# MODIFIED SEIRD MODEL: A NOVEL SYSTEM DYNAMICS APPROACH IN MODELLING THE SPREAD OF COVID-19 IN MALAYSIA DURING THE PRE-VACCINATION PERIOD

## Keywords:

SEIRD model, System Dynamics, Systems Thinking Approach, COVID-19, Simulation, Malaysia

## Abstract

Mathematical modelling is an effective tool for understanding the complex structures and behaviors of natural phenomena, such as coronavirus disease 2019 (COVID-19), which is an infectious disease caused by a life-threatening virus called SARS-CoV-2. It has rapidly spread across the world in the last three years, including Malaysia. Adopting a novel system dynamics approach, this paper aims to explain how mathematics can play a significant role in modelling the COVID-19 spread and suggests practical methods for controlling it. It forecasts the data of infected (I), recovered (R) and death (D) cases for decision-making. This paper proposes a modified Susceptible-Exposed-Infected-Recovered-Death (SEIRD) model with time-varying parameters considering the sporadic cases, the reinfection cases, the implementation of a movement control order, and the percentage of humans abiding by the rules to forecast future growth patterns of COVID-19 in Malaysia and to study the effects of the consideration on the number of forecasted COVID-19 cases, during the pre-vaccination period. This study implemented the preliminary stage of forecasting the COVID-19 data using the proposed SEIRD model and highlighted the importance of parameter optimization. The mathematical model is solved numerically using built-in Python function ‘odeint’ from the Scipy library, which by default uses LSODA algorithm from the Fortran library Odepack that adopts the integration method of non-stiff Adams and stiff Backward Differentiation (BDF) with automatic stiffness detection and switching. This paper suggests that the effects of factors of sporadic cases, reinfection cases, government intervention of movement control order and population behavior are important to be studied through mathematical modelling as it helps in understanding the more complex behavior of COVID-19 transmission dynamics in Malaysia and further helps in decision-making.

ABSTRAK: Pemodelan matematik adalah alat berkesan bagi memahami struktur kompleks dan tingkah laku fenomena semula jadi, seperti penyakit coronavirus 2019 (COVID-19), iaitu penyakit berjangkit yang disebabkan oleh virus pengancam nyawa yang dipanggil SARS-CoV-2. Ia telah merebak dengan pantas ke seluruh dunia sejak tiga tahun lepas, termasuk Malaysia. Mengguna pakai pendekatan baharu sistem dinamik, kajian ini bertujuan bagi menerangkan bagaimana matematik boleh memainkan peranan penting dalam membentuk model penyebaran COVID-19, dan mencadangkan kaedah praktikal bagi mengawalnya. Model ini dapat meramalkan data sebenar kes yang dijangkiti, pulih dan kematian bagi membuat keputusan. Kajian ini mencadangkan model populasi Rentan-Terdedah-Terjangkiti-Pulih-Mati (SEIRD) yang diubah suai bersama parameter masa berbeza seperti kes sporadis, kes jangkitan semula, pelaksanaan perintah kawalan pergerakan, dan peratusan manusia patuh peraturan bagi meramal pertumbuhan corak kes COVID-19 di Malaysia pada masa hadapan dan mengkaji kesan–kesan pertimbangan parameter tersebut ke atas bilangan kes COVID-19 yang diramalkan ketika tempoh sebelum vaksinasi. Kajian ini melaksanakan peringkat awal ramalan data COVID-19 menggunakan model SEIRD yang dicadangkan dan menekankan kepentingan pengoptimuman parameter.  Model matematik ini diselesaikan secara berangka menggunakan fungsi terbina Python ‘odeint’ daripada perpustakaan Scipy, yang menggunakan algoritma LSODA daripada perpustakaan Fortran Odepack menerusi kaedah penyepaduan Adams tidak kaku dan Pembezaan Belakang (BDF) kaku dengan pengesanan dan pertukaran kekakuan automatik. Kajian ini mencadangkan kesan faktor kes sporadis, kes jangkitan semula, campur tangan kerajaan terhadap perintah kawalan pergerakan dan tingkah laku penduduk adalah penting untuk dikaji melalui pemodelan matematik kerana ia membantu dalam memahami tingkah laku yang lebih kompleks dalam dinamik penularan COVID-19 di Malaysia dan seterusnya membantu dalam membuat keputusan.

ABSTRAK: Pemodelan matematik adalah alat berkesan bagi memahami struktur kompleks dan tingkah laku fenomena semula jadi, seperti penyakit coronavirus 2019 (COVID-19), iaitu penyakit berjangkit yang disebabkan oleh virus pengancam nyawa yang dipanggil SARS-CoV-2. Ia telah merebak dengan pantas ke seluruh dunia sejak tiga tahun lepas, termasuk Malaysia. Mengguna pakai pendekatan baharu sistem dinamik, kajian ini bertujuan bagi menerangkan bagaimana matematik boleh memainkan peranan penting dalam membentuk model penyebaran COVID-19, dan mencadangkan kaedah praktikal bagi mengawalnya. Model ini dapat meramalkan data sebenar kes yang dijangkiti, pulih dan kematian bagi membuat keputusan. Kajian ini mencadangkan model populasi Rentan-Terdedah-Terjangkiti-Pulih-Mati (SEIRD) yang diubah suai bersama parameter masa berbeza seperti kes sporadis, kes jangkitan semula, pelaksanaan perintah kawalan pergerakan, dan peratusan manusia patuh peraturan bagi meramal pertumbuhan corak kes COVID-19 di Malaysia pada masa hadapan dan mengkaji kesan–kesan pertimbangan parameter tersebut ke atas bilangan kes COVID-19 yang diramalkan ketika tempoh sebelum vaksinasi. Kajian ini melaksanakan peringkat awal ramalan data COVID-19 menggunakan model SEIRD yang dicadangkan dan menekankan kepentingan pengoptimuman parameter.  Model matematik ini diselesaikan secara berangka menggunakan fungsi terbina Python ‘odeint’ daripada perpustakaan Scipy, yang menggunakan algoritma LSODA daripada perpustakaan Fortran Odepack menerusi kaedah penyepaduan Adams tidak kaku dan Pembezaan Belakang (BDF) kaku dengan pengesanan dan pertukaran kekakuan automatik. Kajian ini mencadangkan kesan faktor kes sporadis, kes jangkitan semula, campur tangan kerajaan terhadap perintah kawalan pergerakan dan tingkah laku penduduk adalah penting untuk dikaji melalui pemodelan matematik kerana ia membantu dalam memahami tingkah laku yang lebih kompleks dalam dinamik penularan COVID-19 di Malaysia dan seterusnya membantu dalam membuat keputusan.

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## Author Biography

### Ibrahim Shogar, Department of Computational and Theoretical Sciences

Assoc. Prof. Dr. in Department of Computational and Theoretical Sciences, Kulliyyah of Science, IIUM, Kuantan, Pahang

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2023-07-04

## How to Cite

Zulkarnain, N., Mohammad, N. F., & Shogar, I. (2023). MODIFIED SEIRD MODEL: A NOVEL SYSTEM DYNAMICS APPROACH IN MODELLING THE SPREAD OF COVID-19 IN MALAYSIA DURING THE PRE-VACCINATION PERIOD. IIUM Engineering Journal, 24(2), 159–183. https://doi.org/10.31436/iiumej.v24i2.2550

## Section

Engineering Mathematics and Applied Science