. The model incorporates cross‐age infection pathways, demographic processes, and Holling Type‐II saturated incidence to reflect behavioral and environmental limitations on disease spread. We establish fundamental qualitative properties of the model, including positivity, boundedness, and well‐posedness of solutions. Using the next‐generation matrix approach, the basic reproduction number is derived and shown to govern the global dynamics of the system. Specifically, the disease‐free equilibrium is globally asymptotically stable when , whereas a unique endemic equilibrium exists and is globally asymptotically stable when . Furthermore, bifurcation analysis reveals the presence of a forward (transcritical) bifurcation at , indicating that disease elimination can be achieved through effective threshold reduction strategies. A comprehensive sensitivity analysis, based on Latin Hypercube Sampling and Partial Rank Correlation Coefficients (LHS‐PRCC), identifies transmission parameters—particularly child‐to‐child and adult‐to‐child contact rates—as the most influential drivers of disease spread, whereas recovery and mortality parameters play a significant mitigating role. Numerical simulations are conducted to evaluate the impact of intervention strategies. Results demonstrate that biannual mass drug administration (MDA) targeting children substantially reduces short‐term prevalence but fails to prevent long‐term resurgence when implemented in isolation. In contrast, adult‐targeted hygiene education reduces transmission intensity and lowers endemic levels. A combined intervention strategy yields a strong synergistic effect, significantly accelerating disease suppression and reducing long‐term prevalence. Taken together, the findings highlight the critical role of integrated control strategies that combine medical treatment with behavioral interventions. In particular, targeting adult‐mediated transmission pathways is essential for sustainable trachoma elimination and aligns with the WHO SAFE strategy.

Source: Journal of Applied Mathematics

DOI: 10.1155/jama/6131866

Authors: Berhe Nerea Kahsay, Teklebrhan Berehe Abraha, Tsegay Teklehaymanot Haftu

Institution: Aksum University

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

SDG: Good health and well-being

Open Access status: gold

Estimated APC paid: $1,130