Diskret vaqtli seir epidemik model dinamikasi
DOI:
https://doi.org/10.5281/Аннотация
Ushbu ishda diskret vaqtli SEIR epidemik modelining dinamik xususiyatlari va bifurkatsion holatlari tadqiq
etilgan. Modelda aholi sezgir, yashirin infeksiyalangan, yuqumli va sog‘aygan guruhlarga ajratilib, epidemiyaning vaqt
bo‘yicha rivojlanishi diskret matematik tenglamalar yordamida ifodalangan. Tadqiqot davomida modelning kasalliksiz va
musbat muvozanat nuqtalari aniqlanib, ularning barqarorlik xususiyatlari Yakobian matritsasining xos qiymatlari asosida
baholangan. Asosiy reproduktiv sonning qiymatiga qarab epidemiyaning rivojlanish shartlari va muvozanat holatlarining
mavjudligi o‘rganilgan. Parametrlarning kritik qiymatlarida yuzaga keladigan flip hamda Neimark–Sacker bifurkatsiyalari
tahlil qilingan. Shuningdek, ikki parametrli sonli davom ettirish usuli yordamida 1:2, 1:3 va 1:4 kuchli rezonans bifurkatsiyalari
aniqlangan. Natijalar parametrlarning o‘zgarishi natijasida modelda barqaror muvozanat, periodik, kvazidavriy va
yuqori davrli dinamik rejimlar shakllanishi mumkinligini ko‘rsatgan. Olingan natijalar diskret vaqtli epidemik jarayonlarning
dinamik mexanizmlarini chuqurroq tushunish va parametrlarning epidemiya rivojlanishiga ta’sirini baholash imkonini
beradi.
Ключевые слова
SEIR modeli, diskret vaqt, epidemik model, muvozanat nuqtasi, barqarorlik, bifurkatsiya, rezonansБиблиографические ссылки
1. Abdelaziz, M. A. M., Ismail, A. I., Abdullah, F. A., & Mohd, M. H. (2020). Codimension one and two bifurcations of a
discrete-time fractional-order SEIR measles epidemic model with constant vaccination. Chaos, Solitons & Fractals,
140, 110120.
2. Ibeas, A., de la Sen, M., Alonso-Quesada, S., & Zamani, I. (2015). Stability analysis and observer design for discrete-
time SEIR epidemic models. Advances in Difference Equations, 2015, 122. https://doi.org/10.1186/s13662-015-
0459-x
3. Ibeas, A., de la Sen, M., & Alonso-Quesada, S. (2014). Adaptive control of SEIR discrete-time epidemic models. AIP
Conference Proceedings, 1637, 37–46. https://doi.org/10.1063/1.4904562
4. Li, B., Eskandari, Z., & Avazzadeh, Z. (2022). Dynamical behaviors of an SIR epidemic model with discrete time. Fractal
and Fractional, 6(11), 659. https://doi.org/10.3390/fractalfract6110659
5. Li, G., & Jin, Z. (2005). Global stability of a SEIR epidemic model with infectious force in latent, infected and immune
period. Chaos, Solitons & Fractals, 25(5), 1177–1184. https://doi.org/10.1016/j.chaos.2004.11.062
6. Li, G., Wang, W., & Jin, Z. (2006). Global stability of an SEIR epidemic model with constant immigration. Chaos, Solitons
& Fractals, 30(4), 1012–1019. https://doi.org/10.1016/j.chaos.2005.09.024
7. Li, M. Y., Smith, H. L., & Wang, L. (2001). Global dynamics of an SEIR epidemic model with vertical transmission. SIAM
Journal on Applied Mathematics, 62(1), 58–69. https://doi.org/10.1137/S0036139999359860
8. Li, X.-Z., & Zhou, L.-L. (2009). Global stability of an SEIR epidemic model with vertical transmission and saturating
contact rate. Chaos, Solitons & Fractals, 40(2), 874–884.
9. Liu, X., Liu, P., & Liu, Y. (2022). The existence of codimension-two bifurcations in a discrete-time SIR epidemic
model. AIMS Mathematics, 7(3), 3360–3378. https://doi.org/10.3934/math.2022187
10. Rozikov, U. A., & Shoyimardonov, S. K. (2021). An application of discrete-time SEIR model to the COVID-19 spread.
11. Wei, F., & Xue, R. (2020). Stability and extinction of SEIR epidemic models with generalized nonlinear incidence. Mathematics
and Computers in Simulation, 170, 1–15. https://doi.org/10.1016/j.matcom.2018.09.029
12. Wang, W. (2014). Stability analysis of a multigroup SEIR epidemic model with general latency distributions. Abstract
and Applied Analysis, 2014, 740256.
13. Xu, R., Wang, Z., & Zhang, F. (2015). Global stability and Hopf bifurcations of an SEIR epidemiological model with
logistic growth and time delay. Applied Mathematics and Computation, 269, 332–342. https://doi.org/10.1016/j.
amc.2015.07.084
14. Zhou, X., Li, X., & Wang, W.-S. (2014). Bifurcations for a deterministic SIR epidemic model in discrete time. Advances
in Difference Equations, 2014, 168.
15. Abdelaziz, M. A. M., Ismail, A. I., Abdullah, F. A., & Mohd, M. H. (2019). Bifurcation analysis for a delayed SEIR epidemic
model with saturated incidence and saturated treatment function. International Journal of Dynamics and Control.
16. Hopf bifurcation analysis of a delayed SEIR epidemic model with infectious force in latent and infected period.
(2018). Advances in Continuous and Discrete Models. https://doi.org/10.1186/s13662-018-1805-6
17. On the discretization and control of an SEIR epidemic model with a periodic impulsive vaccination. (2017). Journal of
Mathematical Analysis and Applications.
18. Dynamic models of epidemiology in discrete time taking into account processes with lag. (2023). Mathematical Modelling
of Natural Phenomena.
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