Journal of Applied Mathematics and Physics, 2019, 7, 1289-1303 http://www.scirp.org/journal/jamp ISSN Online: 2327-4379 ISSN Print: 2327-4352 DOI: 10.4236/jamp.2019.76088 Jun. 27, 2019 1289 Journal of Applied Mathematics and Physics Mathematical Model of the Dynamics of Rumor Propagation Samuel Musa 1 , Mohammed Fori 2 1 Modibbo Adama University of Technology Yola, Yola, Adamawa State, Nigeria 2 Department of Mathematics, College of Education Waka Biu, Waka-Biu, Borno State, Nigeria Abstract In this study, we proposed a deterministic mathematical model that attempts to explain the propagation of a rumor using epidemiological models ap- proach. The population is divided into four classes which consist of ignorant individuals, () It , spreaders targeting community through media, () Mt , spreaders targeting community through verbal communication, () Gt and stiflers, () Rt . We explored existence of the equilibria and analyzed its stabil- ity. It was established that rumour-free equilibrium o E is locally asymptoti- cally stable if 1 o R < ; meaning rumor can seize spreading in a population, and unstable if 1 o R > leads to new rumor spreading in the population. Numerical simulations of the dynamic model are carried out on the system to confirm the analytical results. We see that the dynamics of rumor spreading show similar behavior to that found in the dynamics of infectious diseases except that the spread depends on the classes of spreader. Keywords Rumor, Propagation, Rumor-Free Equilibrium, Rumor-Endemic Equilibrium 1. Introduction The propagation of rumors is a typical form of social interaction that exerts a powerful influence on human affairs. Rumors represent unproven expositions about or interpretations of news, events, or problems that are of public interest. Because rumors are unconfirmed information, it is hard to determine whether they are true or false [1]. Traditionally, rumors are propagated by word of mouth [2] [3] [4]. Nowadays, with the emergence of the internet, rumors spread by instant messengers, emails or publishing blogging and social media that pro- How to cite this paper: Musa, S. and Fori, M. (2019) Mathematical Model of the Dy- namics of Rumor Propagation. Journal of Applied Mathematics and Physics, 7, 1289-1303. https://doi.org/10.4236/jamp.2019.76088 Received: April 28, 2019 Accepted: June 24, 2019 Published: June 27, 2019 Copyright © 2019 by author(s) and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access