Pattern dynamics analysis and parameter identification of spatiotemporal infectious disease models on complex networks

This paper primarily explores the dynamics of reaction–diffusion systems with advection effects on discrete networks and establishes a corresponding infectious disease transmission model incorporating delay effects. Initially, we consider the conditions for the existence of the equilibrium point and linearly approximate the time delay near this equilibrium point. Then we discuss the necessary conditions for Turing instability under various constraints based on the approximate system. We also introduce two types of lower-order network structures. In one of these lower-order networks, we discuss the directional movement of two different populations. To further analyze the dynamic behavior on different networks, we construct a special higher-order network based on another lower-order network. In addition, we use optimal control to solve the problem of parameter identification. We conduct extensive numerical simulations to study the impact of advection effects and higher-order networks on system dynamics, pattern parameter identification under unknown conditions, and model fitting and prediction based on actual data, which validate the model’s effectiveness and practical utility.