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A Covid-19, known as a virus disease originally from Wuhan China, spread globally since November 2019. It was about 213 countries whom have reported a total of 6,726,982 positive patient in 5th of June 2020. Some countries declared a lockdown as new policy to control the spread of the disease, where as another countries preferred to run another policy. Indonesia government made a policy, known as Large Scale Social Restriction, in some area including Surabaya Raya. This policy still allowed people to have some activities outside even to work but with some restrictions. Meanwhile, Indonesia governement also had another policy to divide covid-19 patient into three categories, such as People in Monitoring (ODP), Patients in Oversight (PDP), and Confirm Patients. This study aimed to explore the behaviour of the Covid-19 model which large scale social restriction had been involved in Surabaya, Indonesia. It was not only to figure out the stability analysis of the model but also the judgement of the result through numerical simulation. Firstly, we constructed model for the disease spread based on the characteristic of Covid-19. The basic model of the disease spread (SIR) had been used as a fundamental model. Regard to the characteristic of Covid 19, we separated human population into five sub population, namely Suscpetible (0), Susceptible (1), Exposed, Infected, and Recovered. Each sub population related to the Covid-19 patient which have been defined by Indonesia government. The transmission routes of the disease were formulated mathematically based on the real problem. In the second step, two disease equilibrium points had been obtained. There were a disease-free equilibrium and an endemic equilibrium. Moreover, by using Next Generation Matrix, the basic reproduction number also had been determined. Finally, stability analysis have been done to explore the existence of the disease. This results also have been supported by the numerical simulation.

Covid-19; Mathematical Model; Large Scale Social Restriction; System Dynamics