title: Systematic Approximations to Susceptible-Infectious-Susceptible Dynamics on Networks.
abstract: Network-based infectious disease models have been highly effective in elucidating the role of contact structure in the spread of infection. As such, pair- and neighbourhood-based approximation models have played a key role in linking findings from network simulations to standard (random-mixing) results. Recently, for SIR-type infections (that produce one epidemic in a closed population) on locally tree-like networks, these approximations have been shown to be exact. However, network models are ideally suited for Sexually Transmitted Infections (STIs) due to the greater level of detail available for sexual contact networks, and these diseases often possess SIS-type dynamics. Here, we consider the accuracy of three systematic approximations that can be applied to arbitrary disease dynamics, including SIS behaviour. We focus in particular on low degree networks, in which the small number of neighbours causes build-up of local correlations between the state of adjacent nodes that are challenging to capture. By examining how and when these approximation models converge to simulation results, we generate insights into the role of network structure in the infection dynamics of SIS-type infections.
authors.affiliation: Zeeman Institute: SBIDER, University of Warwick, Coventry, United Kingdom.|Mathematics Institute, University of Warwick, Coventry, United Kingdom.|School of Life Sciences, University of Warwick, Coventry, United Kingdom.
authors.forename: Matt J
authors.identifier: 0000-0003-4639-4765
authors.initials: MJ
authors.lastname: Keeling
authors.affiliation: Zeeman Institute: SBIDER, University of Warwick, Coventry, United Kingdom.|Mathematics Institute, University of Warwick, Coventry, United Kingdom.|School of Mathematics, University of Manchester, Manchester, United Kingdom.
authors.forename: Thomas
authors.identifier: 0000-0001-5835-8062
authors.initials: T
authors.lastname: House
authors.affiliation: School of Engineering, University of Warwick, Coventry, United Kingdom.
authors.forename: Alison J
authors.initials: AJ
authors.lastname: Cooper
authors.affiliation: Zeeman Institute: SBIDER, University of Warwick, Coventry, United Kingdom.|Mathematics Institute, University of Warwick, Coventry, United Kingdom.
authors.forename: Lorenzo
authors.identifier: 0000-0002-3436-6487
authors.initials: L
authors.lastname: Pellis
mesh_terms: D000465:Algorithms; D003141:Communicable Diseases; D019295:Computational Biology; D003198:Computer Simulation; D004198:Disease Susceptibility; D006801:Humans; D008954:Models, Biological; D015995:Prevalence; D013269:Stochastic Processes