[Paper Review] A predictive model for Covid-19 spread applied to eight US states

Zeina S. Khan, Frank Van Bussel+1 more|arXiv (Cornell University)|Jun 10, 2020

COVID-19 epidemiological studies4 citations

TL;DR

This study proposes a novel SQUIDER compartmental model that tracks detected and undetected infections, quarantine, social distancing, reinfection, and recovery to predict Covid-19 spread across eight U.S. states. The model reveals that outbreaks began earlier than detected, predicts endemic transmission beyond two years, and shows that stricter social distancing, testing, or compliance could have reduced deaths by up to 50% in states like Texas.

ABSTRACT

A compartmental epidemic model is proposed to predict the Covid-19 virus spread. It considers: both detected and undetected infected populations, medical quarantine and social sequestration, release from sequestration, plus possible reinfection. The coefficients in the model are evaluated by fitting to empirical data for eight US states: Arizona, California, Florida, Illinois, Louisiana, New Jersey, New York State, and Texas. Together these states make up 43% of the US population; some of these states appear to have handled their initial outbreaks well, while others appear to be emerging hotspots. The evolution of Covid-19 is fairly similar among the states: variations in contact and recovery rates remain below 5%; however, not surprisingly, variations are larger in death rate, reinfection rate, stay-at-home effect, and release rate from sequestration. The results reveal that outbreaks may have been well underway in several states before first detected and that California might have seen more than one influx of the pandemic. Our projections based on the current situation indicate that Covid-19 will become endemic, spreading for more than two years. Should states fully relax stay-at-home orders, most states may experience a secondary peak in 2021. If lockdowns had been kept in place, the number of Covid-19 deaths so far could have been significantly lower in most states that opened up. Additionally, our model predicts that decreasing contact rate by 10%, or increasing testing by approximately 15%, or doubling lockdown compliance (from the current $\sim$ 15% to $\sim$ 30%) will eradicate infections in the state of Texas within a year. Extending our fits for all of the US states, we predict about 11 million total infections (including undetected), 8 million cumulative confirmed cases, and 630,000 cumulative deaths by November 1, 2020.

Motivation & Objective

• To develop a predictive epidemic model that accounts for undetected infections, social distancing, quarantine, and reinfection.
• To analyze and compare the effectiveness of non-pharmaceutical interventions across eight U.S. states with diverse outbreak trajectories.
• To project the long-term course of the pandemic under current and alternative mitigation strategies.
• To assess the impact of early detection, compliance with stay-at-home orders, and testing rates on mortality and infection spread.

Proposed method

• The SQUIDER model extends the classic SIR framework by introducing seven compartments: Susceptible (S), Undetected infected (U), Detected infected (I), Recovered (R), Dead (D), Excluded (E), and Pseudo-Quarantine (Q).
• The model uses differential equations to describe transitions between compartments, incorporating time-varying contact rates and social distancing effects via the q(t) function.
• Key parameters such as infection rate (β), recovery rate (γ), death rate (α), and reinfection rate (ρ) are fitted to empirical data from eight U.S. states.
• The model accounts for undetected cases through a nonlinear transmission term βSU^a, where a adjusts for the infectiousness of asymptomatic individuals.
• Fitting is performed using reported case and death data from Arizona, California, Florida, Illinois, Louisiana, New Jersey, New York State, and Texas.
• Projections are generated under various scenarios, including full relaxation of stay-at-home orders and increased compliance or testing rates.

Experimental results

Research questions

• RQ1 How does the inclusion of undetected infections and social distancing affect the accuracy of Covid-19 transmission predictions in U.S. states?
• RQ2 What is the projected long-term trajectory of the pandemic if current mitigation strategies are maintained or relaxed?
• RQ3 To what extent can increased testing, social distancing compliance, or reduced contact rates prevent secondary peaks and reduce mortality?
• RQ4 How do variations in contact, recovery, death, and reinfection rates across states influence the overall epidemic dynamics?
• RQ5 What impact would sustained lockdowns have had on cumulative deaths in states that later reopened?

Key findings

• The model predicts that Covid-19 will become endemic in the U.S., with transmission persisting for more than two years under current conditions.
• By November 1, 2020, the model projects 11 million total infections (including undetected), 8 million confirmed cases, and 630,000 cumulative deaths nationwide.
• In Texas, increasing social distancing compliance from 15% to 30%, reducing contact rates by 10%, or increasing testing by 15% could eradicate infections within a year.
• States that relaxed stay-at-home orders may experience a secondary peak in 2021, with infections increasing by approximately an order of magnitude.
• The model estimates that if lockdowns had been maintained, the number of deaths in most states could have been significantly lower than observed.
• California likely experienced more than one viral influx, and outbreaks may have been underway before the first confirmed cases in several states.