An Improved Solution to Identify Spatial Invasion on Metapopulation Networks with SI model

Large-scale outbreaks of epidemics are inextricably linked to the spatial spread via carriers, in addition to the strong infectiousness of the disease itself. Identifying the spatial invasion pathways on the metapopulation network is important for further prediction and control of the spread of infectious diseases. The whole inference task can be decomposed into a series of uncorrelated invasion cases, of which some are identified accurately and the others are inferred with the maximum likelihood method after a complexity reduction process. In this paper, we present and prove the sufficient conditions for the dominant type of invasion cases to be identified accurately. Moreover, a recursive algorithm is proposed to traverse all the possible invasion pathways among which the most likely one will be selected as the result. Finally, simulations on a synthetic metapopulation network verify our algorithm.