Araştırma Makalesi
Semptomatik ve Asemptomatik Bulaşmaların Etkisi ile COVID-19 Salgınının Matematiksel Modelinin Analizi
Öz
Bu çalışma, COVID-19 salgın sürecini ifade eden ayrık zamanlı bir SIR modelinin kararlılığını ve flip çatallanmasını ele almaktadır. Aşının etkisini dikkate alan model, hastalığın bulaşmasında semptomatik bireylerin yanı sıra asemptomatik bireylerin de etkisini içerir. Denge çözümleri belirli parametrik koşullar altında elde edilir. Daha sonra bu denge çözümlerinin lokal kararlılıkları araştırılır. Pozitif iç denge çözümü için çatallanmanın varlığı belirlenir.
Anahtar Kelimeler
COVID-19 Salgın Modeli Flip Çatallanma Lokal Asimptotik Kararlılık SIR Modeli
Kaynakça
- W. H. Hamer, Epidemic disease in England-the evidence of variability and of persistence of type, Lancet. 1 (1906), 733-739. doi:10.1016/S0140-6736(01)80187-2
- W. O. Kermack, A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proceedings of the Royal Society of London Series A. 115 (1927), 700-721. doi:10.1098/rspa.1927.0118
- W. O. Kermack, A. G. McKendrick, A contribution to the mathematical theory of epidemics, Part II, The problem of endemicity, Proceedings of the Royal Society of London Series A. 138 (1932), 55-83. doi:10.1098/rspa.1932.0171
- W. O. Kermack, A. G. McKendrick, Contributions to the mathematical theory of epidemics, Part III, Further studies of the problem of Endemicity, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character. 141(1933), 94-122. doi:10.1098/rspa.1933.0106
- D. Wu, T. Wu, Q. Liu, Z. Yang, The SARS-CoV-2 outbreak: What we know, International Journal of Infectious Diseases. 94 (2020), 44–48. doi:10.1016/j.ijid.2020.03.004
- B. Hu, H. Guo, P. Zhou, Z.L. Shi, Characteristics of SARS-CoV-2 and COVID-19. Nature Reviews Microbiology. 19 (2020), 141–145. doi:10.1038/s41579-020-00459-7
- H. Nishiura et al., Estimation of the asymptomatic ratio of novel coronavirus infections (covid-19), International Journal of Infectious Diseases. 94(2020), 154-155. doi:10.1016/j.ijid.2020.03.020
- S. Lee, T. Kim, E. Lee, C. Lee, H. Kim, H. Rhee, et al., Clinical course and molecular viral shedding among asymptomatic and symptomatic patients with SARS-CoV-2 infection in a community treatment center in the Republic of Korea. JAMA International Medicine. 180 (11) (2020), 1447-1452. doi:10.1001/jamainternmed.2020.3862
- F. Bahadır, F.S. Balık., H.S. Yalçınkaya, The Impact of COVID-19 on the financial structure of the construction industry in Turkey, Necmettin Erbakan University Journal of Science and Engineering. 5(2) (2023), 173-188. doi:10.47112/neufmbd.2023.17
- M. Akat, K. Karatas, Psychological effects of COVID-19 pandemic on society and its reflections on education, Turkish Studies. 15(4) (2020) 1-13. https://dx.doi.org/10.7827/TurkishStudies.44336
- J. Lamwong, N. Wongvanich, I.M. Tang, P. Pongsumpun, Optimal control strategy of a mathematical model for the fifth wave of COVID-19 outbreak (Omicron) in Thailand, Mathematics. 12(1) (2024), 14. doi:10.3390/math12010014
- O.A. Gumus, A.G.M Selvam, R. Janagaraj, Dynamics of the mathematical model related to COVID-19 pandemic with treatment, Thai Journal of Mathematics. 20 (2022), 957–970.
- G.A. Muñoz-Fernández, J.M. Seoane, J.B. Seoane-Sepúlveda, A SIR-type model describing the successive waves of COVID-19, Chaos, Solitons & Fractals. 144 (2021), 110682. doi:10.1016/j.chaos.2021.110682
- A. Olivares, E. Staffetti, Uncertainty quantification of a mathematical model of COVID-19 transmission dynamics with mass vaccination strategy, Chaos, Solitons & Fractals. 146 (2021), 110895. doi:10.1016/j.chaos.2021.110895
- K. Özdemir, Ö. Güngör, SWAT model on Filyos creek basin, Necmettin Erbakan University Journal of Science and Engineering. 1(2) (2019), 90-102.
- Y. Asar, Performance of A new bias corrected estimator in beta regression model: A Monte Carlo study, Necmettin Erbakan University Journal of Science and Engineering. 5 (2)(2023), 75-87. doi:10.47112/neufmbd.2023.11
- B. Gökçe, O. B. Özden, Determination of distortions by finite element analysis using the Goldak model in a welded joint structure, Necmettin Erbakan University Journal of Science and Engineering. 5(2) (2023), 53-64. doi:10.47112/neufmbd.2023.9
- E. Madenci, Contribution of micro-mechanical models to static analysis of functionally graded material plates, Necmettin Erbakan University Journal of Science and Engineering. 5(1) (2023) 23 - 37.
- Y.C. Chen, P.E. Lu, C.S. Chang, T.H. Liu, A time-dependent SIR model for COVID19 with undetectable infected persons, IEEE Transactions on Network Science and Engineering. 7(4) (2020), 3279-3294. doi:10.1109/TNSE.2020.3024723
- X. Li, W. Wang, A discrete epidemic model with stage structure, Chaos, Solitons & Fractals. 26 (2005), 947–958. doi:10.1016/j.chaos.2005.01.063
- Z. Hu, Z. Teng, L. Zhang, Stability and bifurcation analysis in a discrete SIR epidemic model. Mathematics and Computers in Simulation. 97(2014), 80-93. doi:10.1016/j.matcom.2013.08.008
- Z. Eskandari, J. Alidousti, Stability and codimension 2 bifurcations of a discrete time SIR model, Journal of the Franklin Institute. 357(2020), 10937–10959. doi:10.1016/j.jfranklin.2020.08.040
- Y.A. Kuznetsov, Elements of Applied Bifurcation Theory, 112, Springer, New-York, 2013. doi:10.1007/978-1-4757-3978-7
- S. Kapçak, Discrete dynamical systems with SageMath, The Electronic Journal of Mathematics & Technology. 12(2) (2018), 292-308.
Analyzing a Mathematical Model of the COVID-19 Pandemic with the Impact Symptomatic and Asymptomatic Transmissions
Öz
This study addresses the stability and flip bifurcation of a discrete-time SIR model expressing the COVID-19 pandemic. The model considers the effect of the vaccine, asymptomatic individuals, as well as symptomatic individuals in the transmission of the disease. Equilibrium solutions are obtained under certain parametric conditions. Then, the local stabilities of these equilibrium solutions are investigated. The existence of bifurcation is determined for the positive interior equilibrium solution.
Anahtar Kelimeler
COVID-19 Pandemic Model Flip Bifurcation Local Asymptotic Stability SIR Model
Kaynakça
- W. H. Hamer, Epidemic disease in England-the evidence of variability and of persistence of type, Lancet. 1 (1906), 733-739. doi:10.1016/S0140-6736(01)80187-2
- W. O. Kermack, A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proceedings of the Royal Society of London Series A. 115 (1927), 700-721. doi:10.1098/rspa.1927.0118
- W. O. Kermack, A. G. McKendrick, A contribution to the mathematical theory of epidemics, Part II, The problem of endemicity, Proceedings of the Royal Society of London Series A. 138 (1932), 55-83. doi:10.1098/rspa.1932.0171
- W. O. Kermack, A. G. McKendrick, Contributions to the mathematical theory of epidemics, Part III, Further studies of the problem of Endemicity, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character. 141(1933), 94-122. doi:10.1098/rspa.1933.0106
- D. Wu, T. Wu, Q. Liu, Z. Yang, The SARS-CoV-2 outbreak: What we know, International Journal of Infectious Diseases. 94 (2020), 44–48. doi:10.1016/j.ijid.2020.03.004
- B. Hu, H. Guo, P. Zhou, Z.L. Shi, Characteristics of SARS-CoV-2 and COVID-19. Nature Reviews Microbiology. 19 (2020), 141–145. doi:10.1038/s41579-020-00459-7
- H. Nishiura et al., Estimation of the asymptomatic ratio of novel coronavirus infections (covid-19), International Journal of Infectious Diseases. 94(2020), 154-155. doi:10.1016/j.ijid.2020.03.020
- S. Lee, T. Kim, E. Lee, C. Lee, H. Kim, H. Rhee, et al., Clinical course and molecular viral shedding among asymptomatic and symptomatic patients with SARS-CoV-2 infection in a community treatment center in the Republic of Korea. JAMA International Medicine. 180 (11) (2020), 1447-1452. doi:10.1001/jamainternmed.2020.3862
- F. Bahadır, F.S. Balık., H.S. Yalçınkaya, The Impact of COVID-19 on the financial structure of the construction industry in Turkey, Necmettin Erbakan University Journal of Science and Engineering. 5(2) (2023), 173-188. doi:10.47112/neufmbd.2023.17
- M. Akat, K. Karatas, Psychological effects of COVID-19 pandemic on society and its reflections on education, Turkish Studies. 15(4) (2020) 1-13. https://dx.doi.org/10.7827/TurkishStudies.44336
- J. Lamwong, N. Wongvanich, I.M. Tang, P. Pongsumpun, Optimal control strategy of a mathematical model for the fifth wave of COVID-19 outbreak (Omicron) in Thailand, Mathematics. 12(1) (2024), 14. doi:10.3390/math12010014
- O.A. Gumus, A.G.M Selvam, R. Janagaraj, Dynamics of the mathematical model related to COVID-19 pandemic with treatment, Thai Journal of Mathematics. 20 (2022), 957–970.
- G.A. Muñoz-Fernández, J.M. Seoane, J.B. Seoane-Sepúlveda, A SIR-type model describing the successive waves of COVID-19, Chaos, Solitons & Fractals. 144 (2021), 110682. doi:10.1016/j.chaos.2021.110682
- A. Olivares, E. Staffetti, Uncertainty quantification of a mathematical model of COVID-19 transmission dynamics with mass vaccination strategy, Chaos, Solitons & Fractals. 146 (2021), 110895. doi:10.1016/j.chaos.2021.110895
- K. Özdemir, Ö. Güngör, SWAT model on Filyos creek basin, Necmettin Erbakan University Journal of Science and Engineering. 1(2) (2019), 90-102.
- Y. Asar, Performance of A new bias corrected estimator in beta regression model: A Monte Carlo study, Necmettin Erbakan University Journal of Science and Engineering. 5 (2)(2023), 75-87. doi:10.47112/neufmbd.2023.11
- B. Gökçe, O. B. Özden, Determination of distortions by finite element analysis using the Goldak model in a welded joint structure, Necmettin Erbakan University Journal of Science and Engineering. 5(2) (2023), 53-64. doi:10.47112/neufmbd.2023.9
- E. Madenci, Contribution of micro-mechanical models to static analysis of functionally graded material plates, Necmettin Erbakan University Journal of Science and Engineering. 5(1) (2023) 23 - 37.
- Y.C. Chen, P.E. Lu, C.S. Chang, T.H. Liu, A time-dependent SIR model for COVID19 with undetectable infected persons, IEEE Transactions on Network Science and Engineering. 7(4) (2020), 3279-3294. doi:10.1109/TNSE.2020.3024723
- X. Li, W. Wang, A discrete epidemic model with stage structure, Chaos, Solitons & Fractals. 26 (2005), 947–958. doi:10.1016/j.chaos.2005.01.063
- Z. Hu, Z. Teng, L. Zhang, Stability and bifurcation analysis in a discrete SIR epidemic model. Mathematics and Computers in Simulation. 97(2014), 80-93. doi:10.1016/j.matcom.2013.08.008
- Z. Eskandari, J. Alidousti, Stability and codimension 2 bifurcations of a discrete time SIR model, Journal of the Franklin Institute. 357(2020), 10937–10959. doi:10.1016/j.jfranklin.2020.08.040
- Y.A. Kuznetsov, Elements of Applied Bifurcation Theory, 112, Springer, New-York, 2013. doi:10.1007/978-1-4757-3978-7
- S. Kapçak, Discrete dynamical systems with SageMath, The Electronic Journal of Mathematics & Technology. 12(2) (2018), 292-308.
Toplam 24 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Biyolojik Matematik |
| Bölüm | Makaleler |
| Yazarlar | |
| Erken Görünüm Tarihi | 29 Aralık 2024 |
| Yayımlanma Tarihi | 31 Aralık 2024 |
| Gönderilme Tarihi | 9 Mayıs 2024 |
| Kabul Tarihi | 18 Temmuz 2024 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 6 Sayı: 3 |
Kaynak Göster
