Evaluating the Application of the SIR Model to a Localized Population

Abstract

Objective Using data collected from the Johns Hopkins COVID-19 Repository, I investigated the reliability of the SIR (Susceptible-Infected-Removed) model. Summary of Background Data Modern pandemic responses have evolved into effective defenses when implemented correctly but present issues in epidemiological modeling efforts. Intervention strategies such as quarantining and masking limit population size (N), which affects the accuracy of modeling population-based rate systems especially in highly transmissible diseases. Methods I begin by reviewing the SIR model retroactively to the initial SARS-CoV-2 Wuhan strain. I compared the parameters available in the published literature (N = 2,717,000, β = 2, γ = 1/14) to the best-fitting SIR-yielded values by minimizing the root mean squared error function. Subsequently, I evaluated its predictive capabilities on the Delta variant using early surge data, which was later compared against a retroactive analysis. Results Using a least-squares error best-fit analysis allowed me to retroactively define remarkably accurate model parameters for the Wuhan waves. Parameters including N = 730, β = 0.46, γ = 0.043 in the first wave and N = 11,200, β = 0.198, γ = 0.07 in the second reflected effective intervention strategies. I show it is an effective predictive tool regarding the Delta variant, yielding parameters N = 50,900, β = 0.87, γ = 1/3.7 that proved accurate when compared with parameters from a full retroactive analysis (N = 60,000, β = 0.94, γ = 1/3.6). Conclusion The similarity of the yielded parameters in my results supports the SIR model’s utility in epidemiological monitoring of high-transmissibility, low-mortality outbreaks vis-à-vis various containment measures.