论文标题
时间依赖于流行病学的SI模型和对Covid-19的应用
Time-dependent SI model for epidemiology and applications to Covid-19
论文作者
论文摘要
对易感感染模型的概括是包括时间依赖性的传输率，从而导致逻辑函数的分析表达紧密。可以将解决方案应用于选择随时间描述传输速率的演变的任何连续函数。从Covid-19的真实数据中汲取灵感，对于累积确认的阳性和死亡的情况，我们提出了一个带有两个自由参数的指数衰减的传输速率，一个用于其初始振幅，另一个用于其衰减率。然后，在额外的条件下恢复标准Gompertz功能形式的最终时间依赖性SI模型与所选国家 /地区的数据及其参数使用贝叶斯推断进行比较。我们对确认的阳性和死亡的渐近数进行了预测，并讨论了每个国家的疾病的可能演变，就我们的传播率参数而言。
A generalisation of the Susceptible-Infectious model is made to include a time-dependent transmission rate, which leads to a close analytical expression in terms of a logistic function. The solution can be applied to any continuous function chosen to describe the evolution of the transmission rate with time. Taking inspiration from real data of the Covid-19, for the case of cumulative confirmed positives and deaths, we propose an exponentially decaying transmission rate with two free parameters, one for its initial amplitude and another one for its decaying rate. The resultant time-dependent SI model, which under extra conditions recovers the standard Gompertz functional form, is then compared with data from selected countries and its parameters fit using Bayesian inference. We make predictions about the asymptotic number of confirmed positives and deaths, and discuss the possible evolution of the disease in each country in terms of our parametrisation of the transmission rate.
