Abstract
Covid-19 is a very extraordinary case not only in one country but all countries in the world. The number of deaths caused by Covid-19 is very large and the rate of spread of this disease is very high and fast. In this paper, we perform an analysis of a covid-19 epidemic model. This model is a development of the SEIR model in general which is equipped with a Quarantine (Q), Fatality (F) compartment, and there is a separation between detected and undetected infected people (I). Our analysis shows that there are two equilibria, namely, disease free equilibrium and endemic equilibrium. by using, Lyapunov function, we demonstrated that disease free is globally asymptotically stable if R0 < 1, and disease-free becomes unstable if R0 > 1. This result reveal that the intervention of infection rate and quarantine process are important to control and achieve global stability of disease-free equilibrium
Highlights
All countries in the world focus on pandemic diseases, namely the Corona virus disease 2019 or COVID-19 caused by severe acute respiratory syndrome corona virus 2 (SARS-Cov-2)
Since early 2020, COVID-19 has begun to spread to various parts of the world and caused millions of people to become infected
We developed the SEIR model by involving the home-stead isolation, detected and undetected asymptomatic cases, and fatality cases
Summary
All countries in the world focus on pandemic diseases, namely the Corona virus disease 2019 or COVID-19 caused by severe acute respiratory syndrome corona virus 2 (SARS-Cov-2). This virus was first identified in late December 2019 in Wuhan, China. Indonesia was recorded 4,147,365 cases with 137,782 deaths [1]. Because no cure method has yet been found for this virus, planning is needed to control the spread of the disease. We do an in-depth mathematical analysis of the global stability of its equilibrium point through Lyapunov function
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