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In this paper, we analyze a model of Influenza spread with an asymptotic transmission rate, wherein the disease transmission rate and death rate are considered as fuzzy sets. Comparative studies of the equilibrium points of the disease for the classical and fuzzy models are performed. Using the concept of probability measure and fuzzy expected value, we obtain the fuzzy basic reproduction number for groups of infected individuals with different virus loads. Further, a basic reproduction number for the classical and the fuzzy model are compared. Finally, a program based on the basic reproduction value of disease control is suggested and the numerical simulations are carried out to illustrate the analytical results.