Alqahtani Rubayyi T
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia.
Adv Differ Equ. 2021;2021(1):2. doi: 10.1186/s13662-020-03192-w. Epub 2021 Jan 4.
In this paper, we study and analyze the susceptible-infectious-removed (SIR) dynamics considering the effect of health system. We consider a general incidence rate function and the recovery rate as functions of the number of hospital beds. We prove the existence, uniqueness, and boundedness of the model. We investigate all possible steady-state solutions of the model and their stability. The analysis shows that the free steady state is locally stable when the basic reproduction number is less than unity and unstable when . The analysis shows that the phenomenon of backward bifurcation occurs when . Then we investigate the model using the concept of fractional differential operator. Finally, we perform numerical simulations to illustrate the theoretical analysis and study the effect of the parameters on the model for various fractional orders.
在本文中，我们考虑卫生系统的影响，研究并分析易感-感染-康复（SIR）动态。我们将一般发病率函数和恢复率视为医院病床数量的函数。我们证明了该模型的存在性、唯一性和有界性。我们研究了该模型所有可能的稳态解及其稳定性。分析表明，当基本再生数小于1时，无病稳态是局部稳定的，而当基本再生数大于1时则是不稳定的。分析表明，当基本再生数处于某一特定范围时会出现向后分岔现象。然后，我们使用分数阶微分算子的概念研究该模型。最后，我们进行数值模拟以说明理论分析，并研究不同分数阶下参数对模型的影响。
