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

¹ School of Mathematics, North University of China - Taiyuan, 030051, Shanxi, China
² School of Computer Science and Technology, North University of China - Taiyuan, 030051, Shanxi, China
³ Complex Systems Research Center, Shanxi University - Taiyuan, 030006, Shanxi, China
⁴ Tangshan Research Institute, Beijing Institute of Technology - Hebei, Tangshan 063000, China
⁵ College of Computer Science, Sichuan University - Chengdu 610065, China
⁶ Physics Department, University of Fribourg - Chemin du Musée 3, 1700 Fribourg, Switzerland

Received: 2 May 2024
Accepted: 2 July 2024

Abstract

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.