Mathematical models to characterize the early phase of the COVID-19 pandemic in New Mexico, USA

In this paper, we use a variety of mathematical models to characterize the early phase of the COVID-19 pandemic in New Mexico. We use both empirical and mechanistic models based on differential equations to examine the dynamics of the pandemic in New Mexico and in carefully selected New Mexico counties. For the empirical model, we use the exponential growth model to compute and estimate the growth rate, basic reproduction number $ \mathcal{R}_0 $ and effective reproduction number $ \mathcal{R}_t $. In addition, we use the SIR model to estimate $ \mathcal{R}_0 $, using the new weekly COVID cases and also cumulative cases. We found that for the beginning of the early phase of the pandemic, the most populous counties had basic reproduction numbers greater than one. In addition, it was found that the transmission rates of some counties varied significantly during the early phase of the pandemic. Moreover, $ \mathcal{R}_0 $ dropped below one during some phases for some counties when using the SIR model. This suggests that non-pharmaceutical interventions had some impact on reducing the burden of the pandemic and that people's behavior changed during this early phase.