In this paper we consider two type of mathematical models for the novel coronavirus (2019-nCov), which are in the form of a nonlinear differential equations system. In the first model the contact rate, , and transition rate of  symptomatic infected indeviduals to the quarantined infected class, , are constant. And in the second model these quantities are time dependent. These models are the SEIR one, where are Susceptible, Exposed, Infected and Recovered classes of human population respectively. We establish the Newton-Taylor polynomial solutions for these system, so that the nonlinear systems are solvable by an iterative and progressive process with a good accuracy. We completely describe the algorithm of such systems in another paper and here we express briefly. This algorithm action on the interval , where  is the length of partial intervals, and  is the number of intervals. In every partial interval, we linearize the problem by the Newton's method and then solve the linear problem by the Taylor polynomial solutions technique. We extensively investigate the numerical analysis of the method.

Keywords: Novel coronavirus (2019-nCov), Newton-Taylor polynomial solutions, Infectiouse disease, Infectiouse classes, Nonlinear differential equations system.

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