A susceptible–infected–susceptible (SIS) model of multiple contagions on multilayer networks is developed to incorporate different spreading channels and disease mutations. Upper and lower bounds of basic reproductive numbers are derived and rapid mutation processes are analytically analyzed. In the special case where only two contagions are considered, analytical results are obtained for the multilayer network model, a competition model with arbitrarily many layers, and a compartmental model. The developed model and the obtained results may help understanding other spreading phenomena including communicable diseases, cultural characteristics, addictions, or information spread through e-mail messages, web blogs and computer networks.

建立了多层网络上多种传染病的易感性-易感性（SIS）模型，以纳入不同的传播渠道和疾病突变。推导了基本生殖数的上限和下限，并分析了快速突变过程。在仅考虑两个传染性的特殊情况下，可以获得多层网络模型，任意层的竞争模型和分区模型的分析结果。开发的模型和获得的结果可能有助于理解其他传播现象，包括传染病，文化特征，成瘾或通过电子邮件，网络博客和计算机网络传播的信息。