Optimal Drug Treatment in a Simple Pandemic Switched System Using Polynomial Approach Abdessamad Tridane, Mohamed Ali Hajji and Eduardo Mojica-Nava Abstract The aim of this work is to investigate the optimal control of the treatment in a simple pandemic model as a switched nonlinear system. We used a newly developed approach based on the theory of moments. This approach allows to transform a nonlinear, non-convex optimal control problem to an equivalent linear and convex one. To illustrate our finding, we used the example of influenza pandemic to compare the full treatment approach to our optimal moment and time switching solution. AMS subject classifications [2010]Primary 93C10; Secondary 93D15, 34A38 Key words: switched systems, epidemic model, optimal control, theory of moment. 1 Introduction In order to avoid high mortalities and as a result of the severity of these outbreaks over years, humans have focused their efforts on finding the best strategies to control the spread of infectious diseases. Abdessamad Tridane (Corresponding author) United Arab Emirates University, Department of Mathematical Sciences, College of Science, United Arab Emirates University, PO Box 15551, Al Ain, United Arab Emirates, e-mail: a-tridane@uaeu.ac.ae Mohamed Ali Hajji United Arab Emirates University, Department of Mathematical Sciences, College of Science, United Arab Emirates University, PO Box 15551, Al Ain, United Arab Emirates, e-mail: mahajji@uaeu.ac.ae Eduardo Mojica-Nava Department of Electrical and Electronics Engineering, Universidad Nacional de Colombia, Bogota, Colombia, e-mail: eamojican@unal.edu.co 1