eprintid: 1473754 rev_number: 16 eprint_status: archive userid: 608 dir: disk0/01/47/37/54 datestamp: 2016-01-08 15:11:45 lastmod: 2019-02-18 04:15:57 status_changed: 2016-01-08 15:11:45 type: article metadata_visibility: show creators_name: Knipl, DH creators_name: Röst, G creators_name: Wu, J title: Epidemic Spread and Variation of Peak Times in Connected Regions Due to Travel-Related Infections - Dynamics of an Antigravity-Type Delay Differential Model ispublished: pub divisions: A01 divisions: B04 divisions: C06 keywords: differential equations, transportation model, epidemic spread, influenza modeling note: First Published in SIAM Journal on Applied Dynamical Systems in Volume 12, Issue 4 (2013), published by the Society of Industrial and Applied Mathematics (SIAM). Copyright © 2013 Society for Industrial and Applied Mathematics. abstract: National boundaries have never prevented infectious diseases from reaching distant territories; however, the speed at which an infectious agent can spread around the world via the global airline transportation network has significantly increased during recent decades. We introduce an SEAIR-based, antigravity model to investigate the spread of an infectious disease in two regions which are connected by transportation. As a submodel, an age-structured system is constructed to incorporate the possibility of disease transmission during travel, where age is the time elapsed since the start of the travel. The model is equivalent to a large system of differential equations with dynamically defined delayed feedback. After describing fundamental but biologically relevant properties of the system, we detail the calculation of the basic reproduction number and obtain disease transmission dynamics results in terms of $\mathcal{R}_0$. We parametrize our model for influenza and use real demographic and air travel data for the numerical simulations. To understand the role of the different characteristics of the regions in the propagation of the disease, three distinct origin-destination pairs are considered. The model is also fitted to the first wave of the influenza A(H1N1) 2009 pandemic in Mexico and Canada. Our results highlight the importance of including travel time and disease dynamics during travel in the model: the invasion of disease-free regions is highly expedited by elevated transmission potential during transportation. date: 2013 date_type: published official_url: http://dx.doi.org/10.1137/130914127 oa_status: green full_text_type: pub language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 1049820 doi: 10.1137/130914127 lyricists_name: Knipl, Diana lyricists_id: DHKNI00 actors_name: Knipl, Diana actors_id: DHKNI00 actors_role: owner full_text_status: public publication: SIAM Journal on Applied Dynamical Systems volume: 12 number: 4 pagerange: 1722-1762 issn: 1536-0040 citation: Knipl, DH; Röst, G; Wu, J; (2013) Epidemic Spread and Variation of Peak Times in Connected Regions Due to Travel-Related Infections - Dynamics of an Antigravity-Type Delay Differential Model. SIAM Journal on Applied Dynamical Systems , 12 (4) pp. 1722-1762. 10.1137/130914127 <https://doi.org/10.1137/130914127>. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/1473754/1/Knipl_Rost_Wu--Antigravity_TravelInfection.pdf