论文标题
葡萄牙案例研究的COVID-19的新的新区流行病学模型
A New Compartmental Epidemiological Model for COVID-19 with a Case Study of Portugal
论文作者
论文摘要
我们提出了一个隔室数学模型，以供葡萄牙的大流行，从该国的第一个记录案例到紧急状态的末端，显示了葡萄牙大流行方面的有用性。新结果包括隔室模型，该模型由七个普通微分方程的系统描述；解决方案的积极性和有限性的证明；研究平衡点及其稳定性分析；基本繁殖数的计算；以及来自葡萄牙卫生当局的官方真实数据的数值模拟。除了全新的新事物外，提出的模型还可以很好地描述Covid-19在葡萄牙的传播，不仅适合活跃感染的个体的数量，而且还适合住院个人的数量，而住院个人的数量则为$ L^2 $错误，$ 9.2152E-04 $和$ 1.6136E-04 $相对于最初的人数。从实际的角度来看，这种结果非常重要，而且从数学角度来看远非微不足道。此外，基本繁殖编号获得的价值与葡萄牙当局在紧急状态结束时给出的价值一致。
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 $9.2152e-04$ and $1.6136e-04$ 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.
