title: Compact pairwise models for epidemics with multiple infectious stages on degree heterogeneous and clustered networks.
abstract: This paper presents a compact pairwise model describing the spread of multi-stage epidemics on networks. The multi-stage model corresponds to a gamma-distributed infectious period which interpolates between the classical Markovian models with exponentially distributed infectious period and epidemics with a constant infectious period. We show how the compact approach leads to a system of equations whose size is independent of the range of node degrees, thus significantly reducing the complexity of the model. Network clustering is incorporated into the model to provide a more accurate representation of realistic contact networks, and the accuracy of proposed closures is analysed for different levels of clustering and number of infection stages. Our results support recent findings that standard closure techniques are likely to perform better when the infectious period is constant.
authors.affiliation: Department of Mathematics, University of Sussex, Brighton BN1 9QH, UK.
authors.forename: N
authors.initials: N
authors.lastname: Sherborne
authors.affiliation: Department of Mathematics, University of Sussex, Brighton BN1 9QH, UK. Electronic address: k.blyuss@sussex.ac.uk.
authors.forename: K B
authors.initials: KB
authors.lastname: Blyuss
authors.affiliation: Department of Mathematics, University of Sussex, Brighton BN1 9QH, UK.
authors.forename: I Z
authors.initials: IZ
authors.lastname: Kiss
mesh_terms: D016000:Cluster Analysis; D003141:Communicable Diseases / Q000453:epidemiology*; D003198:Computer Simulation; D058872:Epidemics; D006801:Humans; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted
keywords: Clustering; Moment closures; Non-Markovian recovery; Pairwise approximation