The explosive evolution of the internet has paved the path for the rise of social networks, which can help people connect remotely. Currently, social networks are commonly used for sharing thoughts, feelings, information, and personal life, which vary from individual to individual. The world has witnessed a tremendous increase in social media usage in the last decade, and more people are expected to spend their time online after the COVID-19 pandemic. This increases the rapid propagation of rumors and fake news within societies and communities. On one end, social networks act as an excellent platform for digital marketing and sharing information. However, on the other end, social network rumors and fake news create a significant impact on society, including riots. To study and analyze social network rumors, several mathematical rumor propagation epidemic models have been proposed. The majority are related to disease-spreading epidemic models and reject the human aspect of social selection. This paper introduces a new mathematical rumor propagation model for social networks by incorporating the human psychological aspect of selection as a separate state. Our mathematical analysis and computational simulation proved that the model exists within the system. It was also proven that the system is always non-negative and there always exists a solution in the system. Our implementation of an intervention mechanism within the discrete compartmental model simulation proved the necessity of an effective interference that can help to prevent the implications of uncontrolled rumor dissemination within social networks.

Digital networks and E-commerce platforms have had a profound effect on people’s personal, educational, and professional life all around the world. They offer space for advertising, sales, and disseminating news and information, even if they are frequently used for social marketing, interacting, and sharing thoughts among people. Currently, most E-commerce platforms utilize digital network space for advertisement and an increasing trend of social commerce is visible in all parts of the world. During the Post-COVID-19 pandemic, a rapid increase in digital media and E-commerce usage was observed in all parts of the world for personal and professional aspects. The increase in misinformation through these platforms is a major challenge that the current governments face today as rumors and fake news creates severe detrimental implications in society. In this work, we consider fake reviews and misinformation in online digital networks as a single disease, and thereby, by considering the recent trends in online social media marketing, we formulate a pandemic model for digital networks with a psychological state of human choice. The positivity and stability of the model are mathematically tested and validated. Our analysis and simulation prove that the system is stable and justifiable in the real-world digital environment. The generated pandemic model can be applied to assess the social and emotional intelligence of communities and consumers who are frequently exposed to misinformation and share fake news.