In this manuscript, we examine the SIR model under convex incidence rate. We first formulate the famous SIR model under the aforesaid incidence rate. Further, we develop some sufficient analysis to examine the dynamical behavior of the model under consideration. We compute the basic reproductive number $\mathcal{R}_0.$ Also we study the global attractivity results via using Dulac function theory. Further, we also provide some information about the stability of the endemic and disease free equilibria for the considered model. In addition, we use nonstandard finite difference scheme to perform numerical simulation of the considered model via using Matlab. We provide different numerical plots for two different values of contact rate and taking various initial values for compartments involved in the considered model.

中文翻译：

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凸发生率下SIR流行病模型的数学研究。

在本文中，我们研究了凸入射率下的SIR模型。首先根据上述发生率，建立著名的SIR模型。此外，我们开发了足够的分析来检查所考虑模型的动力学行为。我们计算基本生殖数$ \ mathcal {R} _0。$。此外，我们还使用Dulac函数理论研究了全局吸引性结果。此外，我们还提供了有关所考虑模型的地方性和无病平衡的稳定性的一些信息。另外，我们使用非标准有限差分方案通过使用Matlab对所考虑模型进行数值模拟。我们为两种不同的接触率值提供了不同的数值图，并为所考虑的模型涉及的隔室提供了各种初始值。