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Mathematical Model and Simulation of the Spread of COVID-19 with Vaccination, Implementation of Health Protocols, and Treatment

Jambura Journal of Biomathematics (JJBM) · Vol. ume (2023) · hlm. 69–79

DOI
10.34312/jjbm.v4i1.19162
ISSN
2723-0317
Terbit
2023-06-30
Penerbit
Department of Mathematics, Universitas Negeri Gorontalo
Bahasa
eng
Lisensi
creativecommons.org/licenses/by-nc/4.0

Abstrak

This research develops the SVEIHQR model to simulate the spread of COVID-19 with vaccination, implementation of health protocols, and treatment. The population is divided into twelve subpopulations, resulting in a mathematical model of COVID-19 in the form of a system of twelve differential equations with twelve variables. From the model, we obtain the disease-free equilibrium point, the endemic equilibrium point, and the basic reproduction number (R0). The disease-free equilibrium point is locally asymptotically stable when R0 1 and ∆5 0, where ∆5 is the fifth-order Routh-Hurwitz matrix of the characteristic polynomial of the Jacobian matrix. Additionally, an endemic equilibrium point exists when R0 1. The results of numerical simulations are consistent with the conducted analysis, and the sensitivity analysis reveals that the significant parameters influencing the spread of COVID-19 are the proportion of symptomatic infected individuals and the contact rate with asymptomatic infected individuals.

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  • Syarif Hidayatullah State Islamic University Jakarta
  • University of Singaperbangsa Karawang
  • Binus University
  • Diponegoro University
  • STAI Sebelas April Sumedang
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Rekan penulisOrganisasiArtikel bersama
Nina FitriyatiSyarif Hidayatullah State Islamic University Jakarta3
Nur Lailiyatul InayahSyarif Hidayatullah State Islamic University Jakarta2
Eti HartatiSyarif Hidayatullah State Islamic University Jakarta2
Madona Yunita WijayaSyarif Hidayatullah State Islamic University Jakarta2
Ikhwal YupintoSyarif Hidayatullah State Islamic University Jakarta1
Maghvirotul AzizahSyarif Hidayatullah State Islamic University Jakarta1
Savira PratiwiSyarif Hidayatullah State Islamic University Jakarta1
Raza Aqil MaulanaSyarif Hidayatullah State Islamic University Jakarta1
Amalia ZahraBinus University1
Suma'inna Suma'innaAfiliasi tidak diketahui1
Tesa Nur PadilahUniversity of Singaperbangsa Karawang1
Iqbal MaulanaUniversity of Singaperbangsa Karawang1
Yanne IreneSyarif Hidayatullah State Islamic University Jakarta1
Mochammad Rafli AlamsyahSyarif Hidayatullah State Islamic University Jakarta1
Nurcahya Yulian AsharDiponegoro University1
Yoga Amanda PutraSyarif Hidayatullah State Islamic University Jakarta1
Wahri IrawanSyarif Hidayatullah State Islamic University Jakarta1
Anida AnidaSTAI Sebelas April Sumedang1
Ristawati RistawatiAfiliasi tidak diketahui1
Muhammad Kevin RamadhanAfiliasi tidak diketahui1
Irma FauziahSyarif Hidayatullah State Islamic University Jakarta1
Andrew FiadeSyarif Hidayatullah State Islamic University Jakarta1
Flori R. SariSyarif Hidayatullah State Islamic University Jakarta1

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Sumber metadata: OAI-PMH (metadata jurnal) http://ejurnal.ung.ac.id/index.php/JJBM/oai, pertama di-harvest 9 Nov 2026, terakhir terlihat 9 Nov 2026.
Metadata asli (oai_dc) 
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	<dc:title xml:lang="en-US">Mathematical Model and Simulation of the Spread of COVID-19 with Vaccination, Implementation of Health Protocols, and Treatment</dc:title>
	<dc:creator>Manaqib, Muhammad</dc:creator>
	<dc:creator>Mahmudi, Mahmudi</dc:creator>
	<dc:creator>Prayoga, Galuh</dc:creator>
	<dc:subject xml:lang="en-US">COVID-19; Vaccination; Application of Health Protocols; Treatment; Stability of Equilibrium Point</dc:subject>
	<dc:description xml:lang="en-US">This research develops the SVEIHQR model to simulate the spread of COVID-19 with vaccination, implementation of health protocols, and treatment. The population is divided into twelve subpopulations, resulting in a mathematical model of COVID-19 in the form of a system of twelve differential equations with twelve variables. From the model, we obtain the disease-free equilibrium point, the endemic equilibrium point, and the basic reproduction number (R0). The disease-free equilibrium point is locally asymptotically stable when R0  1 and ∆5  0, where âˆ†5 is the fifth-order Routh-Hurwitz matrix of the characteristic polynomial of the Jacobian matrix. Additionally, an endemic equilibrium point exists when R0  1. The results of numerical simulations are consistent with the conducted analysis, and the sensitivity analysis reveals that the significant parameters influencing the spread of COVID-19 are the proportion of symptomatic infected individuals and the contact rate with asymptomatic infected individuals.</dc:description>
	<dc:publisher xml:lang="en-US">Department of Mathematics, Universitas Negeri Gorontalo</dc:publisher>
	<dc:contributor xml:lang="en-US"></dc:contributor>
	<dc:date>2023-06-30</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:type xml:lang="en-US">Peer-reviewed Article</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://ejurnal.ung.ac.id/index.php/JJBM/article/view/19162</dc:identifier>
	<dc:identifier>10.34312/jjbm.v4i1.19162</dc:identifier>
	<dc:source xml:lang="en-US">Jambura Journal of Biomathematics (JJBM); Volume 4, Issue 1: June 2023; 69-79</dc:source>
	<dc:source>2723-0317</dc:source>
	<dc:source>10.34312/jjbm.v4i1</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://ejurnal.ung.ac.id/index.php/JJBM/article/view/19162/6718</dc:relation>
	<dc:rights xml:lang="en-US">Copyright (c) 2023 Muhammad Manaqib, Mahmudi Mahmudi, Galuh Prayoga</dc:rights>
	<dc:rights xml:lang="en-US">https://creativecommons.org/licenses/by-nc/4.0</dc:rights>
</oai_dc:dc>