论文标题
当想法传播开来时 - 两阶段传输模型中的复杂分叉
When ideas go viral -- complex bifurcations in a two-stage transmission model
论文作者
论文摘要
我们考虑了具有两个非线性传播阶段的传输动力学的数学模型的定性行为。提出的模型的灵感来自于流行病学（传染病的传播）或社会动态（观点，行为，思想的传播），并通过隔离方法描述的现象。与发起人（传染性的人）接触后，一个天真（易感）的人可以自己成为促进者，或者成为$ \ textit {feelated} $，因此更容易受到伤害。当他们与发起人组的成员第二次接触时，虚弱的个体就会变得具有传染性。在传染室中的一段时间后，个体变得不活跃（不敏感并且无法扩散），并从传播链中删除。我们将这个两阶段的传染过程与幼体人群的更新结合，通过从弱化或不活动状态到易感隔室的过渡模型。这导致了丰富的动力，例如，平衡和周期性轨道的共存和双重性。 （非平凡）平衡的特性进行了分析研究。此外，对参数空间的数值研究揭示了许多分叉，表明这种系统的动力学比经典流行病学模型的动力学更为复杂。
We consider the qualitative behavior of a mathematical model for transmission dynamics with two nonlinear stages of contagion. The proposed model is inspired by phenomena occurring in epidemiology (spread of infectious diseases) or social dynamics (spread of opinions, behaviors, ideas), and described by a compartmental approach. Upon contact with a promoter (contagious individual), a naive (susceptible) person can either become promoter himself or become $\textit{weakened}$, hence more vulnerable. Weakened individuals become contagious when they experience a second contact with members of the promoter group. After a certain time in the contagious compartment, individuals become inactive (are insusceptible and cannot spread) and are removed from the chain of transmission. We combine this two-stage contagion process with renewal of the naive population, modeled by means of transitions from the weakened or the inactive status to the susceptible compartment. This leads to rich dynamics, showing for instance coexistence and bistability of equilibria and periodic orbits. Properties of (nontrivial) equilibria are studied analytically. In addition, a numerical investigation of the parameter space reveals numerous bifurcations, showing that the dynamics of such a system can be more complex than those of classical epidemiological ODE models.
