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This article describes a simple Susceptible Infected Recovered (SIR) modelfitting 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 susceptiblepeople becoming infected is adjusted over time in order to fit the availabledata. The death rate is also secondarily adjusted. Our fitting is made underthe assumption that due to limiting number of tests, a large part of theinfected population has not been tested positive. In the last part, we extendthe model to take into account the daily fluxes between New Jersey (NJ) and NYstates and fit the data for both states. Our simple model fits the availabledata, and illustrates typical dynamics of the disease: exponential increase,apex and decrease. The model highlights a decrease in the transmission rateover the period which gives a quantitative illustration about how lockdownpolicies reduce the spread of the pandemic. The coupled model with NY and NJstates shows a wave in NJ following the NY wave, illustrating the mechanism ofspread from one attractive hot spot to its neighbor. }

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