Dynamic analysis and optimal control of stochastic information cross-dissemination and variation model with random parametric perturbations.

Information dissemination has a significant impact on social development. This paper considers that there are many stochastic factors in the social system, which will result in the phenomena of information cross-dissemination and variation. The dual-system stochastic susceptible-infectious-mutant-recovered model of information cross-dissemination and variation is derived from this problem. Afterward, the existence of the global positive solution is demonstrated, sufficient conditions for the disappearance of information and its stationary distribution are calculated, and the optimal control strategy for the stochastic model is proposed. The numerical simulation supports the results of the theoretical analysis and is compared to the parameter variation of the deterministic model. The results demonstrate that cross-dissemination of information can result in information variation and diffusion. Meanwhile, white noise has a positive effect on information dissemination, which can be improved by adjusting the perturbation parameters.

Dynamic analysis and optimal control of a stochastic investor sentiment contagion model considering sentiments isolation with random parametric perturbations.

Investor sentiment contagion has a profound influence on economic and social development. This paper explores the diverse influences of various investor sentiments in modern society on the economy and society. It also investigates the interference of various uncertain factors on investor sentiments in the modern economy and society. On this basis, the dual-system stochastic SPA2G2R model was constructed, incorporating positive and negative sentiments, as well as a supervision and isolation mechanism. The global existence of positive solutions was established, and sufficient conditions for the disappearance and steady distribution of investor sentiment were calculated. An optimal control strategy for the stochastic model was put forward, with numerical simulation supporting the theoretical analysis results. A comparison with parameter changes in the deterministic model was also conducted. The research reveals a competitive relationship between different investor sentiments. Enhancing societal guidance mechanisms promotes positive investor sentiment contagion. Timely control by the supervisory department effectively curbs the spread of investor sentiment. Additionally, white noise promotes investor sentiment contagion, suggesting effective regulation through control of noise intensity and disturbance parameters.

Dynamic analysis and optimal control considering cross transmission and variation of information.

Cross-transmission of information has a profound influence on the progress of science and technology and the discipline integration in the field of education. In this work, knowledge gained from the viral recombination and variation in COVID-19 transmission is applied to information transmission. Virus recombination and virus variation are similar to the crossing and information fusion phenomena in information transmission. An S2I4MR model with information crossing and variation is constructed. Then, the local and global asymptotic stabilities of the information-free equilibrium and information-existence equilibrium are analyzed. Additionally, the basic reproduction number [Formula: see text] of the model is calculated. As such, an optimal control strategy is hereby proposed to promote the cross-transmission of information and generate variant information. The numerical simulations support the results of the theoretical analysis and the sensitivity of the system towards certain control parameters. In particular, the results show that strengthening information crossing promotes the generation of variant information. Furthermore, encouraging information exchange and enhancing education improve the generation of information crossing and information variation.

Dynamical analysis and optimal control of the developed information transmission model.

Information transmission significantly impacts social stability and technological advancement. This paper compares the phenomenon of "Super transmission" and "Asymptomatic infection" in COVID-19 transmission to information transmission. The former is similar to authoritative information transmission individuals, whereas the latter is similar to individuals with low acceptance in information transmission. It then constructs an S2EIR model with transmitter authority and individual acceptance levels. Then, it analyzes the asymptotic stability of information-free and information-existence equilibrium on a local and global scale, as well as the model's basic reproduction number, R0. Distinguished with traditional studies, the population density function and Hamiltonian function are constructed by taking proportion of "Super transmitter" and proportion of hesitant group turning into transmitters as optimization control variables. Based on the Pontryagin maximum principle, an optimal control strategy is designed to effectively facilitate information transmission. The numerical simulation corroborates the theoretical analysis results and the system's sensitivity to control parameter changes. The research results indicate that the authoritative "Super transmitter" has a beneficial effect on information transmission. In contrast, the "Asymptomatic infected individual" with poor individual acceptance level negatively affects information transmission.