We propose a compartmental mathematical model for the spread of the COVID-19 disease, showing its usefulness with respect to the pandemic in Portugal, from the first recorded case in the country till the end of the three states of emergency. New results include the compartmental model, described by a system of seven ordinary differential equations; proof of positivity and boundedness of solutions; investigation of equilibrium points and their stability analysis; computation of the basic reproduction number; and numerical simulations with official real data from the Portuguese health authorities. Besides completely new, the proposed model allows to describe quite well the spread of COVID-19 in Portugal, fitting simultaneously not only the number of active infected individuals but also the number of hospitalized individuals, respectively with a L 2 error of 9.2152 e − 04 and 1.6136 e − 04 with respect to the initial population. Such results are very important, from a practical point of view, and far from trivial from a mathematical perspective. Moreover, the obtained value for the basic reproduction number is in agreement with the one given by the Portuguese authorities at the end of the emergency states.

中文翻译：

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以葡萄牙为例的 COVID-19 新区室流行病学模型

我们为 COVID-19 疾病的传播提出了一个分区数学模型，显示了它对葡萄牙大流行的有用性，从该国的第一个记录病例到三个紧急状态结束。新结果包括由七个常微分方程组成的系统描述的隔室模型；证明解的正性和有界性；平衡点的调查及其稳定性分析；基本再生数的计算；以及使用葡萄牙卫生当局官方真实数据进行的数值模拟。除了全新的模型外，所提出的模型还可以很好地描述 COVID-19 在葡萄牙的传播，不仅适合活跃感染者的数量，还适合住院人数，相对于初始种群，L 2 误差分别为 9.2152 e - 04 和 1.6136 e - 04。从实践的角度来看，这样的结果非常重要，而从数学的角度来看，这绝非易事。此外，获得的基本再生数值与葡萄牙当局在紧急状态结束时给出的值一致。