Aug 2026· Jagannath University Journal of Science· 0 citations· 20 references
TL;DR
The indispensable role of rigorous mathematical modeling is underscored in guiding dengue preparedness, optimizing control strategies, and strengthening epidemic response capacity in resource-limited settings by integrating epidemiological data with advanced numerical modeling.
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
Background Dengue is a major public health challenge, and predictive models are crucial for early warning systems. However, many current modeling practices rely exclusively on climatic factors or employ complex algorithms that lack the interpretability needed for informed public health decision-making. To address these shortcomings, we developed and validated a multidimensional, interpretable statistical model to predict monthly dengue incidence. Methodology/Principal Findings We used a Generalized Linear Mixed Model (GLMM) with a Negative Binomial distribution to analyze 14 years (2010-2023) of spatiotemporal data from 37 municipalities in Huila, Colombia, an endemic region. The model integrates non-linear and lagged effects of climatic, demographic, and socioeconomic factors. The final model underwent rigorous external validation on an independent test set (2021-2023). Our model demonstrated high predictive discrimination (R2 = 0.743, Spearman's {rho} = 0.657), accurately capturing the timing of epidemic outbreaks. Key findings include the identification of an optimal thermal window for transmission at 27-28{degrees}C, a threshold effect for precipitation above 800 mm, and a saturation dynamic in outbreak autocorrelation. Conclusions/Significance This mechanistically-informed statistical approach provides a robust and transparent tool for epidemiological surveillance, successfully balancing high predictive performance with the explanatory power needed for effective, data-driven public health interventions.
N. Luna-Martinez, E. X. Cruz-Rodríguez, E. A. Bernal-Castro· medRxiv· 0 citations
This study provides a practical, evidence-based tool for health authorities to prioritize interventions in at-risk hub cities by identifying vector control and the reduction of mosquito biting rates as the most critical factors influencing transmission dynamics of dengue.
Qi Tan, J. Wan, Cong Niu et al.· PLoS Neglected Tropical Dise...· 0 citations
Meningitis is a public health threat because it progresses rapidly and has serious clinical impacts, including long-term disability. This research develops a six-compartment mathematical model to examine the dynamics of meningitis transmission by dividing the population into susceptible, exposed, infected, recovered without disability, recovered with disability, and vaccinated groups. The model parameters were fitted using the least squares method based on annual meningitis case data in Indonesia from 1990 to 2023 according to estimates originating from the Institute for Health Metrics and Evaluation (IHME)/Global Burden of Disease, accessed through the archived Our World in Data source. Model validation shows high accuracy performance, with a Mean Absolute Percentage Error value of 3.12%. Local sensitivity analysis indicates that the transmission rate (\beta) and vaccination rate (\xi) are the parameters most influencing changes in R0 resulting from parameter variation. Numerical simulation results show that rapid immunization at the onset of an outbreak is the most effective strategy among the vaccination scenarios examined to expedite herd immunity and limit disease spread.
Aufa Al Musyarof, Faris Nur Hibban, M. Mardlijah et al.· Jambura Journal of Mathemati...· 0 citations
Mathematical modeling is a broad field that greatly impacts and contributes to collaborative research investigations. The models Improve research on the fundamental the quantitative attitude and dynamics of diseases that are infectious that harm humans, including COVID-19, human immunodeficiency virus (HIV), and hepatitis B virus. This paper
introduces a framework that supports the analysis of COVID-19 using an epidemic model that incorporates vaccination and treatment. The framework enables the examination of both non-pharmaceutical interventions and pharmaceutical interventions. The preservation of the basic reproduction number ensures the standardization of the stability of disease-free (DFE) and endemic equilibria. The local stability of the endemic and disease-free equilibria is proven using the Routh-Hurwitz criterion. The demonstration of disease-free and endemic equilibria convergence and divergence is demonstrated through the utilization of Standard and non-standard finite differences (SFD and NSFD, respectively) techniques.
It might be argued that SFD schemes, specifically Runge-Kutta order four (RK-4) and Euler schemes, demonstrate convergence at smaller step sizes. However, the NSFD scheme is intended to enhance understanding of the dynamic behavior of the continuous model. Empirical evidence demonstrates that the NSFD technique converges, irrespective of the chosen step size. The latter refers to a powerful, effective, and dependable technique
that provides a clear representation of the continuous model. Numerical simulations are employed to validate all the data, enhancing our understanding of the causes of the illness. The theoretical and quantitative results of its study can serve a valuable for mechanism tracking the transmission as to COVID-19.
Raed Hameed Mahdi, Shah Zeb, Ayesha Kamran et al.· Punjab University journal of...· 0 citations
Cruise ships, with their dense populations and constant passenger movement, present highly dynamic conditions for the spread of infectious diseases. Although strict health protocols and monitoring systems are widely implemented, their operational effectiveness often varies. In this study, we develop and analyze an improved Susceptible-Infected-Recovered (SIR) model using early outbreak data to characterize epidemic dynamics in cruise-ship environments. The proposed framework extends the classical SIR model by incorporating ship-specific factors such as transmission rates and confined-space contact structures. Building on this formulation, we introduce a new infection-risk index that quantifies the likelihood of disease transmission and serves as an early indicator of outbreak severity. To evaluate the model’s predictive performance and epidemiological relevance, we apply it to empirical data from the MS Voyager COVID-19 outbreak (2021) and an influenza outbreak (2014). Numerical simulations demonstrate that the enhanced model provides more accurate short-term forecasts and facilitates the identification of effective intervention strategies. These results highlight the value of SIR-based modeling approaches for assessing and mitigating epidemic risks in closed, mobile populations such as cruise ships.
Ahmed Abdelrazec, Ali Abu-Nada, Nathan Kawansson et al.· Discover Public Health· 0 citations
A SEIR model with logistic carrying capacity has previously been used to describe dengue infection dynamics, with stability established at a single fixed parameter set via Routh-Hurwitz analysis of the model's Jacobian. This paper extends that single-point stability result into a full sensitivity and stability landscape: a one-at-a-time normalized sensitivity analysis identifies which of the model's seven parameters most strongly influence peak infection severity, and a two-dimensional numerical eigenvalue sweep over carrying capacity K and transmission rate β traces the stability boundary separating locally stable and unstable regimes. The results show that peak infection is most sensitive to carrying capacity K and transmission rate β (both with normalized sensitivity indices above 1.2), and that the stability boundary in (K, β) space is a hyperbola-like curve, such that stability requires either high carrying capacity paired with low transmission, or the reverse — a trade-off not evident from the single-parameter-set analysis in the original model.
Dr. Amandeep Kaur· International Journal of Sci...· 0 citations
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