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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