Applying The Sir Model To A Restricted Population

Abstract

Abstract OBJECTIVE Using data collected from the Johns Hopkins COVID-19 Repository, we investigate 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 the modeling population-based rate systems especially in high-transmissible diseases. METHODS We begin by reviewing the SIR model retroactively to the initial SARS-Cov-2 Wuhan strain. We 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, we 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 us 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=11200, β = 0.198, γ = 0.07 in the second reflected effective intervention strategies. We show it is an effective predictive tool regarding the Delta variant, yielding parameters N = 50,900, β = 0.87, γ = 1/3.7 which proved accurate when compared to parameters from a full retroactive analysis (N = 60,000, β = 0.94, γ = 1/3.6). CONCLUSION The similarity of the yielded parameters in our results supports the SIR Model’s utility in epidemiologically monitoring of high-transmissibility, low-mortality outbreaks vis-à-vis various containment measures.