We propose in the present paper a discrete mathematical model by obtaining it from a continuous time model. We present in brief the mathematical formulation of the model using Euler-backward differences. The discrete model is then analyzed and present its mathematical results. The fundamental results for the discrete mathematical model are explored. We present the stability of the fixed points for our proposed model whenever the threshold ${\mathcal{R}}_0$ less or greater than one. We provide mathematically that the system is globally asymptotically stable whenever ${\mathcal{R}}_0<1$. We show the existences of the endemic equilibria by showing the system has the solution which is unique. Further, we propose suitable Lyapunov function to discuss and analyze the global stability for the endemic case whenever ${\mathcal{R}}_0>1$. We solve the discrete mathematical model numerically and present various graphical results. The effect of quarantine and without quarantine in combinations with some suitable parameters are shown. The results show the significance of the use of the backward differences for an epidemic model. Finally, we provide summarize conclusion based on the achieved results.

通过在连续时间模型中获得离散数学模型，我们提出了一种离散数学模型。我们简要介绍了使用Euler后向差异的模型的数学公式。然后分析离散模型并给出其数学结果。探索了离散数学模型的基本结果。无论何时阈值，我们都会为我们提出的模型提供不动点的稳定性${\mathcal{[R}}_0$小于或大于一个。从数学上讲，每当系统处于全局渐近稳定状态时，${\mathcal{[R}}_0<\mathrm{1个}$。通过显示系统具有唯一的解，我们证明了地方均衡的存在。此外，我们提出适当的李雅普诺夫函数，以讨论和分析该流行病的全局稳定性。${\mathcal{[R}}_0>\mathrm{1个}$。我们用数值方法求解离散数学模型，并给出各种图形结果。显示了隔离和不隔离与某些适当参数组合的效果。结果表明，使用流行病模型的后向差异具有重要意义。最后，我们根据取得的成果提供总结性结论。