Pattern selection and parameter optimization design of reaction-diffusion information propagation model

In modern society, with the rapid development of the Internet, the speed of information dissemination greatly increases. Information security has a profound impact on national and social safety. Therefore, the study of information dissemination is essential. Based on the traditional SIR(Susceptible-Infected-Recovered) model, a three-dimensional information transmission model is proposed. To understand the distribution of populations near the system’s equilibrium point, we combine image features and the definition of Turing instability. We derive the necessary conditions for Turing instability. To investigate Turing pattern morphology, amplitude equations are derived using the method of multiple scales. For continuous systems, optimal-control and parameter-identification frameworks are formulated. Numerical simulations assess parameter sensitivity. In numerical simulations, we analyze the sensitivity of different parameters in the continuous system. With the remaining parameters fixed, varying one parameter. This reveals how each parameter shapes the Turing patterns. This confirms that the model has strong robustness. Next, visualize the amplitude equations and identify the Turing patterns across parameter ranges. For effective control of information dissemination, an optimal-control–based parameter identification study applies three algorithms. These algorithms include the BB algorithm (Barzilai-Borwein algorithm), PG algorithm (Projected Gradient algorithm), and BFGS algorithm (Broyden-Fletcher-Goldfarb-Shanno algorithm). The convergence of the algorithms is analyzed, and their strengths and limitations are compared. The results show that the choice of algorithm significantly impacts the iteration outcomes. The BB algorithm works well for simple problems with few parameters. The PG algorithm is highly stable when dealing with fewer parameters but may face difficulties with more complex issues. On the other hand, the BFGS algorithm shows excellent robustness and achieves good convergence in multidimensional parameter spaces and complex problems. To validate the model’s applicability based on the data of COVID-19 tweets posted on Twitter in Indonesia, the least squares method and random walk fitting model are used, combined with the Data-Enhanced Residual Gradient Adjustment (DERGA) method for prediction. Thus, in real-life situations, we can control information dissemination by adjusting parameters like the decay rate and propagation rate through government measures and media interventions. It is important to achieve the target values of these parameters in order to control the spread of information, which is crucial for today’s information management.