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

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 ...

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