Can border controls and travel restrictions suppress epidemics? This is an important and recurring question for public health policymaking and pandemic preparedness. Although there is a consensus that infections imported from external locations are critical to sustaining local epidemic growth and driving the endemic equilibria of the disease, there remains ongoing debate on the effectiveness of interventions aimed at curbing importations. Most studies contributing to this debate rely on complex metapopulation, models that preclude generalisable insights and formal control principles are rarely used. Here we demonstrate how classical control theory applied to an analytic but flexible and widely used transmission model provides conclusive evidence that border and travel restrictions fail to stabilise spread. These restrictions always enter as precompensators and hence fail to shift the epidemic poles. Consequently, regions cannot respond to emergent outbreaks in isolation. We find that coordinating interventions across both the local and external regions converts precompensation into feedback control and derive new criteria for overall stability. We further develop formulae specifying how border controls shape performance, such as disease equilibria and total infections. During growing epidemic phases, cooperative control is crucial for stability. Once stability is assured, border control can be sufficient to meet performance targets.

This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.

KVP acknowledges funding from the MRC Centre for Global Infectious Disease Analysis (Reference No. MR/X020258/1) funded by the UK Medical Research Council. This UK-funded grant is carried out in the frame of the Global Health EDCTP3 Joint Undertaking.

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