A Reaction–Diffusion PDE Model for Cyberattack Propagation in Medical IoT Networks

Resumen

Medical Internet of Things (MIoT) networks are now deeply embedded in clinical environments, but their increasing connectivity also creates pathways for cyberattacks that can spread across devices rather than remain localized. Most existing studies emphasize intrusion detection or vulnerability analysis, offering limited insight into the spatio-temporal conditions under which attacks persist or die out in real hospital settings. This paper develops a reaction–diffusion partial differential equation model. By the use of reaction–diffusion partial differential equation model to study cyberattack propagation in MIoT networks while explicitly accounting for spatial device distribution, nonlinear interaction between devices, recovery through patching, and permanent isolation of compromised nodes.

The proposed framework models secure, compromised, and recovered devices as spatially distributed populations. A basic reproduction number is derived to characterize a sharp threshold separating attack extinction from long-term persistence. Rigorous analysis establishes existence and uniqueness of solutions, positivity, boundedness, invariant regions, local stability of the disease-free equilibrium, and uniform persistence when the threshold is exceeded. Numerical simulations using finite difference methods validate the analytical results and reveal diffusion-driven spread, spatial clustering, and clear threshold behavior.

The findings show that cyberattacks in MIoT networks behave as structured spreading processes rather than isolated events. The model provides a mathematically grounded basis for assessing cyber resilience and for designing mitigation strategies that balance vulnerability reduction, rapid recovery, and effective isolation in spatially distributed medical environments.