STOCHASTIC MODELING OF EPIDEMIC DYNAMICS: SCALING BEHAVIOR AND UNIVERSALITY IN SIR AND SIS SYSTEMS

The spread of infectious diseases is inherently stochastic, with random fluctuations shaping epidemic outcomes. While mean-field models such as susceptible–infected–recovered (SIR) and susceptible–infected–susceptible (SIS) describe large populations, they miss spatiotemporal variability, extinction events, and scaling near epidemic thresholds. This project investigates stochastic SIR and SIS dynamics to identify universal features governing outbreaks.

We use individual-based simulations on spatial lattices to study how fluctuations and correlations affect outcomes, focusing on the critical region where stochasticity dominates. Analyses of survival probabilities, infection counts, and autocorrelations reveal power-law behavior, with SIS aligning with directed percolation and SIR with dynamic isotropic percolation.

Seed simulations from a single infection further probe survival and correlations, enabling extraction of scaling exponents. Building on this, we incorporate diffusion into SIR and SIS dynamics to examine its influence on universality and thresholds. Our findings show where deterministic models fail and stochastic effects prevail. By linking epidemic dynamics to statistical physics, this work reveals universal scaling laws and sharpens understanding of critical behavior in disease spread.