标题： 复杂网络上的竞争流行病 显示英文标题

标题： Competing epidemics on complex networks

摘要： 人类疾病通过个体之间的接触网络传播，最近有大量的研究集中在传播过程的动力学上。 在这里，我们研究了一个模型，其中两种竞争性疾病在同一网络上同时传播，其中感染任何一种疾病会使个体对两者都产生后续的免疫力。 通过分析和数值方法的结合，我们推导了系统的相图以及每种疾病感染个体的预期最终数量的估计。 该系统在一种疾病占主导地位和另一种疾病占主导地位之间表现出一种不寻常的动力学转变，这种转变是相对于它们的增长率而言的。 接近这一转变时，最终结果对增长早期阶段的随机波动有很强的依赖性，这种依赖性随着网络规模的增加而减小，但减小得足够缓慢，以至于在包含数百万或数十亿个体的系统中仍很容易观察到。 在相图的大多数区域，我们发现一种疾病最终占主导地位，而另一种疾病只达到网络中可忽略不计的比例，但系统也显示了一个显著的共存区域，在这个区域中，两种疾病都达到流行的程度，并感染网络中的大量个体。 显示英文摘要

摘要： Human diseases spread over networks of contacts between individuals and a substantial body of recent research has focused on the dynamics of the spreading process. Here we examine a model of two competing diseases spreading over the same network at the same time, where infection with either disease gives an individual subsequent immunity to both. Using a combination of analytic and numerical methods, we derive the phase diagram of the system and estimates of the expected final numbers of individuals infected with each disease. The system shows an unusual dynamical transition between dominance of one disease and dominance of the other as a function of their relative rates of growth. Close to this transition the final outcomes show strong dependence on stochastic fluctuations in the early stages of growth, dependence that decreases with increasing network size, but does so sufficiently slowly as still to be easily visible in systems with millions or billions of individuals. In most regions of the phase diagram we find that one disease eventually dominates while the other reaches only a vanishing fraction of the network, but the system also displays a significant coexistence regime in which both diseases reach epidemic proportions and infect an extensive fraction of the network.