A deterministic model of the spread of scam rumor and its numerical simulations

In an attempt to illustrate the dynamics of the spread of scam rumors and its impact in a heterogeneous population or social network we adopt the epidemiological model approach. In this work the SpEIsScSt (Susceptible, Exposed, Ignorant, Scammers and Stiflers) model was developed. A diagrammatic representation of the flow of individuals from one class/group to another is given from which a system of five differential equations are obtained. The Basic reproduction number, the equilibrium point of scam rumor-free and the endemic equilibrium state were obtained and discussed. For the local stability of the scam rumor-free and endemic equilibrium state the Next Generation Matrix was used. We were able to show the conditions for the existence of global stability by defining a Lyapunov function with respect to the state variables. Numerical simulation of the system was carried out in order to get a clear picture of the dynamics of the spread of scam rumor in a population or social networks, its impact in a population, and the efficiency of government/admin policies in curbing the spread of scam rumor.