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 \(R_{0}\) is less than unity and unstable when \(R_{0} > 1\). The analysis shows that the phenomenon of backward bifurcation occurs when \(R_{0}<1\). 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，研究和分析易感者-感染者消除（SIR）动态。我们将一般发病率函数和康复率视为医院床位数量的函数。我们证明了模型的存在性、唯一性和有界性。我们研究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\(R_{0}\)小于1时，自由稳态是局部稳定的；当\(R_{0} > 1\)时，自由稳态是不稳定的。分析表明，当\(R_{0}<1\)时，出现后向分叉现象。然后我们使用分数阶微分算子的概念研究模型。最后，我们进行数值模拟来说明理论分析并研究参数对各种分数阶模型的影响。