Fuzzy Modelling of Covid-19 in Turkey and Some Countries in The World

Year 2020, Volume: 12 Issue: 2, 136 - 150, 31.12.2020

Harun Baldemir , Agah Akın Ömer Akın

https://doi.org/10.47000/tjmcs.751730

Cited By: 1

Abstract

Coronaviruses are a large family of viruses that are found in many different species of animals and are deadly illnesses for human. In late December 2019, China first announced the outbreak of a new coronavirus: Corona Virus Disease 2019 (or COVID-19), in which the symptoms are similar to common colds and flu. However it can sometimes be more serious, particularly for the elderly as well as patients with weak immune systems. The World Health Organization declared COVID-19 a global pandemic on March 11, 2020. As of date \changemarker{October 14}, 2020, confirmed coronavirus cases exceeded \changemarker{38} million including more than \changemarker{one million} deaths worldwide.

In this paper, we use dynamical modelling approach, namely Fuzzyfied Richards Growth Model, to understand the dynamic behaviour of the COVID-19 based on the real data and to predict possible future scenarios applying fuzzy approaches for some countries around the world including China, the United States, the top five countries with the highest population in Europe and Turkey.

Keywords

Novel coronavirus (COVID-19), Population dynamics, Fuzzy modelling, Zadeh's extention principle

References

• Ak{\i}n, O., Khaniyev, T., Turksen, I., Oruc, O., {\em Some possible fuzzy solutions for second order fuzzy initial value problems involving forcing terms}, {Applied and Computational Mathematics}, (2014).
• Ak{\i}n, O., Oru{\c{c}}, O., {\em A prey predator model with fuzzy initial values}, {Hacettepe Journal of Mathematics and Statistics}, \textbf{41}(3)(2012), 387-395.
• Ball, F.G., {\em Dynamic population epidemic models}, {Mathematical Biosciences}, \textbf{107}(2)(1991), 299-324.
• Bauch, C.T. Lloyd-Smith, J.O., Coffee, M.P., Galvani, A.P., {\em Dynamically modeling {SARS} and other newly emerging respiratory illnesses: past, present, and future}, {Epidemiology}, (2005), 791-801.
• Brauer, F., Castillo-Chavez, C., Mathematical Models in Population Biology and Epidemiology. Springer, 2012.
• Chan, J.F.-W., Yuan, S., Kok, K.-H., To, K.K.-W., Chu, H., Yang, J., Xing, F., Liu, J., Yip, C.C.-Y., Poon, R.W.-S., {\em et~al.}, {\em A familial cluster of pneumonia associated with the 2019 novel coronavirus indicating person-to-person transmission: {A} study of a family cluster}, The Lancet \textbf{395}(10223)(2020), 514-523.
• Chow, N., Fleming-Dutra, K., Gierke, R., Hall, A., Hughes, M., Pilishvili, T., Ritchey, M., { et~al.}, {\em Preliminary estimates of the prevalence of selected underlying health conditions among patients with coronavirus disease 2019--{U}nited {S}tates, {F}ebruary 12--{M}arch 28, 2020}, {Morbidity and Mortality Weekly Report}, \textbf{69}(13)(2020), 382.
• Chowell, G., Sattenspiel, L., Bansal, S., Viboud, C., {\em Mathematical models to characterize early epidemic growth: {A} review}, {Physics of Life Reviews}, \textbf{18}(2016), 66-97.
• Funk, S., Camacho, A., Kucharski, A.J., Lowe, R., Eggo, R.M., Edmunds, W.J., {\em Assessing the performance of real-time epidemic forecasts: {A} case study of ebola in the western area region of {S}ierra {L}eone, 2014-15}, {PLoS Computational Biology}, \textbf{15}(2)(2019).
• Guan, W., Ni, Z., Hu, Y., Liang, W., Ou, C., He, J., Liu, L., Shan, H. Lei, C., Hui, D., { et~al.}, {\em China medical treatment expert group for {C}ovid-19. clinical characteristics of coronavirus disease 2019 in {C}hina}, Clinical characteristics of coronavirus disease (2019), 1708-1720.
• Hogg, S., Essential microbiology. John Wiley \& Sons, 2013.
• Hsieh, Y.-H., Cheng, Y.-S., {\em Real-time forecast of multiphase outbreak}, {Emerging Infectious Diseases}, \textbf{12}(1)(2006), 122.
• Kaleva, O., {\em Fuzzy differential equations}, {Fuzzy Sets and Systems}, \textbf{24}(3)(1987), 301-317.
• Lee, K.H., {\em First course on fuzzy theory and applications}, {Springer Science \& Business Media}, \textbf{27} (2004).
• Liang, W., Guan, W., Chen, R., Wang, W., Li, J., Xu, K., Li, C., Ai, Q., Lu, W., Liang, H., {et~al.}, {\em Cancer patients in {SARS}-{C}o{V}-2 infection: {A} nationwide analysis in {C}hina}, {The Lancet Oncology}, \textbf{21}(3)(2020), 335-337.
• Li, Q., Guan, X., Wu, P., Wang, X., Zhou, L., Tong, Y., Ren, R., Leung, K.S., Lau, E.H., Wong, J.Y., { et~al.}, {\em Early transmission dynamics in {W}uhan, {C}hina, of novel coronavirus--infected pneumonia}, New England Journal of Medicine, 2020.
• Lighter, J., Phillips, M., Hochman, S., Sterling, S., Johnson, D., Francois, F., Stachel, A., {\em Obesity in patients younger than 60 years is a risk factor for {C}ovid-19 hospital admission}, {Clin Infect Dis}, \textbf{9}(10)(2020), 1093.
• Lu, R., Zhao, X., Li, J., Niu, P., Yang, B., Wu, H., Wang, W., Song, H., Huang, B., Zhu, N., {et~al.}, {\em Genomic characterisation and epidemiology of 2019 novel coronavirus: implications for virus origins and receptor binding}, {The Lancet}, \textbf{395}(10224)(2020), 565-574.
• Mehra, M.R., Desai, S.S., Kuy, S., Henry, T.D. , Patel, A.N., {\em Cardiovascular disease, drug therapy, and mortality in {C}ovid-19}, {New England Journal of Medicine}, (2020).
• Mizukoshi, M.T. , Barros, L.d., Chalco-Cano, Y., Rom{\'a}n-Flores, H., Bassanezi, R.C., {\em Fuzzy differential equations and the extension principle}, {Information Sciences}, \textbf{177}(17)(2007), 3627-3635.
• Oberguggenberger, M., Pittschmann, S., {\em Differential equations with fuzzy parameters}, {Mathematical and Computer Modelling of Dynamical Systems}, \textbf{5}(3)(1999), 181-202.
• Petersen, E., Gokengin, A.D., {\em {SARS}-{C}o{V}-2 epidemiology and control, different scenarios for Turkey}, {Turkish Journal of Medical Sciences}, \textbf{50} (2020), 509-514.
• Petrilli, C.M., Jones, S.A., Yang, J., Rajagopalan, H., O'Donnell, L., Chernyak, Y., Tobin, K.A., Cerfolio, R.J., Francois, F., Horwitz, L.I., {\em Factors associated with hospital admission and critical illness among 5279 people with coronavirus disease 2019 in {N}ew {Y}ork {C}ity: {P}rospective cohort study}, {BJM}, \textbf{369}(2020).
• Richards, F., {\em A flexible growth function for empirical use}, {Journal of Experimental Botany}, \textbf{10}(2)(1959), 290-301.
• Tsoularis, A., Wallace, J., {\em Analysis of logistic growth models}, {Mathematical Biosciences}, \textbf{179}(1)(2002), 21-55.
• Wang, D., Hu, B., Hu, C., Zhu, F., Liu, X., Zhang, J., Wang, B., Xiang, H., Cheng, Z., Xiong, Y., { et~al.}, {\em Clinical characteristics of 138 hospitalized patients with 2019 novel coronavirus--infected pneumonia in {W}uhan, {C}hina}, {Jama}, \textbf{323}(11)(2020), 1061-1069.
• World Health Organization {et~al.}, Consensus document on the epidemiology of severe acute respiratory syndrome ({SARS}), {WHO}, 2003.
• World Health Organization { et~al.}, {\em {WHO} director-general's remarks at the media briefing on 2019-n{C}o{V} on 11 {F}ebruary 2020}, WHO, (2020).
• Wu, Z., McGoogan, J.M., {\em Characteristics of and important lessons from the coronavirus disease 2019 ({C}ovid-19) outbreak in {C}hina: {S}ummary of a report of 72 314 cases from the {C}hinese center for disease control and prevention}, {Jama}, \textbf{323}(13)(2020), 1239-1242.
• Zadeh, L.A., {\em The concept of a linguistic variable and its application to approximate reasoning}, {Information Sciences}, \textbf{8}(4)(1975), 301-357.
• Zhou, P., Yang, X.-L., Wang, X.-G., Hu, B., Zhang, L., Zhang, W., Si, H.-R., Zhu, Y., Li, B., Huang, C.-L., {et~al.}, {\em A pneumonia outbreak associated with a new coronavirus of probable bat origin}, {Nature}, \textbf{579}(7798)(2020), 270-273.
• Zhou, F., Yu, T., Du, R., Fan, G., Liu, Y., Liu, Z., Xiang, J., Wang, Y., Song, B., Gu, X., {et~al.}, Clinical course and risk factors for mortality of adult inpatients with {C}ovid-19 in {W}uhan, {C}hina: {A} retrospective cohort study, {The Lancet}, 2020.
• Zhou, G., Yan, G., {\em Severe acute respiratory syndrome epidemic in {A}sia}, {Emerging Infectious Diseases}, \textbf{9}(12)(2003), 1608-1610.
• Zhu, N., Zhang, D., Wang, W., Li, X., Yang, B., Song, J., Zhao, X., Huang, B., Shi, W., Lu, R., {et~al.}, {\em A novel coronavirus from patients with pneumonia in {C}hina, 2019}, {New England Journal of Medicine}, (2020).