MATHEMATICAL MODELING OF EPIDEMIC DYNAMICS WITH STOCHASTIC AI PREDICTION MODELS

Abstract

Epidemic modeling has long relied on deterministic approaches such as the SIR and SEIR frameworks, which assume uniform transmission dynamics and neglect stochastic fluctuations arising from real-world variability. However, infectious disease spread is inherently uncertain affected by random contact patterns, environmental factors, and behavioral dynamics. This study presents a hybrid stochastic–AI framework for epidemic prediction that integrates classical mathematical models with artificial intelligence–driven uncertainty quantification. The stochastic model extends the SIR formulation by incorporating probabilistic distributions for transmission and recovery rates, simulated through Monte Carlo methods. Concurrently, deep learning models such as Long Short-Term Memory (LSTM) networks and Bayesian neural predictors are employed to forecast infection trends using real epidemiological data. The hybridization allows continuous calibration of the stochastic model parameters based on AI-derived forecasts, enhancing adaptability and predictive accuracy. Results demonstrate that the hybrid stochastic–AI approach captures dynamic outbreak evolution more accurately than traditional models, providing probabilistic confidence intervals that quantify uncertainty in epidemic peaks and durations. This modeling paradigm offers a data-driven pathway toward real-time epidemic forecasting, vital for decision-making in public health policy and resource allocation.