合作传染过程的基本性质
Fundamental properties of cooperative contagion processes
摘要：
我们研究了在宿主人群中传播和持续的传染过程之间的协同效应。我们提出并分析了一个动态模型，在该模型中，受一个传染性代理$A$的个人表现出高于基线的倾向，受到第二代理$B$，反之亦然。该模型是传统的SIS（易感-感染-易感）模型用于建模单传染过程的自然扩展。我们表明，协同性改变了系统的动力学相当强的协同性时。该系统表现出不连续的相变中没有观察到的单剂传染，多稳定性，一个分离的传统的流行病阈值为不同的阈值开始和灭绝以及滞后。这些属性是强大的，并证实了随机模拟格和通用网络拓扑结构。最后，我们调查波的传播和瞬态的空间扩展版本的模型，并表明，特别是对于中间值的基线再现比的系统的特点是由各种类型的波前速度。该系统可以表现出空间异构的一些参数和负的波前速度（后退波前）的定态。两个代理模型可以作为一个起点，更复杂的传染过程，涉及几个相互作用的代理，一个模型框架，特别适合于模拟宿主种群中的微生物生态系统的传播和动态。
英文摘要：
We investigate the effects of cooperativity between contagion processes that spread and persist in a host population. We propose and analyze a dynamical model in which individuals that are affected by one transmissible agent $A$ exhibit a higher than baseline propensity of being affected by a second agent $B$ and vice versa. The model is a natural extension of the traditional SIS (Susceptible-Infected-Susceptible) model used for modeling single contagion processes. We show that cooperativity changes the dynamics of the system considerably when cooperativity is strong. The system exhibits discontinuous phase transitions not observed in single agent contagion, multi-stability, a separation of the traditional epidemic threshold into different thresholds for inception and extinction as well as hysteresis. These properties are robust and are corroborated by stochastic simulations on lattices and generic network topologies. Finally, we investigate wave propagation and transients in a spatially extended version of the model and show that especially for intermediate values of baseline reproduction ratios the system is characterized by various types of wave-front speeds. The system can exhibit spatially heterogeneous stationary states for some parameters and negative front speeds (receding wave fronts). The two agent model can be employed as a starting point for more complex contagion processes, involving several interacting agents, a model framework particularly suitable for modeling the spread and dynamics of microbiological ecosystems in host populations.
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