Epidemic Spread and Variation of Peak Times in Connected Regions Due to Travel-Related Infections---Dynamics of an Antigravity-Type Delay Differential Model

Abstract

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 SEAIRbased, 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 R0. 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.

Global analysis for spread of infectious diseases via transportation networks

“…Here, the mobility rate is assumed to depend on the region where the individual currently resides, and the individuals are homogeneously mixed into the local population upon arrival, thus our model fits into the framework of the usual patch models in the literature (Arino 2009;Brauer and Driessche 2001;Cui et al 2006;Gao and Ruan 2012;Hsieh et al 2007;Li and Zou 2010;Wang andZhao 2004, 2005), that accounts for long-term mobility such as immigration of infectives. As examples describing short-term mobility such as tourism and business travels, we refer to Arino and Driessche (2003) and Knipl et al (2013), where the mobility rates depend on the individual's original and current locations as well.…”

Modelling the global spread of diseases: A review of current practice and capability

“…Six records, [5,11,51,57,73,77], made explicit reference to adopting this approach. Record [50] developed a gravity model for comparison with another approach, and [48] developed an anti-gravity model, where the speed of disease spread between regions is inversely proportional to the distance between regions.…”

“…OAG is an air travel intelligence company which has a large network of air travel data, also available for purchase (OAG). [1,2,3,4,5,6,7,10,11,12,14,16,17,18,19,20,22,23,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,48,50,51,52,53…”

Classification of Asymptotic Behavior in a Stochastic SIR Model

“…Since epidemic models were first introduced by Kermack and McKendrick in [15,16], the study on mathematical models has been flourished. Much attention has been devoted to analyzing, predicting the spread, and designing controls of infectious diseases in host populations; see [1,2,4,6,8,18,19,15,16,26,27] and the references therein. One of classic epidemic models is the SIR (Susceptible-Infected-Removed) model that is suitable for modeling some diseases with permanent immunity such as rubella, whooping cough, measles, smallpox, etc.…”