This article studies a threshold autoregressive model with the dependent thinning structure for modeling nonlinear time series of counts. Some properties are derived for the model and two approaches in estimation are applied, the modified conditional least square and conditional maximum likelihood methods which are adjusted by the Min-Min algorithm. The unknown threshold parameter is estimated using the nested sub-sample search algorithm and the minimum of maximized log-likelihood function methods. The efficiency of the estimators is evaluated using a simulation study. The application of the model is discussed on the COVID-19 data set.
