<p>In this paper, we develop a spatio-temporal diffusion model of infectious diseases with the Allee effect. First, based on the social phenomenon of shortening the spatio-temporal distance among individuals in real life, we replace the Laplace operator in the traditional reaction-diffusion model for infectious diseases with a Laplace matrix. This matrix serves to encapsulate the interconnection relationships between nodes, where each individual is represented as a distinct node within the network framework. By considering different structures between homogeneous and heterogeneous networks, we separately compute the necessary conditions for the occurrence of Turing instability. At the same time, we use multiscale analysis to derive the amplitude equations on the network structure. It is hoped that it is possible to predict the shape of Turing pattern under complex network structures by linking theory to practice. We further apply three different algorithms to study the parameter identification under optimal control, and select the optimal method through the parameter convergence plot as well as the error plot. To ensure the feasibility of the model, we use Monte Carlo simulation to compare the error of the model fitted data with the actual data, and apply the idea of least squares to fit the actual data.By employing a Physics-Informed Neural Network for data fitting and conducting residual analysis, we ultimately derive the epidemic model parameters for each county.</p>