DOI: https://doi.org/10.14710/jfma.v7i1.19750

MATHEMATICAL MODELLING OF THE SPREAD OF COVID-19 WITH FIRST, SECOND AND THIRD DOSES OF VACCINATION IN SEMARANG CITY

*Mahardika Karunia Dewi Purnamasari  -  Departement of Mathematics, Universitas Islam Negeri Walisongo Semarang, Jl. Prof. Dr. Hamka No.3, RW.5, Tambakaji, Kec. Ngaliyan, Kota Semarang, Jawa Tengah 50185, Indonesia
Aini Fitriyah  -  Departement of Mathematics, Universitas Islam Negeri Walisongo Semarang, Jl. Prof. Dr. Hamka No.3, RW.5, Tambakaji, Kec. Ngaliyan, Kota Semarang, Jawa Tengah 50185, Indonesia
Zulaikha Zulaikha  -  Departement of Mathematics, Universitas Islam Negeri Walisongo Semarang, Jl. Prof. Dr. Hamka No.3, RW.5, Tambakaji, Kec. Ngaliyan, Kota Semarang, Jawa Tengah 50185, Indonesia

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Abstract

This research models the spread of Covid-19 by developing the  model. In this model there are seven compartments, namely the susceptible subpopulation (S), the subpopulation that has received the first dose of vaccine (V1), the subpopulation that has received the second dose of vaccine (V2), the subpopulation that has received the third dose of vaccine (V3), the exposed subpopulation (E), infected subpopulation (I), and recovered subpopulation (R). From the model that has been formed, a search for disease-free and endemic equilibrium points is carried out, then looking for the basic reproduction number (R0) as a benchmark for the presence or absence of the spread of Covid-19 in a population, then numerically simulating it using the Matlab R2017a software. The results of this numerical simulation are in accordance with the dynamic analysis carried out, namely if the condition is  then Covid-19 cannot spread, whereas if the condition is  then Covid-19 can spread in a certain area. In addition, the disease cannot spread quickly if the proportion of those who are vaccinated is increased, so that the use of vaccines can be used as an effort to prevent the spread of Covid-19.

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Keywords: Covid-19; Model; Vaccination; Equilibrium Point; Basic Reproductive Number

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Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : EN
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  7. Keputusan Menteri Kesehatan Republik Indonesia, “Keputusan Menteri Kesehatan Republik Indonesia Nomor HK.01.07/MenKes/413/2020 Tentang Pedoman Pencegahan dan Pengendalian Corona Virus Disease 2019 (Covid-19),” MenKes/413/2020, vol. 2019, hal. 207, 2020
  8. D. Pal, D. Ghosh, P. K. Santra, dan G. S. Mahapatra, “Mathematical Analysis of a COVID-19 Epidemic Model by Using Data Driven Epidemiological Parameters of Diseases Spread in India,” Biophys. (Russian Fed., vol. 67, no. 2, hal. 231–244, 2022, doi: 10.1134/S0006350922020154
  9. J. Wu et al., “Early antiviral treatment contributes to alleviate the severity and improve the prognosis of patients with novel coronavirus disease (COVID-19),” J. Intern. Med., vol. 288, no. 1, hal. 128–138, 2020, doi: 10.1111/joim.13063
  10. M. H. G. Fonseca, T. de F. G. de Souza, F. M. de Carvalho Araújo, dan L. O. M. de Andrade, “Dynamics of antibody response to CoronaVac vaccine,” J. Med. Virol., vol. 94, no. 5, hal. 2139–2148, 2022, doi: 10.1002/jmv.27604
  11. A. Simatupang, “Mengupas vaksin covid-19 dan nutrisi untuk lansia,” Repository.Uki.Ac.Id, hal. 1–21, 2021
  12. O. Dyer, “Covid-19: Omicron is causing more infections but fewer hospital admissions than delta, South African data show,” BMJ, vol. 375, no. December, hal. n3104, 2021, doi: 10.1136/bmj.n3104
  13. C. Menni et al., “COVID-19 vaccine waning and effectiveness and side-effects of boosters: a prospective community study from the ZOE COVID Study,” Lancet Infect. Dis., vol. 22, no. 7, hal. 1002–1010, 2022, doi: 10.1016/S1473-3099(22)00146-3
  14. J. Nainggolan, “Optimal Prevention and Treatment Control on SVEIR Type Model Spread of COVID-19,” CAUCHY J. Mat. Murni dan Apl., vol. 7, no. 1, hal. 40–48, 2021, doi: 10.18860/ca.v7i1.12634
  15. Badan Pusat Statistik Kota Semarang. (2022). Jumlah Penduduk Menurut Jenis Kelamin (Jiwa), 2020-2022. Semarang
  16. Dinas Kesehatan Kota Semarang. (2022). Update Kasus COVID-19 tahun 2022. Retrieved Desember 9, 2022

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