[Paper Review] Susceptible-Infected-Recovered (SIR) Dynamics of COVID-19 and Economic Impact

Alexis Akira Toda|arXiv (Cornell University)|Mar 25, 2020

COVID-19 epidemiological studies172 citations

TL;DR

The paper estimates a heterogeneous SIR model for COVID-19 across countries, assesses peak infection under mitigation, and links the epidemic to brief stock-market impacts via a stylized asset-pricing model.

ABSTRACT

I estimate the Susceptible-Infected-Recovered (SIR) epidemic model for Coronavirus Disease 2019 (COVID-19). The transmission rate is heterogeneous across countries and far exceeds the recovery rate, which enables a fast spread. In the benchmark model, 28% of the population may be simultaneously infected at the peak, potentially overwhelming the healthcare system. The peak reduces to 6.2% under the optimal mitigation policy that controls the timing and intensity of social distancing. A stylized asset pricing model suggests that the stock price temporarily decreases by 50% in the benchmark case but shows a W-shaped, moderate but longer bear market under the optimal policy.

Motivation & Objective

• Motivate epidemic modeling to inform decision-making under COVID-19 uncertainty.
• Estimate country-specific transmission rates and epidemic peaks using a 14-day data window.
• Analyze optimal mitigation timing to reduce peak infections within healthcare capacity.
• Assess short-run economic impact and asset prices through a stylized production-based model.

Proposed method

• Use Kermack-McKendrick SIR model with parameters beta (transmission) and gamma (recovery).
• Parametric exact solution for x(t), y(t), z(t) via a single variable v with t as a function of v.
• Estimate beta and initial infected y0 by nonlinear least squares on 14-day data, fixing gamma=0.1 and z0≈0.
• Derive no-epidemic condition beta x0 <= gamma and peak infection y_max from y(t_max).
• Simulate mitigation by reducing beta to 0.2 or 0.1 after c reaches a threshold, and compute peak reduction.
• Calibrate a stylized asset-pricing model to link labor disruption to stock price dynamics.

Experimental results

Research questions

• RQ1 What transmission rates (beta) best fit the early 14-day COVID-19 data across countries?
• RQ2 How large can the peak infection be under natural progression vs. mitigation policies?
• RQ3 What timing and intensity of mitigation minimize the epidemic peak given healthcare constraints?
• RQ4 What are the implied stock-market implications of the epidemic and mitigation within a simple asset-pricing framework?

Key findings

• Estimated beta is heterogeneous across countries, typically around 0.2–0.4 outside China, Japan, and Korea.
• Absent mitigation, the model implies a peak infection around 28–30% of the population in many countries.
• Under optimal mitigation, the peak infection can be reduced to about 6.2% of the population.
• China, Japan, and Korea exhibit much lower beta estimates, reflecting containment or different data dynamics.
• A stylized asset-pricing model suggests a 50% stock-price drop during the epidemic, with a W-shaped but milder decline under optimal policy.