论文标题
Modelos Modificados para la laevolucióndel covid19
Modelos SIR modificados para la evolución del COVID19
论文作者
论文摘要
我们研究了具有可变传染率的SIR流行病学模型，该模型应用于古巴的Covid19的演变。强调的是，预测特征的增加取决于理解传染率$β^*$的时间演变的动力学。制定了该动力学的半经验模型，在该模型中，由于疾病的平均持续时间$τ= 1/γ$，由于隔离而达到$β^*\ of to $β^*\大约，其中被关闭的家族中受感染的数量减少了。据认为，$β^*（t）$在开始时应该突然减少并减少，直到在间隔$τ$结束时取消。该分析描述了德国的感染曲线。该模型用于预测古巴的感染曲线，该曲线估计5月中旬的最大感染数量小于2000，具体取决于隔离的严格性。这是由每日检测到的病例与总数之间的比率提出的。我们考虑观察到的和实际感染病例（K）小于统一的比率。当$β^*-γ> 0 $ $时，k的低值降低了获得的最大值。观察到的进化与线性区域中的K无关。还通过时间间隔研究了$β^*$的价值，并适应古巴，德国和韩国的数据。我们将古巴与传染率的演变推断到16.04.20，并在4月底严格的隔离率获得。这个具有可变$β^*$的模型正确描述了观察到的感染进化曲线。我们强调，SIR感染曲线的所需最大值不是常数$β^*$的最大标准，而是当$ \ tilde r_0 =β^*/γ<1 $时由于隔离而获得的最大标准。对于控制流行病的国家，最大值位于SIR方程是线性的区域。
We study the SIR epidemiological model, with a variable contagion rate, applied to the evolution of COVID19 in Cuba. It is highlighted that an increase in the predictive character depends on understanding the dynamics for the temporal evolution of the rate of contagion $β^*$. A semi-empirical model for this dynamics is formulated, where reaching $β^*\approx0$ due to isolation is achieved after the mean duration of the disease $τ=1/γ$, in which the number of infected in the confined families has decreased. It is considered that $β^*(t)$ should have an abrupt decrease on the day of initiation of confinement and decrease until canceling at the end of the interval $τ$. The analysis describes appropriately the infection curve for Germany. The model is applied to predict an infection curve for Cuba, which estimates a maximum number of infected as less than 2000 in the middle of May, depending on the rigor of the isolation. This is suggested by the ratio between the daily detected cases and the total. We consider the ratio between the observed and real infected cases (k) less than unity. The low value of k decreases the maximum obtained when $β^*-γ>0$. The observed evolution is independent of k in the linear region. The value of $β^*$ is also studied by time intervals, adjusting to the data of Cuba, Germany and South Korea. We compare the extrapolation of the evolution of Cuba with the contagion rate until 16.04.20 with that obtained by a strict quarantine at the end of April. This model with variable $β^*$ correctly describes the observed infected evolution curves. We emphasize that the desired maximum of the SIR infected curve is not the maximum standard with constant $β^*$, but one achieved due to quarantine when $\tilde R_0=β^*/γ<1$. For the countries controlling the epidemic the maxima are in the region in which SIR equations are linear.
