Epidemiologic network inference

In many epidemiologic models, a disease is assumed to spread along a contact network. We aim to infer this network, in addition to the epidemiologic model parameters, from the binary status of individuals observed throughout time. We perform an exact evaluation of the probability for each edge to be part of the network by using the matrix-tree theorem on the set of vertices made of the individual status at all times. This leads to a computational complexity of order $${\mathcal {O}}(mn^2)$$ O ( m n 2 ) , where n is the number of individuals and m the length of the time series. Simulations are provided to demonstrate the efficiency of the proposed method, and it is applied on data concerning seed choices by farmers in India and on data on a measles outbreak.

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