In this paper, a latent infection susceptible–exposed–infectious–recovered model with demographic effects is used to understand the dynamics of the COVID-19 pandemics. We calculate the basic reproduction number ( $${R}_{0}$$ ) by solving the differential equations of the model and also using next-generation matrix method. We also prove the global stability of the model using the Lyapunov method. We showed that when the $${R}_{0}<1$$ or $${R}_{0}\le 1$$ and $${R}_{0}>1$$ or $${R}_{0}\ge 1$$ the disease-free and endemic equilibria asymptotic stability exist theoretically. We provide numerical simulations to demonstrate the detrimental impact of the direct and latent infections for the COVID-19 pandemic.

中文翻译：

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具有人口统计学影响的COVID-19大流行的数学模型

在本文中，使用具有人口统计学影响的潜在感染易感性，传染性，传染性恢复模型来了解COVID-19大流行的动态。我们通过求解模型的微分方程并使用下一代矩阵方法来计算基本再现数（$$ {R} _ {0} $$）。我们还使用Lyapunov方法证明了模型的全局稳定性。我们表明，当$$ {R} _ {0} <1 $$或$$ {R} _ {0} \ le 1 $$和$$ {R} _ {0}> 1 $$或$$ {R} _ {0} \ ge 1 $$理论上存在无病和地方平衡的渐近稳定性。我们提供了数值模拟，以证明直接和潜伏感染对COVID-19大流行的有害影响。