A Novel Mathematical Model of the Dynamics of COVID-19

Year 2023, Volume: 36 Issue: 3, 1302 - 1309, 01.09.2023

Elif Demirci

https://doi.org/10.35378/gujs.1096827

Cited By: 1

Abstract

The severity of the COVID-19 pandemic requires a better understanding of the spread of SARS-COV2. As of December 2019, several mathematical models have been developed to explain how SARS-COV2 spreads within populations, and proposed models have evolved as more is learned about the dynamics of the outbreak. In this study, we propose a new mathematical model that includes demographic characteristics of the population. Social isolation and vaccination are also taken into account in the model. Besides transmission arising from intercourse with undiagnosed infected persons, we also consider transmission by contact with the exposed group. In this study, after the model is established, the basic reproduction number is calculated and local stability analysis of disease-free equilibrium is given. Finally, we give numerical simulations for the proposed model.

Keywords

Epidemic model, Basic reproduction number, Stability

Supporting Institution

TÜBİTAK

Project Number

120F307

Thanks

This research is supported by The Scientific and Technological Research Council of Turkey (TUBITAK) within the scope of the 1001-Scientific and Technological Research Project (120F307)

References

• [1] Brauer, F., “Castillo-Chavez, C. and Feng, Z., Mathematical Models in Epidemiology 1st ed.”. Springer-Verlag New York, (2019).
• [2] Nistal, R., De la Sen, M., Gabirond, J., Alonso-Quesada, S., Garrido, A.J., Garrido, I., “A Study on COVID-19 Incidence in Europe through Two SEIR Epidemic Models Which Consider Mixed Contagions from Asymptomatic and Symptomatic Individuals”, Applied Sciences, 11: 6266, (2021). DOI: 10.3390/app11146266
• [3] Arino, J., Protet, S., “A simple model for COVID-19”, Infectious Disease Modelling, 5: 309-315, (2020).
• [4] Cakir, Z., Savas, H. B., “A mathematical modelling for the COVID-19 pandemic in Iran”, Ortadogu Tıp Dergisi, 12(2): 206-210, (2020).
• [5] Ivorra, B., Ferrandez, M. R., Vela-Perez, M., Ramos, A. M., “Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. The case of China”, Communications in Nonlinear Science and Numerical Simulation, 88: 105303, (2020).
• [6] Liu, Z., Magal, P., Seydi, O., Webb, G., “A COVID-19 epidemic model with latency period.”, Infectious Disease Modelling, 5: 323-337, (2020).
• [7] Ndairou, F., Area, I., Nieto, J. J., Torres, D. F. M., “Mathematical modeling of COVID-19 transmission Dynamics with a case study of Wuhan”, Chaos, Solitons & Fractals, 135: 109846, (2020).
• [8] Vega, D.I., “Lockdown, one, two, none, or smart. Modeling containing COVID-19 infection. A conceptual model”, Science of the Total Environment, 730: 138917, (2020).
• [9] https://www.who.int/docs/default-source/coronaviruse/situationreports/20200402-sitrep-73-covid-19.pdf?sfvrsn=5ae25bc76. Access date: 25.06.2020
• [10] https://www.cdc.gov/coronavirus/2019-ncov/daily-life-coping/contact-tracing.html. Access date: 10.02.2022.
• [11] Ahmed, I, Modu, G. U., Yusuf, A., Kumam, P., Yusuf, I., “A mathematical model of Coronavirus Disease (COVID-19) containing asymptomatic and symptomatic classes”, Results in Physics, (2021). DOI: 10.1016/j.rinp.2020.103776
• [12] Riyapan, P., Shuaib, S. E., Intarasit, A., “A Mathematical Model of COVID-19 Pandemic: A Case Study of Bangkok, Thailand”, Computational and Mathematical Methods in Medicine, (2021). DOI: https://doi.org/10.1155/2021/6664483
• [13] Van den Driessche P., Watmough J., “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission”, Mathematical Biosciences, 180(1-2): 29–48, (2002).
• [14] https://data.tuik.gov.tr/Bulten/Index?p=Olum-ve-Olum-Nedeni-Istatistikleri-2019-33710. Access date: 15.11.2022.