Coronavirus disease 2019 (COVID-19) is an infection that can result in lung issues such as pneumonia and, in extreme situations, the most severe acute respiratory syndrome. COVID-19 is widely investigated by researchers through mathematical models from different aspects. Inspired from the literature, in the present paper, the generalized deterministic COVID-19 model is considered and examined. The basic reproduction number is obtained which is a key factor in defining the nonlinear dynamics of biological and physical obstacles in the study of mathematical models of COVID-19 disease. To better comprehend the dynamical behavior of the continuous model, two unconditionally stable schemes, i.e., mixed Euler and nonstandard finite difference (NSFD) schemes are developed for the continuous model. For the discrete NSFD scheme, the boundedness and positivity of solutions are discussed in detail. The local stability of disease-free and endemic equilibria is demonstrated by constructing Jacobian matrices for NSFD scheme; nevertheless, the global stability of aforementioned equilibria is verified by using Lyapunov functions. Numerical simulations are also presented that demonstrate how both the schemes are effective and suitable for solving the continuous model. Consequently, the outcomes obtained through these schemes are completely according to the solutions of the continuous model.

中文翻译：

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广义COVID-19确定性疾病模型的流行病学特征

2019 年冠状病毒病 (COVID-19) 是一种感染，可能导致肺炎等肺部问题，在极端情况下，可能导致最严重的急性呼吸道综合症。研究人员通过不同方面的数学模型对COVID-19进行了广泛的研究。受文献启发，本文考虑并检验了广义确定性 COVID-19 模型。获得的基本繁殖数是在COVID-19疾病数学模型研究中定义生物和物理障碍的非线性动力学的关键因素。为了更好地理解连续模型的动态行为，我们为连续模型开发了两种无条件稳定格式，即混合欧拉格式和非标准有限差分（NSFD）格式。对于离散 NSFD 方案，详细讨论了解的有界性和正性。通过构建 NSFD 方案的雅可比矩阵证明了无病平衡和地方病平衡的局部稳定性；尽管如此，上述均衡的全局稳定性是通过使用李雅普诺夫函数来验证的。还提供了数值模拟，证明这两种方案如何有效且适合求解连续模型。因此，通过这些方案获得的结果完全符合连续模型的解。还提供了数值模拟，证明这两种方案如何有效且适合求解连续模型。因此，通过这些方案获得的结果完全符合连续模型的解。还提供了数值模拟，证明这两种方案如何有效且适合求解连续模型。因此，通过这些方案获得的结果完全符合连续模型的解。