KaydedilenlerDerginizi ekleyin

Dergiler / Turkish Journal of Mathematics / 2022 / Cilt: 46 - Sayı: SI-1

Mathematical analysis of local and global dynamics of a new epidemic model

Sümeyye ÇAKAN
Sayfa
533–551
Yayın Tarihi
2022-11-01
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Also, we present a mathematical analysis for the global dynamics in the equilibrium points of this model using LaSalle’s Invariance Principle associated with Lyapunov functional technique and Li-Muldowney geometric approach, respectively.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we construct a new SEIR epidemic model reflecting the spread of infectious diseases.
📊
Temel Bulgular & Veri:The model exhibits threshold behavior according to whether the basic reproduction number R0 is greater than unity or not.
💡
Sonuç & Katkı:Also, we present a mathematical analysis for the global dynamics in the equilibrium points of this model using LaSalle’s Invariance Principle associated with Lyapunov functional technique and Li-Muldowney geometric approach, respectively.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this paper, we construct a new SEIR epidemic model reflecting the spread of infectious diseases. After calculating basic reproduction number Ro by the next generation matrix method, we examine the stability of the model. The model exhibits threshold behavior according to whether the basic reproduction number R0 is greater than unity or not. By using well-known Routh-Hurwitz criteria, we deal with local asymptotic stability of equilibrium points of the model according to Ro. Also, we present a mathematical analysis for the global dynamics in the equilibrium points of this model using LaSalle’s Invariance Principle associated with Lyapunov functional technique and Li-Muldowney geometric approach, respectively.

🔖

Bu Makaleye Atıf Yap

ÇAKAN, S. (2022). Mathematical analysis of local and global dynamics of a new epidemic model. Turkish Journal of Mathematics, Cilt: 46 - Sayı: SI-1, 533–551. https://ajindex.com/articles/605759

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (14)

  1. Adebimpe O, Bashiru KA, Ojurongbe TA. Stability analysis of an SIR epidemic with non-linear incidence rate and treatment. Open Journal of Modelling and Simulation 2015; 3 (3): 104-110
  2. Aghdaoui H, Alaoui AL, Nisar KS, Tilioua M. On analysis and optimal control of a SEIRI epidemic model with general incidence rate. Results in Physics 2021; 20: 1-9
  3. Ak Gümüş Ö. Global and local stability analysis in a nonlinear discrete-time population model. Advances in Difference Equations 2014; 299: 1-9
  4. Butler G, Waltman P. Persistence in dynamical systems. Journal of Differential Equations 1986; 63: 255-263 [5] Chatibi Y, El Kinani EH, Ouhadan A. Lie symmetry analysis of conformable differential equations. AIMS Mathematics 2019; 4 (4): 1133-1144
  5. Chatibi Y, El Kinani EH, Ouhadan A. Lie symmetry analysis and conservation laws for the time fractional BlackScholes equation. International Journal of Geometric Methods in Modern Physics 2020; 17 (1): 1-14
  6. Chatibi Y, El Kinani EH, Ouhadan A. On the discrete symmetry analysis of some classical and fractional differential equations. Mathematical Methods in the Applied Sciences 2021; 44 (4): 2868-2878
  7. Coppel WA. Stability and asymptotic behavior of differential equations. Boston: Heath, 1965
  8. Çakan S. Dynamic analysis of a mathematical model with health care capacity for COVID-19 pandemic. Chaos, Solitons and Fractals 2020; 139: 1-8
  9. Çay İ. On the local and global stability of an sirs epidemic model with logistic growth and information intervention. Turkish Journal of Mathematics 2021; 45 (4): 1668-1677
  10. Diekmann O, Heesterbeek JAP, Metz JAJ. On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology 1990; 28 (4): 365-382
  11. Driessche PVD, Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences 2002; 180: 29-48
  12. Elazzouzi A, Alaoui AL, Tilioua M, Torres DFM. Analysis of a SIRI epidemic model with distributed delay and relapse. Statistics, Optimization and Information Computing 2019; 7 (3): 545-557
  13. Elazzouzi A., Alaoui AL, Tilioua M, Tridane A. Global stability analysis for a generalized delayed SIR model with vaccination and treatment. Advances in Difference Equations 2019; 532: 1-19
  14. Freedman HI, Ruan S, Tang M. Uniform persistence and flows near a closed positively invar