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The SI mathematical model has long been introduced by Kermack and Mc.Kendrick through its publication in 1927 [1] as a system of two-dimensional differential equations by dividing the human population based on their health status. In 2017, F.Novkaniza [2] improved the model into an SIS model through a stochastic and deterministic approach involving the intervention of medical treatment and medicinal mask to an infected person.In this article, the first optimal control problem arises from an issue of how to estimate daily incident data with the SIS model. One is the SARS incidence data in Hong Kong (14 March 2003 to 23 June 2003). The optimal control problem here is discussed how to minimize the Euclidean error between simulation result and the incident data with finding the best-fit parameters in this model. In addition to the above optimal control studies, some analytical result related to the model analysis (equilibria and the basic reproduction number), the existence of the optimal control solution and numerical simulations will be discussed in this talk.

SIS model, optimal control, parameter estimation, basic reproduction number