Abstract In this paper we address a parameter estimation, sensitivity and control strategies analyses for influenza disease using a model the flows of people between four states: susceptible, exposed, infectious, recovered. We solved a curve-fitting mathematical model to Mexican influenza data using a nonlinear least-square method and the Landweber iteration. An optimal control problem is formulated and analyzed based on models between four states: susceptible, exposed, infectious, recovered; model considering educational campaign, vaccination and medical treatment as strategies for disease control. The sensitivity analysis is performed to determine which model parameters are the most important to disease transmission and prevalence. The numeric results suggest that an adequate implementation of these strategies during the outbreak of an epidemic could significantly mitigate the propagation of the disease.