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.

投资者情绪传染对经济和社会发展具有深远影响。本文探讨了现代社会中各种投资者情绪对经济和社会的不同影响。它还调查了现代经济和社会中各种不确定因素对投资者情绪的干扰。在此基础上，构建了双系统随机 SPA2G2R 模型，融合了积极和消极的情绪，以及监督和隔离机制。建立了积极解决方案的全球存在，并计算了投资者情绪消失和稳定分布的充分条件。提出了一种随机模型的优化控制策略，数值模拟支持了理论分析结果。还与确定性模型中的参数变化进行了比较。该研究揭示了不同投资者情绪之间的竞争关系。加强社会指导机制可促进积极的投资者情绪传染。监管部门的及时控制有效遏制了投资者情绪的蔓延。此外，白噪声会促进投资者情绪的传染，表明通过控制噪声强度和干扰参数进行有效监管。