ANALYZING COVID-19 DYNAMICS IN TWO NON-INTERACTING REGIONS THROUGH A STRUCTURED COMPARTMENTAL MODEL
Abstract
COVID-19 is an infectious disease caused by the corona virus. Corona Virus or Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) is a virus that attacks the respiratory system. This paper will discuss the effect of the absence of human mobility on the spread of COVID-19. The proposed model consists of ten compartments, including susceptible, exposed, infected (symptomatic and asymptomatic), and recovered individuals in both regions. The model construction in this paper is quite simple, namely it does not involve human mobility at all. This is important because by understanding the characteristics of COVID-19 in a closed population, the spread of COVID-19 locally can be anticipated. Both analytical and numerical approaches are used. The numerical study involves elasticity analysis to identify key influential parameters and autonomous simulations to observe the long-term behavior of the system.
Keywords
Full Text:
PDFReferences
Aldila, D., Ndii, M. Z., & Samiadji, B. M. (2020). Optimal control on COVID-19 eradication program in Indonesia under the effect of community awareness. Mathematical Biosciences and Engineering, 17(6), 6355–6389. https://doi.org/10.3934/mbe.2020335
Aldila, D., Samiadji, B. M., Simorangkir, G. M., Khosnaw, S. H. A., & Shahzad, M. (2021). Impact of early detection and vaccination strategy in COVID-19 eradication program in Jakarta, Indonesia. BMC Research Notes, 14(1), 1–7. https://doi.org/10.1186/s13104-021-05540-9
Anton, H., & Rorres, C. (2005). Elementary Linear Algebra. In New York: John Wiley and Sons, Inc.
Balya, M. A., Dewi, B. O., Lestari, F. I., Ratu, G., Rosuliyana, H., Windyhani, T., Fadhlia, Z. R., Samiadji, B. M., Aldila, D., Khoshnaw, S. H. A., & Shahzad, M. (2021). Investigating the impact of social awareness and rapid test on a covid-19 transmission model. Communication in Biomathematical Sciences, 4(1), 46–64. https://doi.org/10.5614/cbms.2021.4.1.5
Boyce, W. E., & DiPrima, R. C. (2009). Elementary Differential Equations and Boundary Value Problems, Textbook and Student Solutions Manual Set. 796. http://books.google.com/books?id=q3lmPgAACAAJ&dq=elementary+differential+equations+and+boundary+value+problems&hl=&cd=16&source=gbs_api%5Cnpapers3://publication/uuid/9096B1C5-0F87-4FEA-AA72-C3E07E930C19
Chitnis, N., Hyman, J. M., & Cushing, J. M. (2008). Determining Important Parameters in the Spread of Malaria Through the Sensitivity Analysis of a Mathematical Model. Bulletin of Mathematical Biology, 70(5), 1272–1296. https://doi.org/10.1007/s11538-008-9299-0
Diekmann, O., Heesterbeek, J. A. P., & Roberts, M. G. (2010). The construction of next-generation matrices for compartmental epidemic models. Journal of the Royal Society Interface, 7(47), 873–885. https://doi.org/10.1098/rsif.2009.0386
Driessche, P. Van Den, & Watmough, J. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission (Vol. 180).
Feng, Z., & Velasco-Hernández, J. X. (1997). Competitive exclusion in a vector-host model for the dengue fever. Journal of Mathematical Biology, 35(5), 523–544. https://doi.org/10.1007/s002850050064
Ferguson, N. M., Laydon, D., Nedjati-Gilani, G., Imai, N., Ainslie, K., Baguelin, M., Bhatia, S., Boonyasiri, A., Cucunubá, Z., Cuomo-Dannenburg, G., Dighe, A., Dorigatti, I., Fu, H., Gaythorpe, K., Green, W., Hamlet, A., Hinsley, W., Okell, L. C., Van Elsland, S., … Ghani, A. C. (2020). Report 13: Estimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in 11 European countries. Imperial College COVID-19 Response Team, March. https://doi.org/10.25561/77482.
He, S., Peng, Y., & Sun, K. (2020). SEIR modeling of the COVID-19 and its dynamics. Nonlinear Dynamics, 101(3), 1667–1680. https://doi.org/10.1007/s11071-020-05743-y
Jia, J. S., Lu, X., Yuan, Y., Xu, G., Jia, J., & Christakis, N. A. (2020). Population flow drives spatio-temporal distribution of COVID-19 in China. Nature, 582(7812), 389–394. https://doi.org/10.1038/s41586-020-2284-y
Li, Q., Guan, X., Wu, P., Wang, X., Zhou, L., Tong, Y., Ren, R., Leung, K. S. M., Lau, E. H. Y., Wong, J. Y., Xing, X., Xiang, N., Wu, Y., Li, C., Chen, Q., Li, D., Liu, T., Zhao, J., Liu, M., … Feng, Z. (2020). Early Transmission Dynamics in Wuhan, China, of Novel Coronavirus–Infected Pneumonia. New England Journal of Medicine, 382(13), 1199–1207. https://doi.org/10.1056/nejmoa2001316
Martcheva, M. (2015). An Introduction to Mathematical Epidemiology (Vol. 61 of Texts in Applied Mathematics). In New York: Springer.
Pei, S., & Shaman, J. (2020). Initial Simulation of SARS-CoV2 Spread and Intervention Effects in the Continental US. MedRxiv, 2020.03.21.20040303.
Yang, C., & Wang, J. (2020). A mathematical model for the novel coronavirus epidemic in Wuhan, China. Mathematical Biosciences and Engineering, 17(3), 2708–2724. https://doi.org/10.3934/mbe.2020148
Zlojutro, A., Rey, D., & Gardner, L. (2019). A decision-support framework
to optimize border control for global outbreak mitigation. Scientific Reports, 9(1), 1–14. https://doi.org/10.1038/s41598-019-38665-w
DOI: https://doi.org/10.20527/epsilon.v19i1.15383
Refbacks
- There are currently no refbacks.
Copyright (c) 2025 EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS)
Indexed by:

EDITORIAL OFFICE

All articles published in "Epsilon: Jurnal Matematika Murni dan Terapan" are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License (CC BY-NC-SA 4.0). Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.


