Decoding Infectious Disease Dynamics: A Stochastic Approach to Population Heterogeneity and Epidemic Outcomes

In this study, we develop a stochastic Susceptible-Infectious-Recovered (SIR) model to explore the dynamics of infectious diseases in heterogeneous populations. The model accounts for variability in transmission and recovery rates across subpopulations, allowing for more realistic predictions of epidemic outcomes. Using the Gillespie algorithm, we simulate epidemic scenarios across different population structures and analyze the effects of heterogeneity on outbreak size, duration, and the probability of disease extinction. Our results show that heterogeneity in transmission rates significantly impacts the dynamics of disease spread. For populations with homogeneous transmission rates (????0=2.5), we observe a median outbreak size affecting 75% of the population, with an average epidemic duration of 60 days. In contrast, for populations with a high degree of heterogeneity (variance in ???????? across subpopulations is 1.2), the median outbreak size increases to 85% of the population, and the epidemic duration extends to 90 days, demonstrating the disproportionate influence of high-transmission subgroups. Furthermore, the probability of disease extinction before a major outbreak occurs is reduced from 35% in homogeneous populations to just 15% in heterogeneous populations, indicating that heterogeneity reduces the chances of natural epidemic fade-out. These findings are consistent with the work of Lloyd-Smith et al. (2005), who showed that "super-spreaders" can sustain disease transmission even when overall transmission rates are low. Our study also highlights the importance of targeted interventions. Simulations indicate that prioritizing high-risk subpopulations (i.e., those with ???????? > 3.0) for vaccination reduces the total outbreak size by 30%, compared to a uniform vaccination strategy across all subgroups. These results underscore the critical role of stochasticity and heterogeneity in infectious disease dynamics and suggest that public health policies should be tailored to address these complexities.