Dynamics driven by spatiotemporal heterogeneity in reaction–diffusion epidemic systems

Spatiotemporal heterogeneity is a key factor influencing the dynamics and controlling effectiveness of infectious disease transmission; however, research on how the form and degree of heterogeneity affect epidemic evolution and system stability remains limited. For the reason of this limitation, this study develops a reaction–diffusion SI model incorporating spatiotemporally heterogeneous interventions and integrates optimal control theory with entropy-based metrics to establish a quantitative framework linking heterogeneity to epidemic outcomes. The results reveal that: (i) under the same total cost constraint, heterogeneous interventions significantly outperform homogeneous ones in reducing average infection levels and suppressing high-risk areas; (ii) the spatial complexity of heterogeneous structures is strongly coupled with intervention effectiveness — higher degrees of spatial heterogeneity enhance epidemic suppression and lead to more balanced risk distributions; and (iii) the system exhibits markedly different responses to homogeneous and heterogeneous perturbations, highlighting the crucial regulatory role of heterogeneity in shaping spatial stability and recovery capacity. This study provides a new theoretical perspective for understanding heterogeneity-driven epidemic pattern formation and resilience mechanisms, and offers methodological guidance for the design of spatially adaptive and precision control strategies.