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We propose a unified stochastic SIR model driven by L\'{e}vy noise. The modelis structural enough to allow for time-dependency, nonlinearity, discontinuity,demography and environmental disturbances. We present concise results on theexistence and uniqueness of positive global solutions and investigate theextinction and persistence of the novel model. Examples and simulations areprovided to illustrate the main results.

A Unified Stochastic SIR Model Driven By L\'{e}vy Noise With Time-Dependency