The COVID 19 pandemic caused by the novel corona virus (SARS-CoV-2) has been one of the major public health concerns across the globe, currently more than 3.5 million individuals have been infected, and the number of deaths has passed 250,000. The world wide burden of the disease has been massive, and the governments are in dilemma to protect the health system of the country while safeguarding the economy. There is no vaccine or antivirus drug found against this virus while multiple research groups are actively working on a suitable candidate. The only available mode of minimizing the disease burden has been to control its transmission among the population. Since the occurrence of first COVID 19 local case on 11 March 2020, the government of Sri Lanka introduced serious social distancing and public health interventions in its fullest capacity as a developing nation to effectively combat with the disease spread. This study focuses to develop a mathematical model to investigate the dynamic of this novel disease using an extended version of an SEIR compartmental structure considering the heterogeneity of cases such as asymptomatic, symptomatic with mild indications and the cases required intensive care treatments. All the measures and interventions are in progress with a significantly large social and economic cost, thus, optimal control techniques are used to identify the most appropriate strategies to minimize this cost. The results of the simulations prove that optimal control measures can be worked out as the epidemic curves are flattened while delaying the outbreak so that the health system might not be under pressure to treat and care the patients.