Show/Hide Menu
Hide/Show Apps
anonymousUser
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Açık Bilim Politikası
Açık Bilim Politikası
Frequently Asked Questions
Frequently Asked Questions
Browse
Browse
By Issue Date
By Issue Date
Authors
Authors
Titles
Titles
Subjects
Subjects
Communities & Collections
Communities & Collections
On the classical Maki-Thompson rumour model in continuous time
Date
2011-03-01
Author
Belen, Selma
Kropat, Erik
Weber, Gerhard Wilhelm
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
6
views
0
downloads
In this paper, the Maki-Thompson model is slightly refined in continuous time, and a new general solution is obtained for each dynamics of spreading of a rumour. It is derived an equation for the size of a stochastic rumour process in terms of transitions. We give new lower and upper bounds for the proportion of total ignorants who never learned a rumour and the proportion of total stiflers who either forget the rumour or cease to spread the rumour when the rumour process stops, under general initial conditions. Simulation results are presented for the analytical solutions. The model and these numerical results are capable to explain the behaviour of the dynamics of any other dynamical system having interactions similar to the ones in the stochastic rumour process and requiring numerical interpretations to understand the real phenomena better. The numerical process in the differential equations of the model is investigated by using error-estimates. The estimated error is calculated by the Runge-Kutta method and found either negligible or zero for a relatively small size of the population. This pioneering paper introduces a new mathematical method into Operations research, motivated by various areas of scientific, social and daily life, it presents numerical computations, discusses structural frontiers and invites the interested readers to future research.
Subject Keywords
Management Science and Operations Research
URI
https://hdl.handle.net/11511/57044
Journal
CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH
DOI
https://doi.org/10.1007/s10100-009-0120-4
Collections
Graduate School of Applied Mathematics, Article