论文标题
与社会异质性的流行动力学动力学模型
Kinetic models for epidemic dynamics with social heterogeneity
论文作者
论文摘要
我们通过将流行病学动态与基于人群的接触的动力学建模整合在一起，介绍了社会性在传染病传播中的影响的数学描述。动力学描述导致研究了玻尔兹曼型方程的演变，描述了易感，感染和恢复个体的社会接触的数量密度，它们的比例是由流行病学中经典的sir型隔室模型驱动的。显式计算表明，疾病的传播与接触分布的矩密切相关。此外，动力学模型允许仅通过减少经历大量每日接触的人来假设如何假设选择性控制来实现最小的锁定策略。我们进行数值模拟，以证实该模型描述流行病快速传播的不同现象特征的能力。由COVID-19大流行的激励，最后一部分致力于将所提出模型的数值解决方案与来自不同欧洲国家 /地区的感染数据一起使用。
We introduce a mathematical description of the impact of sociality in the spread of infectious diseases by integrating an epidemiological dynamics with a kinetic modeling of population-based contacts. The kinetic description leads to study the evolution over time of Boltzmann-type equations describing the number densities of social contacts of susceptible, infected and recovered individuals, whose proportions are driven by a classical SIR-type compartmental model in epidemiology. Explicit calculations show that the spread of the disease is closely related to moments of the contact distribution. Furthermore, the kinetic model allows to clarify how a selective control can be assumed to achieve a minimal lockdown strategy by only reducing individuals undergoing a very large number of daily contacts. We conduct numerical simulations which confirm the ability of the model to describe different phenomena characteristic of the rapid spread of an epidemic. Motivated by the COVID-19 pandemic, a last part is dedicated to fit numerical solutions of the proposed model with infection data coming from different European countries.
