A general framework of covid-19 model with control strategies: the application of large-scale social restrictions, self-quarantine, and immune system improvement in Surabaya, Indonesia

Abstract

A covid-19 is a virus disease of worldwide importance which spread not only in a small country such as Mongolia but also in a large country like the United State. It is caused by a severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and well known as droplet-borne disease. The droplets containing coronavirus are spread through the air within a meter and deposited on the mucous membranes of suscpetible person. The aim of this study was to produce a general framework model of corona virus disease with the application of large-scale social restriction, self-quarantine and immune system improvement as control strategies to reduce the spread of the disease. This study was conducted in Surabaya, Indonesia with a total of 299 positive patients infected with covid-19 until the fourth week of April, 2020. The transmission routes of the disease had been constructed based on the real problem. Therefore, human population have been divided into some sub-population based on the characteritics of disease symptoms. The spread of covid-19 have been formulated mathematically by using compartment model. Stability analysis had been done for a free disease equilbrium and an endemic equilibrium. Moreover, numerical simulation were also provided to quantify the disease dynamics.