Epidemiological models, traditionally used to study disease spread, can effectively analyze mob behavior on social media by treating ideas, sentiments, or behaviors as ``contagions" that propagate through user networks. In this research, we introduced a mathematical model to analyze social behavior related to COVID-19 spread by examining Twitter activity from April 2020 to June 2020. Our analysis focused on key terms such as ``lockdown" and ``quarantine" to track public sentiment and engagement trends during the pandemic. The threshold number $\Re_{0}$ is derived, and the stability of the steady states is established. Numerical simulations and sensitivity analysis of applicable parameters are carried out. The results show that negative sentiment on Twitter has less influence on COVID-19 spread compared to positive sentiment. However, the effect of negative sentiment on the spread of COVID-19 remains remarkably strong. Moreover, we use the Caputo operator with different parameter values to study the impact of social media platforms on the transmission of COVID-19 diseases.