Nonlinear Dynamics and Sensitivity of R₀ to Epidemiological Parameters in a Structured Disease Model - Nwagor, Peters; Okoro, Joyce Adaobi; Igwe, Precious Yomi (Faculty of Natural and Applied Sciences Journal of Mathematical and Statistical Computing, 2025)
The understanding the role of asymptomatic carriers in disease transmission is critical for effective epidemic control. This study presents a compartmental SEIR-type model that explicitly incorporates carrier transmission through a dedicated exposed compartment and transmission coefficient β1. Using the Next Generation Matrix approach, the study derive an analytical expression for the basic reproduction number R0, evaluating its sensitivity to β1 and other key parameters. A parametric analysis was conducted by varying β1 while holding other parameters constant. The results reveal a nearly linear positive relationship between β1 and R0, confirmed through both linear and nonlinear regression models. The nonlinear model provided a slightly better fit, but the linear model remains interpretable and robust across the range of values analyzed. Sensitivity analysis further demonstrated that R0 is highly responsive to changes in carrier transmission compared to other parameters such as recovery rate (γ) and symptomatic transmission (β2). The findings in this study underscores the critical role of asymptomatic individuals in sustaining outbreaks and highlights the need for public health interventions which focused on early detection and isolation of carriers. This study contributes a mathematically grounded framework for evaluating carrier-driven transmission dynamics and provides actionable insights for epidemic modeling and control strategies.