@article { , title = {An epidemic model with short-lived mixing groups}, abstract = {Almost all epidemic models make the assumption that infection is driven by the interaction between pairs of individuals, one of whom is infectious and the other of whom is susceptible. However, in society individuals mix in groups of varying sizes, at varying times, allowing one or more infectives to be in close contact with one or more susceptible individuals at a given point in time. In this paper we study the effect of mixing groups beyond pairs on the transmission of an infectious disease in an SIR (susceptible → infective → recovered) model, both through a branching process approximation for the initial stages of an epidemic with few initial infectives and a functional central limit theorem for the trajectories of the numbers of infectives and susceptibles over time for epidemics with many initial infectives. We also derive central limit theorems for the final size of (i) an epidemic with many initial infectives and (ii) a major outbreak triggered by few initial infectives. We show that, for a given basic reproduction number R0, the distribution of the size of mixing groups has a significant impact on the probability and final size of a major epidemic outbreak. Moreover, the standard pair-based homogeneously mixing epidemic model is shown to represent the worst case scenario, with both the highest probability and the largest final size of a major epidemic.}, doi = {10.1007/s00285-022-01822-3}, eissn = {1432-1416}, issn = {0303-6812}, issue = {6-7}, journal = {Journal of Mathematical Biology}, note = {Article not yet published online. On temp embargo sheet. Will need to change status to published. Will need to add official url, volume, issue, pagination and doi. Will need to set 12 month embargo on publication. Will need to add set statement "This version of the article has been accepted for publication, after peer review but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/[insert DOI]" KJB 7.10.22}, publicationstatus = {Published}, publisher = {Springer Science and Business Media LLC}, url = {https://nottingham-repository.worktribe.com/output/12034956}, volume = {85}, keyword = {Applied Mathematics, Agricultural and Biological Sciences (miscellaneous), Modeling and Simulation}, year = {2022}, author = {Ball, Frank and Neal, Peter} }