COVID-19 global pandemic has been significantly damaging the human well-being, life style of people, and the global economy. At the beginning of the epidemic, there were no successful candidates available even though scientists rushed to find one since the start of the official declaration of the pandemic by the World Health Organization (WHO). Thus the countries around the world mostly practiced nonpharmaceutical interventions (NPIs) in various combinations to combat the virus expecting to minimize the public health burden. Since the identification of the first COVID-19 local case on March 11, 2020, the government of Sri Lanka introduced serious social distancing and public health interventions in their fullest capacity as a developing nation to effectively combat the disease spread. These measures had been considerably successful as they contributed to flattening the epidemic curve within two months. However, the nation was at significant risk to the virus due to evolving global epidemic situation, and several clusters of cases have subsequently emerged from a number of jurisdictions in the country.

Mathematical models are used to predict the epidemic, to assess the efficacy of public health interventions and social distancing measures recommended by health authorities, to evaluate the national policies to ease lock-down measures in highly affected countries, and the model-based outcomes are extremely useful in various optimal decision-making in public health. Multiple SEIR (Susceptible-Exposed-Infected-Recovered) class models were applied to investigate the early stage of the COVID-19 transmission dynamic in Sri Lanka. These models coupled with optimization techniques were used to estimate the initial transmission rate and the initial epidemic size of the outbreak. A theoretical optimal control problem was developed to identify best allocation of resources in three types of control measures that minimizes the infection in the community. A sensitivity analysis of parameters such as the efficacy of NPIs over the early phase of the outbreak, their timing of implementation, and management of imported overseas cases was carried out mainly addressing their importance in mild and critically ill cases projections.