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Türkiye'de COVID-19'un SEIR Temelli Salgın Modellemesi

Year 2022, , 306 - 310, 31.01.2022
https://doi.org/10.31590/ejosat.842560

Abstract

Koronavirüs hastalığı 2019 (COVID-19) salgını, hızlı yayılması ve yüksek ölüm oranı nedeniyle dünya çapında yerel bir salgın olmaktan çok uluslararası bir pandemi olarak ilan edilmiştir. Bulaşıcı hastalıkların görülme sıklığının modellenmesi hem bilim alanının hem de hükümetlerin, halk sağlığı ve müdahale planlamasının önemli bir bölümünün oldukça ilgisini çekmiş ve son on yılda önemli bir araştırma konusu haline gelmiştir. Bu çalışmada, COVID-19 için SEIR modeliyle ilgili olarak genişletilmiş bir model önermekte, modeli ve koronavirüs verileriyle uyumlu hale getirmekteyiz. Bu çalışmada, Türkiye için bir SEIR modeli oluşturmak için kamuya açık bir veri seti kullandık. Bu çalışma Türkiye'de COVID-19 hastalığının yayılışını göstermeye odaklanmaktadır. SEIR model parametreleri ile en iyi yaklaşımını göstermekteyiz. Sonuçlar, SEIR modelinin yayılmasını doğru bir şekilde modellemek için ek değişkenler gerektirdiğini göstermektedir. Ayrıca, modelin her zaman aynı vaka tanımı olan verilerden oluşması gerekliliğine inanmaktayız. Modelimizin grafiğine baktığımızda benzer desen modeli gözlemlenmiştir.

References

  • Annas, S., Rifandi, P., 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.
  • Arino, J., McCluskey, C.C., wan den Driessche, P. (2003). Global results for an epidemic model with vaccination that exhibits backward bifurcation, SIAM J. Appl. Math., 64, 260–276.
  • Bailey, N. (1975). The mathematical theory of infectious diseases and its applications, Griffin, 28,479–480. Diekmann., O., Heesterbeek, J.A.P. (2000). Mathematical Epidemiology of Infectious Diseases, Model Building, Analysis and Interpretation, Wiley.
  • Egonmwan, A. O, Okuonghae, D. (2018). Analysis of a mathematical model for tuberculosis with diagnosis, J Appl Math Comput, 59, 129–62.
  • Elif, D., Arzu, U., Nuri, O. (2011), A fractional order SEIR model with density dependent death rate. Hacet J Math Stat, 40(2), 287–95.
  • Hethcote, H.W. (2000). The Mathematics of Infectious Disease, SIAM Review, 42, 653.
  • Jackson, A. (1989). Modeling the Aids Epidemic, Notices of the American Mathematical Society, 36, 983.
  • Keeling, M. (2004). The mathematics of diseases, http://plus.maths.org (Date accessed: May 2020).
  • Kermack, W.O., & McKendrick, A. (1927). A Contribution to the Mathematical Theory of Epidemics. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 115(772), 700–721.
  • Keshet, L. (2005). Mathematical Models in Biology, SIAM, 586.
  • Liu, Z., Magal, P., Seydi, O., Webb, G. (2020). A COVID-19 epidemic model with latency period, Infectious Disease Modelling, 5, 323-337.
  • Sattenspiel, L., Lloyd, A. (2009). The Geographic Spread of Infectious Disease, Models and Applications, NJ Princeton University Press, 304.
  • Stehle, J., Voirin, N., Barrat, A., Cattuto, C., Colizza, V., Isella, L., Regis, C., Pinton, J. F., Khanafer, N., Van den Broeck, W., Vanhems, P. (2011) Simulation of an SEIR infectious disease model on the dynamic contact network of conference attendees. BMC Med, 9, 87.
  • Syafruddin, S., Mulbar, U., Sidjara, S., Sanusi, W. (2017). A SEIR Model for transmission of tuberculosis. AIP conference proceedings, 1830.
  • Tang, B., Wang, X., Li, Q., Bragazzi, N.L., Tangi S , Xiao, Y, et al. Estimation of the transmission risk of 2019-nCoV and its implication for public health interventions. J Clin Med 9, 462.
  • Waziri, A. S., Massawe, E. S., Makinde, O. (2012). Mathematical modelling of HIV/AIDS dynamics with treatment and vertical transmission, Appl Math, 3, 77–89.
  • Weinstein, S., J., Morgan, S., Rogers, K. E., Barlow, N.S. (2020). Analytic solution of the SEIR epidemic model via asymptotic approximant, Physica D, 411.
  • Yang, C., Wang, J. (2020). A mathematical model for the novel coronavirus epidemic in Wuhan, China. Math Biosci Eng, 17(3), 2708–24.
  • Zhang, X., Xiang, H. & Meng, X. (2014). Dynamics of the deterministic and stochastic SIQS epidemic model wiht non-linear incidence, Appl. Math. Comput., 243, 546–558.

SEIR Based Epidemic Modeling of COVID-19 in Turkey

Year 2022, , 306 - 310, 31.01.2022
https://doi.org/10.31590/ejosat.842560

Abstract

The coronavirus disease 2019 (COVID-19) outbreak was declared as an international pandemic rather than a local epidemic worldwide due to its rapid spread and high mortality. Countries have planned to return a new normal under some specific situations cope with economic effects that caused by the curfew and closure of companies when they reach the infection peak. Modeling the incidence of infectious diseases has attracted increasing attention from both scientific community and governments and a significant part of public health and intervention planning and have become a hot research topic in the last decades. Since epidemic diseases are effective in large populations, mathematical modeling has been used for a long time and has made important contributions in the analysis of these populations, in determining and controlling the spread rate of the epidemic. In this paper, we propose an extended model and calibrate the model and fitting with the coronavirus data by concerning with Susceptible-Exposed-Infected-Recovered (SEIR) model. In this study, we used an open public dataset to create a SEIR model for Turkey. This paper focuses on demonstrating the spreade of disease in Turkey. We gathered best approximation with the SEIR model parameters. The results suggest that SEIR model requires additional variables to model diasese spread accurately. Furthermore, the model needs to consist of data that always be the same case definition. The model plot results indicate the similar pattern.

References

  • Annas, S., Rifandi, P., 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.
  • Arino, J., McCluskey, C.C., wan den Driessche, P. (2003). Global results for an epidemic model with vaccination that exhibits backward bifurcation, SIAM J. Appl. Math., 64, 260–276.
  • Bailey, N. (1975). The mathematical theory of infectious diseases and its applications, Griffin, 28,479–480. Diekmann., O., Heesterbeek, J.A.P. (2000). Mathematical Epidemiology of Infectious Diseases, Model Building, Analysis and Interpretation, Wiley.
  • Egonmwan, A. O, Okuonghae, D. (2018). Analysis of a mathematical model for tuberculosis with diagnosis, J Appl Math Comput, 59, 129–62.
  • Elif, D., Arzu, U., Nuri, O. (2011), A fractional order SEIR model with density dependent death rate. Hacet J Math Stat, 40(2), 287–95.
  • Hethcote, H.W. (2000). The Mathematics of Infectious Disease, SIAM Review, 42, 653.
  • Jackson, A. (1989). Modeling the Aids Epidemic, Notices of the American Mathematical Society, 36, 983.
  • Keeling, M. (2004). The mathematics of diseases, http://plus.maths.org (Date accessed: May 2020).
  • Kermack, W.O., & McKendrick, A. (1927). A Contribution to the Mathematical Theory of Epidemics. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 115(772), 700–721.
  • Keshet, L. (2005). Mathematical Models in Biology, SIAM, 586.
  • Liu, Z., Magal, P., Seydi, O., Webb, G. (2020). A COVID-19 epidemic model with latency period, Infectious Disease Modelling, 5, 323-337.
  • Sattenspiel, L., Lloyd, A. (2009). The Geographic Spread of Infectious Disease, Models and Applications, NJ Princeton University Press, 304.
  • Stehle, J., Voirin, N., Barrat, A., Cattuto, C., Colizza, V., Isella, L., Regis, C., Pinton, J. F., Khanafer, N., Van den Broeck, W., Vanhems, P. (2011) Simulation of an SEIR infectious disease model on the dynamic contact network of conference attendees. BMC Med, 9, 87.
  • Syafruddin, S., Mulbar, U., Sidjara, S., Sanusi, W. (2017). A SEIR Model for transmission of tuberculosis. AIP conference proceedings, 1830.
  • Tang, B., Wang, X., Li, Q., Bragazzi, N.L., Tangi S , Xiao, Y, et al. Estimation of the transmission risk of 2019-nCoV and its implication for public health interventions. J Clin Med 9, 462.
  • Waziri, A. S., Massawe, E. S., Makinde, O. (2012). Mathematical modelling of HIV/AIDS dynamics with treatment and vertical transmission, Appl Math, 3, 77–89.
  • Weinstein, S., J., Morgan, S., Rogers, K. E., Barlow, N.S. (2020). Analytic solution of the SEIR epidemic model via asymptotic approximant, Physica D, 411.
  • Yang, C., Wang, J. (2020). A mathematical model for the novel coronavirus epidemic in Wuhan, China. Math Biosci Eng, 17(3), 2708–24.
  • Zhang, X., Xiang, H. & Meng, X. (2014). Dynamics of the deterministic and stochastic SIQS epidemic model wiht non-linear incidence, Appl. Math. Comput., 243, 546–558.
There are 19 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Kevser Şahinbaş 0000-0002-8076-3678

Ferhat Çatak This is me 0000-0002-2434-9966

Publication Date January 31, 2022
Published in Issue Year 2022

Cite

APA Şahinbaş, K., & Çatak, F. (2022). SEIR Based Epidemic Modeling of COVID-19 in Turkey. Avrupa Bilim Ve Teknoloji Dergisi(33), 306-310. https://doi.org/10.31590/ejosat.842560