Tracking the Rhythm of Heat: Seasonal SEIR Modelling and Machine Learning for Heat Wave Forecasting.

Heatwaves pose serious risks to human health, infrastructure, and the environment, with rising frequency, intensity, and duration linked to increased morbidity and mortality – particularly among vulnerable populations. While numerous studies have analyzed heatwaves statistically, few have applied mechanistic modeling. In this study, we extend the classical SEIR framework by introducing a temperature-dependent transmission function ϕ(T) to model heatwave impacts on disease dynamics in Dhaka, Bangladesh. Seasonal forcing was incorporated via sinusoidal modulation of the reproduction number R_0, capturing oscillatory behavior driven by annual temperature cycles. Analytical derivations identified two equilibria – Heat Impacted Free Equilibrium (HIFE) and Heat-Impacted Equilibrium (HIE) – representing heatwave-free and heatwave-endemic states. To evaluate model robustness, we performed local sensitivity and Partial Rank Correlation Coefficient (PRCC) analyses, identifying transmission rate (β) and progression rate (γ) as the most influential parameters. Simulations revealed that higher β and faster progression (γ) amplified outbreak size, whereas increased recovery (α) and reduced immunity loss (σ) substantially mitigated transmission and delayed epidemic peaks. These findings underscore that if β>α, outbreaks expand rapidly, but when α≥β, the system stabilizes near equilibrium. Complementing the mechanistic approach, meteorological data (January 2014 – February 2024) were analyzed using statistical tools and machine learning models, including Logistic Regression, SVM, and ensemble regressors. Logistic Regression achieved 95.8% accuracy, while SVM yielded the highest cross-validation score (0.9311) and AUC (0.9972). XGBRegressor provided robust short-term temperature forecasts, whereas Decision Trees offered smoother long-term projections. Taken together, these results demonstrate that integrating temperature-modulated SEIR modeling with machine learning provides a comprehensive framework for predicting heat-related morbidity, identifying early-warning thresholds, and informing public health preparedness under climate variability.