On a coupled time-dependent SIR models fitting with New York and New-Jersey states COVID-19 data

TL;DR

This paper develops a non-autonomous SIR model fitted to COVID-19 data from New York and New Jersey, capturing disease dynamics and the impact of lockdowns, including inter-state transmission effects.

Contribution

It introduces a coupled SIR model with time-dependent rates to fit COVID-19 data for NY and NJ, accounting for inter-state fluxes and policy impacts.

Findings

Model fits COVID-19 data well, showing exponential growth, peak, and decline.

Decreasing transmission rate reflects lockdown effectiveness.

Coupled model demonstrates disease spread from NY to NJ.

Abstract

This article describes a simple Susceptible Infected Recovered (SIR) model fitting with COVID-19 data for the month of march 2020 in New York (NY) state. The model is a classical SIR, but is non-autonomous; the rate of susceptible people becoming infected is adjusted over time in order to fit the available data. The death rate is also secondarily adjusted. Our fitting is made under the assumption that due to limiting number of tests, a large part of the infected population has not been tested positive. In the last part, we extend the model to take into account the daily fluxes between New Jersey (NJ) and NY states and fit the data for both states. Our simple model fits the available data, and illustrates typical dynamics of the disease: exponential increase, apex and decrease. The model highlights a decrease in the transmission rate over the period which gives a quantitative illustration about how lockdown policies reduce the spread of the pandemic. The coupled model with NY and NJ states shows a wave in NJ following the NY wave, illustrating the mechanism of spread from one attractive hot spot to its neighbor. }