Abstract: The class of bivariate integer-valued time series models is gaining rapid popularity. However, its efficiency and adaptability are being challenged because of zero-inflation of count time series (ZITS) and algorithm techniques. In this presentation, the bivariate copula is presented with ZITS. The computational algorithm is proposed via copula theory. Each series follows a Markov chain with the serial dependence captured using copula-based transition probability functions with Poisson and zero-inflated Poisson margins. The copula theory is also used to capture bivariate ZITS where the dependence between the two series using the bivariate Gaussian and t-copula functions. Likelihood based inference is used to estimate the models’ parameters for simulated and real data with the bivariate integrals of the Gaussian and t-copula functions being evaluated using standard randomized Monte Carlo methods.