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Analytical investigation of fractional SEIRVQD measles mathematical model | ||
| Journal of Mathematical Modeling | ||
| مقاله 10، دوره 13، شماره 2، مرداد 2025، صفحه 393-413 اصل مقاله (483.81 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2024.28379.2514 | ||
| نویسندگان | ||
| Milad Fahimi؛ Kazem Nouri* ؛ Leila Torkzadeh | ||
| Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran | ||
| چکیده | ||
| In this paper, we construct and formulate a new mathematical model for the spread of epidemic diseases with vaccination especially for Chinese measles. This model including susceptible $(S)$, exposed $(E)$, infected $(I)$, recovered $(R)$, vaccinated $(V)$, quarantined $(Q)$ and died individuals $(D)$ is been studied by applying Caputo fractional derivatives (CFD). We introduce the feasibility region and prove positively invariant property for this region. Then we prove the existence of a unique solution of our fractional measles model. Furthermore, the equilibrium points of the model are presented and the stability analysis of the model is proved based on Lyapunov and Ulam-Hyer criteria. The basic reproduction number $(R_0)$ is calculated by the next generation matrix method in order to demonstrate the level of measles virus invasion. Moreover, numerical simulations including data fitting are performed for different fractional orders to illustrate and validate the efficiency of the proposed model. | ||
| کلیدواژه‌ها | ||
| Epidemic model؛ fractional SEIRVQD model؛ transmission simulation؛ differential equation؛ Ulam-Hyer stability؛ measles؛ Lyapunov stability | ||
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آمار تعداد مشاهده مقاله: 118 تعداد دریافت فایل اصل مقاله: 128 |
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