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