Optimizing infectious disease control: A study on local and boundary control strategies in spatial domains

Abstract

Effective infectious disease control is critical for public health, yet challenges remain in optimizing spatial control strategies, particularly regarding the balance between local interventions and boundary control. Existing approaches often overlook the combined effects of interior and boundary controls on disease spread. This paper investigates optimal control strategies for managing infectious diseases using a reaction–diffusion SIR model, with an emphasis on local control within the domain and Robin boundary control applied to the infected population. By varying the number of control areas and their coverage ratios, we aim to reduce the complexity of infected population distributions under high infection rates. The results show that multi-point control is more effective for lower coverage ratios, while concentrated control performs comparably as coverage increases. These findings provide valuable insights for optimizing control strategies in resource-constrained environments and highlight the diminishing returns of increasing coverage beyond a certain threshold.