We study the dynamics of secondary infections on networks, in which only the individuals currently carrying a certain primary infection are susceptible to the secondary infection. In the limit of large sparse networks, the model is mapped to a branching process spreading in a random time-sensitive environment, determined by the dynamics of the underlying primary infection. When both epidemics follow the Susceptible-Infective-Recovered model, we show that in order to survive, it is necessary for the secondary infection to evolve on a timescale that is closely matched to that of the primary infection on which it depends.

中文翻译：

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网络继发感染存活的重入相变

我们研究了网络上继发感染的动态，其中只有当前携带某种原发感染的个体才容易受到继发感染的影响。在大型稀疏网络的限制下，该模型被映射到在随机时间敏感环境中传播的分支过程，由潜在的主要感染的动态决定。当两种流行病都遵循易感-感染-恢复模型时，我们表明，为了生存，继发感染必须在与其依赖的原发感染密切匹配的时间尺度上进化。