Fractional Derivative Model on Rumors Causing Stress Within a Family

The act of spreading rumors within a society can have detrimental effects on individuals, including stress, hypertension, and anxiety. Given the complexity of life as a dynamic system, it is crucial to address this chaos with utmost attention. The proposed fractional derivative epidemic model for transmitting rumors in social networks highlights the importance of effective counseling and medical intervention in reducing the severity of rumors. The fractional order parameter ρ is crucial in determining the stability of individuals recovering from the stress caused by rumor attacks. This model incorporates Holling type II recovery rate to observe the effects of measures taken by the susceptible and infectious populations. Our observations indicate that a decrease in the fractional order leads to an increase in stress and a decrease in recovery, while an increase in the fractional order results in a decrease in stress and an increase in recovery. The simulation results indicate that the increase in the recovery rate can be attributed to the successful implementation of counseling and medical interventions. It is recommended to prioritize addressing lower values of ρ and take measures to identify and address individuals who spread rumors to reduce stress and anxiety within society.