An Epidemic on a Weighted Partially Directed Network

• We introduce a weighted partially directed configuration model graph, where the weights on undirected and directed edges correspond to the probability of transmitting an infection. The model is especially useful when the degree distribution is known, but not the exact structure of the network. On such graphs, we study SIR epidemics in discrete time and determine the basic reproduction number R0, the probability of a large outbreak and the relative final size of the outbreak. The analytical results of the model are compared with simulated epidemics on three empirical networks. While the networks are large and have a very high maximum degree, thanks to the sparse nature of the degree distribution for many empirical networks, the analysis is still computationally feasible on standard computers. While results are different on the three networks, we see that for two of them the proposed model is compatible with the simulated epidemics on the empirical networks. This makes the model useful for analyzing such networks.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Epidemics

Reproduction number

Final size

Large outbreak

Weighted network

Partially directed

Configuration model

Mathematical Statistics

matematisk statistik

Publikations- och innehållstyp

vet (ämneskategori)

ovr (ämneskategori)