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We investigate the parameter estimation and forecasting of two forms of thestochastic SIR model driven by small L\'{e}vy noises. We accomplish this byutilizing least squares estimators. We include simulation studies of both formsusing the method of projected gradient descent to aid in the parameterestimation.

Parameter estimation of stochastic SIR model driven by small L\'{e}vy noises with time-dependent periodic transmission