Fractional stochastic nonlinear differential equation approach is used in the analysis of evolution in time of the infected number by COVID-19 in countries where the number of cases is large. The rises and falls of novel cases are treated as randomness in the model for spreading of novel cases. The rescaled range analysis (RS) is used to determine the Hurst index of the time series of novel cases of epidemiologic week that exhibits a Hurst exponent greater than 1/2, meaning that the time series has a behavior that is distinct from a random walk i.e., that nth value is independent of all the values before this.