In order to understand the behavior of disease transmission and develop better policies to overcome the problem, time series modeling and forecasting of infectious diseases are crucial. Therefore, a flexible INAR(1) time series model based on dependent zero inflated count series is proposed. We consider a flexible discrete model for innovation terms of the process with some interesting behavior. We provided some statistical properties of the proposed INAR(1) time series model with showing its interpretation to contagious diseases. The unknown parameters of the proposed process are estimated through conditional maximum likelihood estimation method. Fitting, modeling and analysis to some recent contagious cases are investigated, namely the weekly counts of Hantavirus, Chickenpox and Tuberculosis diseases. Forecasting of the earlier data sets under both classical and modified Sieve bootstrap approaches are investigated.
