Performance Analysis of SIR Model for Comparing to Classical Logistic Model

Abstract

Dengue fever has emerged as one of the most devastating vector-borne diseases in Bangladesh. Understanding the mechanisms driving transmission is therefore a scientific and public-health priority. This study presents a comprehensive and methodologically robust analysis of the 2023 dengue epidemic in Bangladesh by integrating epidemiological data with advanced numerical modeling. It formulates the transmission dynamics using the classical SIR (Susceptible–Infected–Recovered) framework and benchmark its performance against the logistic growth model, thereby revealing the fundamental differences between mechanistic and phenomenological approaches. Recognizing that the SIR system lacks a closed-form analytical solution, it employs a suite of high-accuracy numerical solvers—including Taylor’s Series Method, RK2, and RK4 to faithfully capture the nonlinear transmission process. Using real-world infection and mortality data from IEDCR (2023), it simulates reproduce the full epidemic arc with high fidelity, identifying the critical peak and the subsequent downturn induced by susceptible depletion and rising immunity. Comparative evaluation demonstrates that the logistic model, while useful for approximating cumulative trends, is structurally incapable of capturing core epidemic mechanisms. In contrast, the numerically solved SIR model delivers superior predictive realism, mechanistic transparency, and epidemiological interpretability. This work underscores the indispensable role of rigorous mathematical modeling in guiding dengue preparedness, optimizing control strategies, and strengthening epidemic response capacity in resource-limited settings. Jagannath University Journal of Science, Volume 12, Number 1, Jun. 2025, pp. 29−38