Stability Analysis of Covid-19 Model Based on Compliance and Carrier Transmission

¹ Mathematics Graduate Program, Universitas Syiah Kuala, Banda Aceh, Nangroe Aceh Darussalam, Indonesia
² Department of Mathematics, Universitas Syiah Kuala, Banda Aceh, Nangroe Aceh Darussalam, Indonesia

^* Corresponding author: marwan.math@usk.ac.id

Abstract

The Covid-19 pandemic has officially ended with the lifting of the Public Health Emergency of International Concern (PHEIC) status by the World Health Organization (WHO). The world has begun the transition from a pandemic to an endemic period through policy updates such as healthy living habits, wearing masks if sick, vaccination, self-quarantine, contact tracing or testing, increasing understanding or awareness of diseases and treatment. This research aims to analyze the role of individuals in the pandemic transition period and the addition of the Carrier subpopulation to the COVID-19 model. This model produces two equilibrium points: a disease-free equilibrium points and an endemic equilibrium point. Furthermore, stability analysis was carried out around the equilibrium point and obtained three basic reproduction numbers that became the threshold for the spread of disease around the equilibrium point, namely R0 less than one (R0 < 1) and greater than one (R0 > 1). This shows that increasing policies such as disease awareness or understanding, healthy living habits, and vaccination can prevent the spread of COVID-19 so that the pandemic period does not occur and the disease will disappear over time.