Dynamics analysis and optimal control of an infectious disease model on networks under the coupling effect of multidimensional media information

Infectious diseases not only pose a threat to human health, but also have an impact on social order and economic stability. Given the complexity and dynamism of the transmission process of infectious diseases, single dimensional information is difficult to provide comprehensive and accurate understanding of infectious diseases when characterizing transmission patterns and evolutionary characteristics. Therefore, it is crucial to delve into the interaction mechanism of multiple types of information, including positive, negative, and policy regulatory information, in the process of infectious disease transmission. Based on this, this paper innovatively constructs an infectious disease transmission model based on multidimensional media information interaction, which fully considers the heterogeneity characteristics of networks blocks and the co-evolution between information transmission and disease transmission. First, a two-layer infectious disease networks model based on multidimensional media information influence and regional heterogeneity was constructed. The basic reproduction number [Formula: see text] of the model was derived by using methods such as differential equation dynamics and matrix analysis. And with the help of Lyapunov function stability theory and Lasalle invariance principle, the dynamic properties of disease-free equilibrium points and endemic equilibrium points were rigorously proved. Second, in order to achieve effective intervention and optimized control of the transmission process of infectious diseases, the optimal control equation for infectious disease transmission was designed with the objective function of minimizing the number of infected people and control costs. The numerical solution of the optimal control strategy was obtained by introducing the Pontryagin maximum principle and using numerical algorithms. Finally, a series of numerical simulation experiments were conducted to verify the effectiveness and accuracy of the theoretical analysis of the model. Therefore, it is of great significance to reasonably guide and regulate the dissemination characteristics and content of multidimensional media information in order to achieve effective prevention and control of infectious diseases.