Bounded risk disposition explains Turing patterns and tipping points during spatial contagions.

Spatial contagions, such as pandemics, opinion polarization, infodemics and civil unrest, exhibit non-trivial spatio-temporal patterns and dynamics driven by complex human behaviours and population mobility. Here, we propose a concise generic framework to model different contagion types within a suitably defined contagion vulnerability space. This space comprises risk disposition, considered in terms of bounded risk aversion and adaptive responsiveness and a generalized susceptibility acquisition. We show that resultant geospatial contagion configurations follow intricate Turing patterns observed in reaction-diffusion systems. Pattern formation is shown to be highly sensitive to changes in underlying vulnerability parameters. The identified critical regimes (tipping points) imply that slight changes in susceptibility acquisition and perceived local risks can significantly alter the population flow and resultant contagion patterns. We examine several case studies using Australian datasets (COVID-19 pandemic; crime incidence; conflict exposure during COVID-19 protests; real estate businesses and residential building approvals) and demonstrate that these spatial contagions generated Turing patterns in accordance with the proposed model.