Mathematical Analysis of SEIR Model to Prevent COVID-19 Pandemic
DOI:
https://doi.org/10.26458/jedep.v11i4.763Keywords:
SEIR epidemic model, COVID-19 pandemic, Basic reproduction number, Immunity, Vaccinated, Latent periodAbstract
This paper is to analyze Susceptible-Exposed-Infectious-Recovered (SEIR) COVID-19 pandemic model. In this article, a modified SEIR model is constructed and discusses various aspects of it with mathematical analysis to study the dynamic behavior of this model. Spread of this disease through immigration can be represented by the SEIR model. COVID-19 is a highly infectious disease that spread through talking, sneezing, coughing, and touching. In this model, there is an incubation period during the spread of the disease. During the gestation period, a patient is attacked by SARS-CoV-2 coronavirus and shows symptoms of COVID-19, but does not spread of the disease. The horizontal transmission of COVID-19 worldwide can be represented and explained by SEIR model. Maximal control of the pandemic disease COVID-19 can be possible by the optimum vaccination policies. The study also investigates the equilibrium of the disease. In the study a Lyapunov function is created to analyze the global stability of the disease-free equilibrium. The generation matrix method is analyzed to obtain the basic reproduction number and has discussed the global stability for COVID-19 spreading.References
Al-Sheikh, S. A. (2012). Modeling and Analysis of an SEIR Epidemic Model with a Limited Resource for Treatment. Global Journal of Science Frontier Research Mathematics and Decision Sciences, 12(14), 57-66.
Annas, S., Pratama, M. I., Rifandi, M., Sanusi, W., & Side, S. (2020). Stability Analysis and Numerical Simulation of SEIR Model for Pandemic COVID-19 Spread in Indonesia. Chaos, Solitons and Fractals, 139, 110072.
Berger, D., Herkenhoff, K. F., & Mongey, S. (2020). An SEIR Infectious Disease Model with Testing and Conditional Quarantine. Working Paper 26901, National Bureau of Economic Research.
Biswas, M. H. A., Paiva, L. T., & de Pinho, M. (2014). SEIR Model for Control of Infectious Diseases with Constraints. Mathematical Biosciences and Engineering, 11(4), 761-784.
CDC (2020). Prevention and Treatment. US Centre for Disease Control and Prevention. US Department of Health & Human Services.
Demirci, E., Unal, A., & Ozalp, N. (2011). A Fractional Order SEIR Model with Density Dependent Death Rate. Hacettepe Journal of Mathematics and Statistics, 40(2), 287-295.
ECDC (2020). Outbreak of Sever Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2): Increased Transmission beyond China- Fourth Update. European Centre for Disease Prevention and Control (ECDC).
Fine, P. E. (2003). The Interval between Successive Cases of an Infectious Disease. American Journal of Epidemiology, 158(11), 1039-1047.
Green, M. S., Swartz, T., Mayshar, E., Lev, B., Leventhal, A., Slater, P. E., & Shemer, J. (2002). When is an Epidemic an Epidemic? The Israel Medical Association Journal, 4(1), 3-6.
Greenhalgh, D. (1992). Some Results for an SEIR Epidemic Model with Density Dependence in the Death Rate. IMA Journal of Mathematics Applied in Medicine & Biology, 9, 67-106.
Heng, K., & Althaus, C. L. (2020). The Approximately Universal Shapes of Epidemic Curves in the Susceptible‑Exposed‑Infectious‑Recovered (SEIR) Model. Scientific Reports, 10, 19365.
Hornstein, A. (2020). Social Distancing, Quarantine, Contact Tracing, and Testing: Implications of an Augmented SEIR Model. Working Paper 20-04. Federal Reserve Bank of Richmond, Baltimore.
Huang, C., Wang, Y., Li, X., Ren, L., Zhao, J., & Hu, Y. et al. (2020). Clinical Features of Patients Infected with 2019 Novel Coronavirus in Wuhan, China. Lancet, 395(10223), 497-506. https://doi.org/10.1016/S0140-6736(20)30183-5
Intermountain Healthcare (2021). A Not-for-Profit Healthcare. Salt Lake City, Utah, USA.
Li, Q., Guan, X., Wu, P., Wang, X., Zhou, L., & Tong, Y. et al., (2020). Early Transmission Dynamics in Wuhan, China, of Novel Coronavirus-Infected Pneumonia. The New England Journal of Medicine, 1-8. https://doi.org/10.1056/NEJMoa2001316
Lin, Q., Zhao, S., Gao, D., Lou, Y., Yang, S., Musa, S. S., Wang, M. H., Cai, Y., Wang, W., Yang, L., & He, D. (2020). A Conceptual Model for the Coronavirus Disease 2019 (COVID-19) Outbreak in Wuhan, China with Individual Reaction and Governmental Action. International Journal of Infectious Diseases, 93, 211-216.
Mohajan, H. K. (2017). Two Criteria for Good Measurements in Research: Validity and Reliability. Annals of Spiru Haret University Economic Series, 17(3), 58-82.
Mohajan, H. K. (2018). Qualitative Research Methodology in Social Sciences and Related Subjects. Journal of Economic Development, Environment and People, 2(1), 19-46.
Mohajan, H. K. (2020a). The COVID-19 in Italy: Remedies to Reduce the Infections and Deaths. Malaysian Journal of Medical and Biological Research, 7(2), 59-66.
Mohajan, H. K. (2020b). Most Fatal Pandemic COVID-19 Outbreak: An Analysis of Economic Consequences. Annals of Spiru Haret University Economic Series, 20(2), 127-146.
Mohajan, H. K. (2020c). Quantitative Research: A Successful Investigation in Natural and Social Sciences. Journal of Economic Development, Environment and People, 9(4), 52-79.
Mohajan, H. K. (2021a). Aspects of Global COVID-19 Pandemic. Lambert Academic Publishing, Germany.
Mohajan, H. K. (2021b). Global COVID-19 Pandemic: Prevention and Protection Techniques. Journal of Economic Development, Environment and People, 10(1), 51-72.
Mohajan, H. K. (2021c). Mathematical Analysis of SIR Model for COVID-19 Transmission (Unpublished Manuscript).
Nicho, J. (2010). The SIR Epidemiology Model in Predicting Herd Immunity. Undergraduate Journal of Mathematical Modeling, 2(2), 8.
Niu, R., & Wong, E. W. M. et al. (2020). Modeling the COVID-19 Pandemic Using an SEIHR Model with Human Migration. IEEE Access, 8, 195503-195514.
Ojo, M. M. & Akinpelu, F. O. (2017). Lyapunov Functions and Global Properties of SEIR Epidemic Model. International journal of Chemistry, Mathematics and Physics, 1(1), 11-16.
Perko, L. (2013). Differential Equations and Dynamical Systems (3rd Ed.). Volume 7, Springer Science & Business Media, Springer, London.
Phillips, N. (2021). The Coronavirus is here to Stay- Here’s What That Means- A Nature Survey Shows Many Scientists Expect the Virus That Causes COVID-19 to Become Endemic, But It Could Pose Les Danger over Time. Nature, 590, 382-384.
Pongsumpun, P., & Kongnuy, R. et al. (2013). Contact Infection Spread in an SEIR Model: An Analytical Approach. ScienceAsia, 39, 410-415.
Ratchagar, N. P., & Subramanian, S. P. (2015). SEIR Model of Seasonal Epidemic Diseases using HAM. Applications and Applied Mathematics: An International Journal, 10(2), 1066-1081.
Ren, L. L., Wang, Y. M., Wu, Z. Q., Xiang, Z. C., Guo, L., & Xu, T. et al. (2020). Identification of a Novel Coronavirus Causing Severe Pneumonia in Human: A Descriptive Study. Chinese Medical Journal, 1-10. https://doi.org/10.1097/CM9.0000000000000722
Samsuzzoha, M. (2012). A Study on Numerical Solutions of Epidemic Models. PhD Thesis, Faculty of Engineering and Industrial Sciences, Swinburne University of Technology, Australia.
Tang, T., Cao, L., Lan, C.-Y., & Cao, L. (2020). SIR Model for Novel Coronavirus-Infected Transmission Process and Its Application. Research Square, Pre-print.
van den Driessche, P. (2017). Reproduction Numbers of Infectious Disease Models. Infectious Disease Modelling, 2, 288-303.
Wang, W., Tang, J., & Wei, F. (2020b). Updated Understanding of the Outbreak of 2019 Novel Coronavirus (2019-nCoV) in Wuhan, China. Journal of Medical Virology, 92(4), 441-447. https://doi.org/10.1002/jmv.25689
WHO (2020). WHO Characterizes COVID-19 as a Pandemic. World Health Organization (WHO).
Widyaningsih, P., Saputro, D. R. S., & Nugroho, A. W. (2018). Susceptible Exposed Infected Recovery (SEIR) Model with Immigration: Equilibria Points and Its Application. AIP Conference Proceedings 2014, 020165 (2018), AIP Publishing.
Wintachai, P., & Prathom, K. (2021). Stability Analysis of SEIR Model Related to Efficiency of Vaccines for COVID-19 Situation. Heliyon, 7(11), e06812.
Worldometer (2022). COVID-19 Coronavirus Pandemic. American Library Association (ALA).
Yang, C., Wang, R., Gao, F., Sun, D., Tang, J. & Abdelzaher, T. (2020). Quantifying Projected Impact of Social Distancing Policies on COVID-19 Outcomes in the US. arXiv:2005.00112v2 [physics.soc-ph] 11 May 2020. https://covid19predictions.csl.illinois.edu/
Yang, W., Zhang, D., Peng, L., Zhuge, C., & Hong, L. (2021). Rational Evaluation of Various Epidemic Models Based on the COVID-19 Data of China. Epidemics, 37, 100501. https://doi.org/10.1016/j.epidem.2021.100501
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Haradhan Kumar Mohajan
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Journal of Economic Development, Environment and People by Authors is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Based on a work at http://ojs.spiruharet.ro/index.php/jedep/issue/archive.
