Dynamics of diseases spreading on networks in the forms of reaction-diffusion systems

In the face of persistent threats posed by infectious diseases, despite remarkable medical advancements, understanding and efficiently controlling their spatial spread through mathematical modeling remain imperative. Networked reaction-diffusion systems offer a promising avenue to effectively delineate population discrete distribution and individual movement heterogeneity. However, the dynamics of spatial diseases within these systems and the formulation of optimal control strategies are currently undergoing vigorous development. In this letter, we illustrate the dynamics of spatial disease spread in networked reaction-diffusion systems through the lens of optimal control, considering various network complexities from pairwise networks to higher-order networks. It then emphasizes their applicability in designing effective spatial disease control strategies across diverse network complexities. Finally, we discuss the existing challenges.