MODELING THE SPREAD OF COVID-19 DISEASE WITH TIME DELAY IN PONTIANAK CITY

Coronavirus disease 2019 (COVID-19) is an infectious disease caused by a coronavirus originating from the city of Wuhan in 2019. This disease affects the respiratory system. The city of Pontianak has the highest population density in West Kalimantan. This density results in a higher spread of Covid-...

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Main Authors: Fatma Arum Fatonah, Evi Noviani, Meliana Pasaribu
Format: Article
Language:English
Published: Universitas Pattimura 2024-05-01
Series:Barekeng
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Online Access:https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/11181
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author Fatma Arum Fatonah
Evi Noviani
Meliana Pasaribu
author_facet Fatma Arum Fatonah
Evi Noviani
Meliana Pasaribu
author_sort Fatma Arum Fatonah
collection DOAJ
description Coronavirus disease 2019 (COVID-19) is an infectious disease caused by a coronavirus originating from the city of Wuhan in 2019. This disease affects the respiratory system. The city of Pontianak has the highest population density in West Kalimantan. This density results in a higher spread of Covid-19. In this article, the spread of COVID-19 is formulated into a mathematical model, equilibrium points are sought, stability is analyzed, and a delay time is introduced to reduce the spread of COVID-19. The magnitude of the delay time given during quarantine complies with health protocols, which is between 2 – 14 days. This article aims to analyze the influence of the delay time in modeling the spread of Covid-19. The problem of COVID-19 spread is constructed into an SIQR model, with a sub-population of recovered individuals returning to the susceptible sub-population. The population is divided into four sub-populations: susceptible (S), Infected (I), Quarantined (Q), and Recovered (R). The parameters used  include the natural birth rate ( ), the rate of susceptibility to infection ( ), the rate of infection under quarantine ( ), the recovery rate from infection ( ), the recovery rate from infection under quarantine ( ), the death rate from infection ( ), the death rate under quarantine ( ), the delay time from infection to quarantine process ( ), the natural death rate ( ), and the rate of recovered immunity returning to susceptibility ( ). The simulation results show that when the basic reproduction number is less than , the disease-free equilibrium is stable, and when the basic reproduction number is greater than , the endemic equilibrium point is stable. The addition of a time delay ( ) in the SIQR model affects the stability of the endemic equilibrium point but does not affect the stability of the disease-free equilibrium point.
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spelling doaj-art-0288894fa01e4defb9162e146ea069082025-08-20T03:05:31ZengUniversitas PattimuraBarekeng1978-72272615-30172024-05-011820903091410.30598/barekengvol18iss2pp0903-091411181MODELING THE SPREAD OF COVID-19 DISEASE WITH TIME DELAY IN PONTIANAK CITYFatma Arum Fatonah0Evi Noviani1Meliana Pasaribu2Department of Mathematics, Faculty of Mathematics and Natural Sciences, Tanjungpura University, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Tanjungpura University, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Tanjungpura University, IndonesiaCoronavirus disease 2019 (COVID-19) is an infectious disease caused by a coronavirus originating from the city of Wuhan in 2019. This disease affects the respiratory system. The city of Pontianak has the highest population density in West Kalimantan. This density results in a higher spread of Covid-19. In this article, the spread of COVID-19 is formulated into a mathematical model, equilibrium points are sought, stability is analyzed, and a delay time is introduced to reduce the spread of COVID-19. The magnitude of the delay time given during quarantine complies with health protocols, which is between 2 – 14 days. This article aims to analyze the influence of the delay time in modeling the spread of Covid-19. The problem of COVID-19 spread is constructed into an SIQR model, with a sub-population of recovered individuals returning to the susceptible sub-population. The population is divided into four sub-populations: susceptible (S), Infected (I), Quarantined (Q), and Recovered (R). The parameters used  include the natural birth rate ( ), the rate of susceptibility to infection ( ), the rate of infection under quarantine ( ), the recovery rate from infection ( ), the recovery rate from infection under quarantine ( ), the death rate from infection ( ), the death rate under quarantine ( ), the delay time from infection to quarantine process ( ), the natural death rate ( ), and the rate of recovered immunity returning to susceptibility ( ). The simulation results show that when the basic reproduction number is less than , the disease-free equilibrium is stable, and when the basic reproduction number is greater than , the endemic equilibrium point is stable. The addition of a time delay ( ) in the SIQR model affects the stability of the endemic equilibrium point but does not affect the stability of the disease-free equilibrium point.https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/11181siqr modelequilibrium pointquarantinebasic reproduction
spellingShingle Fatma Arum Fatonah
Evi Noviani
Meliana Pasaribu
MODELING THE SPREAD OF COVID-19 DISEASE WITH TIME DELAY IN PONTIANAK CITY
Barekeng
siqr model
equilibrium point
quarantine
basic reproduction
title MODELING THE SPREAD OF COVID-19 DISEASE WITH TIME DELAY IN PONTIANAK CITY
title_full MODELING THE SPREAD OF COVID-19 DISEASE WITH TIME DELAY IN PONTIANAK CITY
title_fullStr MODELING THE SPREAD OF COVID-19 DISEASE WITH TIME DELAY IN PONTIANAK CITY
title_full_unstemmed MODELING THE SPREAD OF COVID-19 DISEASE WITH TIME DELAY IN PONTIANAK CITY
title_short MODELING THE SPREAD OF COVID-19 DISEASE WITH TIME DELAY IN PONTIANAK CITY
title_sort modeling the spread of covid 19 disease with time delay in pontianak city
topic siqr model
equilibrium point
quarantine
basic reproduction
url https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/11181
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AT evinoviani modelingthespreadofcovid19diseasewithtimedelayinpontianakcity
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