论文标题
无限维SIS模型
An Infinite-Dimensional SIS Model
论文作者
论文摘要
在本文中，我们介绍了一个无限的确定性SIS模型，该模型考虑了大量人群中感染和社交网络的异质性。我们研究动态的长期行为。 我们确定基本的复制号$ r_0 $，该数字决定是否存在稳定的地方性稳态（超临界情况：$ r_0> 1 $），或者唯一唯一的平衡是无病的（关键和临界案例：$ r_0 \ leq1 $）。 作为这项一般研究的应用，我们证明了所谓的``漏水''和``全或全或全或无效''疫苗接种机制对$ r_0 $具有相同的影响。 该框架也非常自然且直观地模型锁定政策并研究其影响。
In this article, we introduce an infinite-dimensional deterministic SIS model which takes into account the heterogeneity of the infections and the social network among a large population. We study the long-time behavior of the dynamic. We identify the basic reproduction number $R_0$ which determines whether there exists a stable endemic steady state (super-critical case: $R_0>1$) or if the only equilibrium is disease-free (critical and sub-critical case: $R_0\leq1$). As an application of this general study, we prove that the so-called ``leaky'' and ``all-or-nothing'' vaccination mechanism have the same effect on $R_0$. This framework is also very natural and intuitive to model lockdown policies and study their impact.
