A Mathematical Model of Political Rumour in Assakio Community with Conditional Latent Period in a Varying Population

Abstract

In this paper a rumour propagation model with conditional latent period and varying population is considered. In the literature, classical model assume that an ignorant individual enters the latent period and decide whether to become a spreader or stifler. In our model we introduce a new compartment called the blackmailers, another type of spreaders who spread the rumour for selfish reason. The model equations are first transformed into proportions, thus reducing the model equations from five to four differential equations. The model exhibit two equilibra, namely the Rumour Free Equilibrium (RFE) and the Rumour Endemic Equilibrium (REE). Using the method of linearized stability, we establish that the RFE state exist and is locally asymptomatically stable when R₀ < 1  and that when R₀ > 1 the endemic state exist. The model allows us to discuss the relationship between spreaders and blackmailers, and the effect of blackmailers on the stiflers. Finally, we present numerical simulations that show the impact of political motivated rumours and how its control can be achieved.

Keywords: Rumor propagation, Political motivated rumour, Epidemiological models; stability analysis, Transition parameter