Dynamics analysis and optimal control of SIR-w infectious disease model under the influence of multidimensional information

Abstract

Multidimensional information plays a crucial role in the spread of infectious diseases by facilitating scientific decision-making for prevention and control, enhancing public awareness and participation in preventive measures, optimizing resource allocation to improve treatment efficiency, advancing scientific research to refine prevention and control strategies, as well as guiding public opinion and stabilizing social sentiment. Hence, it is essential to focus on the analysis and utilization of multidimensional information to more effectively tackle the challenges posed by infectious diseases. This paper introduces the SIR-w infectious disease model, which incorporates the influence of multidimensional information. By considering the impact of such information, it examines the interaction mechanisms and the counteracting effects on the spread and control of infectious diseases, and accurately depicts the influence of positive, negative, and legal policies on epidemic spread and control. Employing the next-generation matrix theory, the basic reproduction number is determined. Utilizing stability theory and the Lyapunov function, the dynamical behaviors of the disease-free and endemic equilibrium points are analyzed and discussed. Drawing on the interaction and support mechanisms among multidimensional information such as positive, negative, and legal policies, the study explores how the corresponding parameters affect the compartmental changes. Consequently, an optimal control analysis is conducted for the dissemination rate of positive and negative information generated by confirmed cases, medical resources, and policies and regulations, with numerical solutions for optimal control being obtained. Finally, the four solutions are simulated and verified by numerical simulation, it is found that the simultaneous implementation of the five control measures is the most effective and the least costly.