Chaos Theory of 0-1 Test and Logistic Map in New Confirmed COVID-19 Cases
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Keywords:
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Logistic Map, 0-1 Test, Chaos, Forecast, COVID-19
Abstract
This study aims to forecast the new number of positive cases of COVID-19 using the logistic map, where the presence of chaos is determined using the 0-1 Test. There are a small number of investigations on chaos utilizing the 0-1 Test and logistic map in the literature. This study provides a straightforward technique of forecasting and a current way of determining chaos. Information on new confirmed COVID-19 cases and population of ten countries involving China, Vietnam, Korea, Malaysia, Singapore, New Zealand, India, USA, Brazil, and Mexico for six months from January 20 to June 15, 2020, are selected as samples. The logistic map runs through three stages: data training, forecasting, and validation using the Mean Absolute Error method (MAE). The data training procedure is critical for determining the best growth rate, r, for the logistic map. In chaotic investigations of the 0-1 Test, there appears to be an inverse expectation toward a logistic map. The 0-1 Test in the data of new confirmed COVID-19 cases in all the selected countries reveals the presence of non-chaotic. This contrasts with the existence of chaos in the logistic map forecasts for the USA, Brazil, and Mexico. Regardless, the logistic map was found to be capable of forecasting new COVID-19 positive cases with low error instances. Beginning in the middle of May 2020, new COVID-19 positive cases are forecasted to be on the rise in the USA, Brazil, and Mexico.
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Storch, L. S., Pringle, J. M., Alexander, K. E., & Jones, D. O. (2017). Revisiting the logistic map: A closer look at the dynamics of a classic chaotic population model with ecologically realistic spatial structure and dispersal. Theoretical Population Biology, 114, 10–18. https://doi.org/10.1016/j.tpb.2016.11.004
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Tahmina Akter, M. (2018). Observation of Different Behaviors of Logistic Map for Different Control Parameters. International Journal of Applied Mathematics and Theoretical Physics, 4(3), 84. https://doi.org/10.11648/j.ijamtp.20180403.14
Tiwari, H., & Hamsapriye, N. (2018). Logistic map based image encryption scheme. International Journal of Applied Engineering Research, 13(23), 16573–16577.
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World Health Organization. (2021). https://covid19.who.int/.
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Zeb, A., Alzahrani, E., Erturk, V. S., & Zaman, G. (2020). Mathematical Model for Coronavirus Disease 2019 ( COVID-19 ) Containing Isolation Class. 2020.
Ahmar, A. S. (2020). Forecast Error Calculation with Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE). JINAV: Journal of Information and Visualization, 1(2 SE-Articles). https://doi.org/10.35877/454RI.jinav303
Albostan, A., & Önöz, B. (2015). Implementation of Chaotic Analysis on River Discharge Time Series. March, 81–92.
Ausloos, M., & Dirickx, M. (2006). The logistic map and the route to chaos : from the beginnings to modern
applications.
Cartwright, T. J. (1991). Planning and Chaos Theory. Journal of the American Planning Association, 57(1), 44–56. https://doi.org/10.1080/01944369108975471
Choi, S., & Ki, M. (2020). Estimating the reproductive number and the outbreak size of COVID-19 in Korea. Epidemiology and Health, 42, e2020011–e2020011. https://doi.org/10.4178/epih.e2020011
Effah-Poku, S., Obeng-Denteh, W., & Dontwi, I. K. (2018). A Study of Chaos in Dynamical Systems. 2018(1), 0–5.
Ghorbani, M. A., Kisi, O., & Aalinezhad, M. (2010). A probe into the chaotic nature of daily streamflow time series by correlation dimension and largest Lyapunov methods. Applied Mathematical Modelling, 34(12), 4050–4057. https://doi.org/https://doi.org/10.1016/j.apm.2010.03.036
Gottwald, G. A., & Melbourne, I. (2016). The 0 - 1 Test for Chaos : A review. Lect. Notes Phys, 915, 221–247. https://doi.org/10.1007/978-3-662-48410-4_7
Huang, C., & Ding, Q. (2020). Performance of Finite Precision on Discrete Chaotic Map Based on a Feedback Shift Register. Complexity, 2020, 4676578. https://doi.org/10.1155/2020/4676578
Jianbo, G. A. O., Peng, F., & Lihua, Y. (2019). Analyses of geographical observations in the Heihe River Basin : Perspectives from complexity theory. 29(71661002), 1441–1461.
Jones, A., & Strigul, N. (2021). Is spread of COVID-19 a chaotic epidemic? Chaos, Solitons & Fractals, 142, 110376. https://doi.org/https://doi.org/10.1016/j.chaos.2020.110376
Juan C, M., Sandra, P., Ignacio, R., Asuncion, N., & Alla, D. (2020). Application of a Semi-empirical Dynamic Model to Forecast the Propagation of the COVID-19 Epidemics in Spain. 1–26.
Kamrujjaman, M., Ghosh, U., & Islam, M. S. (2020). Pandemic and the Dynamics of SEIR Model : Case. April, 1–15. https://doi.org/10.20944/preprints202004.0378.v1
Kendall, B. E., & Fox, G. A. (1998). Spatial Structure , Environmental Heterogeneity , and Population Dynamics : Analysis of the Coupled Logistic Map. 37, 11–37.
Koltsova, E., Kurkina, E., & Vasetsky, A. (2020). Mathematical Modeling of the Spread of COVID-19 in Moscow and Russian Regions. ArXiv: Populations and Evolution.
Lloyd, A. L. (1995). The Coupled Logistic Map : A Simple Model for the Effects of Spatial Heterogeneity on Population Dynamics. 217–230.
Mangiarotti, S., Peyre, M., Zhang, Y., Huc, M., Roger, F., & Kerr, Y. (2020). Chaos theory applied to the outbreak of COVID- 19 : an ancillary approach to decision making in pandemic context.
Moysis, L., Tutueva, A., Volos, C., Butusov, D., Munoz-pacheco, J. M., & Nistazakis, H. (2020). SS symmetry A Two-Parameter Modified Logistic Map and Its Application to Random Bit Generation. 1–11. https://doi.org/10.3390/sym12050829
Moysis, L., Volos, C., Jafari, S., Munoz-Pacheco, J. M., Kengne, J., Rajagopal, K., & Stouboulus, I. (2020). Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption. https://doi.org/10.3390/e22040474
Pelinovsky, E., Kurkin, A., Kurkina, O., Kokoulina, M., & Epifanova, A. (2020). Logistic equation and COVID-19. Chaos, Solitons, and Fractals, 140, 110241. https://doi.org/10.1016/j.chaos.2020.110241
Postavaru, O., Anton, S. R., & Toma, A. (2021). COVID-19 pandemic and chaos theory. Mathematics and Computers in Simulation, 181, 138–149. https://doi.org/https://doi.org/10.1016/j.matcom.2020.09.029
Raghuvanshi, K. K., Kumar, S., & Kumar, S. (2020). A data encryption model based on intertwining logistic map. Journal of Information Security and Applications, 55, 102622. https://doi.org/https://doi.org/10.1016/j.jisa.2020.102622
Sapini, M. L., Adam, N. S., Ibrahim, N., Rosmen, N., & Yusof, N. M. (2017). The presence of chaos in rainfall by using 0-1 test and correlation dimension The presence of chaos in rainfall by using 0-1 test and correlation dimension
Muhamad Luqman Sapini , Nor Syahira Adam , Nursyahirah Ibrahim , Nursyaziella Rosmen , and Norliza. November. https://doi.org/10.1063/1.5012259
Sapkota, N., Karwowski, W., Davahli, M. R., Al-Juaid, A., Taiar, R., Murata, A., Wróbel, G., & Marek, T. (2021). The Chaotic Behavior of the Spread of Infection During the COVID-19 Pandemic in the United States and Globally. IEEE Access, 9, 80692–80702. https://doi.org/10.1109/ACCESS.2021.3085240
Shaikh, A. S., Shaikh, I. N., & Nisar, K. S. (2020). Open Access A mathematical model of COVID-19 using fractional derivative : outbreak in India with dynamics of transmission and control. Adv Differ Equ, 3. https://doi.org/10.1186/s13662-020-02834-3
Sivakumar, B., Berndtsson, R., Olsson, J., Jinno, K., Olsson, J., & Jinno, K. (2009). Evidence of chaos in the rainfall-runoff process. 6667. https://doi.org/10.1080/02626660109492805
Sivakumar, B., & Jayawardena, A. W. (2009). An investigation of the presence of low- dimensional chaotic behaviour in the sediment transport phenomenon. 6667. https://doi.org/10.1080/02626660209492943
Slingo, J., & Palmer, T. (2011). Uncertainty in weather and climate prediction. Philosophical Transactions: Mathematical, Physical and Engineering Sciences, 369(1956), 4751–4767. http://www.jstor.org/stable/23057217
Storch, L. S., Pringle, J. M., Alexander, K. E., & Jones, D. O. (2017). Revisiting the logistic map: A closer look at the dynamics of a classic chaotic population model with ecologically realistic spatial structure and dispersal. Theoretical Population Biology, 114, 10–18. https://doi.org/10.1016/j.tpb.2016.11.004
Sunthornwat, R., & Areepong, Y. (2021). Reproduction number , discrete forecasting model , and chaos analytics for Coronavirus Disease 2019 outbreak in India , Bangladesh , and Myanmar. https://doi.org/10.1080/24709360.2021.1960122
Tahmina Akter, M. (2018). Observation of Different Behaviors of Logistic Map for Different Control Parameters. International Journal of Applied Mathematics and Theoretical Physics, 4(3), 84. https://doi.org/10.11648/j.ijamtp.20180403.14
Tiwari, H., & Hamsapriye, N. (2018). Logistic map based image encryption scheme. International Journal of Applied Engineering Research, 13(23), 16573–16577.
Wang, P., Zheng, X., Li, J., & Zhu, B. (2020). Prediction of epidemic trends in COVID-19 with logistic model and machine learning technics. January.
World Health Organization. (2021). https://covid19.who.int/.
Worldometers. (2020). https://www.worldometers.info/coronavirus/
Zeb, A., Alzahrani, E., Erturk, V. S., & Zaman, G. (2020). Mathematical Model for Coronavirus Disease 2019 ( COVID-19 ) Containing Isolation Class. 2020.
Authors
Yusof, N. M., Sapini, M. L. ., Az’hari, L. I. ., Roslee, . N. A. H. ., Rahmat, S. N. A. ., & Salleh, S. H. M. . (2022). Chaos Theory of 0-1 Test and Logistic Map in New Confirmed COVID-19 Cases. Science and Technology Indonesia, 7(2), 179–185. https://doi.org/10.26554/sti.2022.7.2.179-185
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