# On the classical Maki-Thompson rumour model in continuous time

2011-03-01
Belen, Selma
Kropat, Erik
Weber, Gerhard Wilhelm
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.
CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH

# Suggestions

 Neural network calibrated stochastic processes: forecasting financial assets Giebel, Stefan; Rainer, Martin (Springer Science and Business Media LLC, 2013-03-01) If a given dynamical process contains an inherently unpredictable component, it may be modeled as a stochastic process. Typical examples from financial markets are the dynamics of prices (e.g. prices of stocks or commodities) or fundamental rates (exchange rates etc.). The unknown future value of the corresponding stochastic process is usually estimated as the expected value under a suitable measure, which may be determined from distribution of past (historical) values. The predictive power of this estimati...
 Effective optimization with weighted automata on decomposable trees Ravve, E. V.; Volkovich, Z.; Weber, Gerhard Wilhelm (Informa UK Limited, 2014-01-02) In this paper, we consider quantitative optimization problems on decomposable discrete systems. We restrict ourselves to labeled trees as the description of the systems and we use weighted automata on them as our computational model. We introduce a new kind of labeled decomposable trees, sum-like weighted labeled trees, and propose a method, which allows us to reduce the solution of an optimization problem, defined in a fragment of Weighted Monadic Second Order Logic, on such a tree to the solution of effec...
 A NEW HEURISTIC APPROACH FOR THE MULTIITEM DYNAMIC LOT-SIZING PROBLEM KIRCA, O; KOKTEN, M (Elsevier BV, 1994-06-09) In this paper a framework for a new heuristic approach for solving the single level multi-item capacitated dynamic lot sizing problem is presented. The approach uses an iterative item-by-item strategy for generating solutions to the problem. In each iteration a set of items are scheduled over the planning horizon and the procedure terminates when all items are scheduled. An algorithm that implements this approach is developed in which in each iteration a single item is selected and scheduled over the planni...
 An approximate model for kanban controlled assembly systems Topan, Engin; Avşar, Zeynep Müge; Department of Industrial Engineering (2005) In this thesis, an approximation is proposed to evaluate the steady-state performance of kanban controlled assembly systems. The approximation is developed for the systems with two components making up an assembly. Then, it is extended to systems with more than two components. A continuous-time Markov model is aggregated keeping the model exact, and this aggregate model is approximated replacing some state-dependent transition rates with constant rates. Decomposition of the approximate aggregate model into ...
 An interactive solution approach for a bi-objective semi-desirable location problem Karasakal, Esra (Springer Science and Business Media LLC, 2008-10-01) In this study, we consider a semi-desirable facility location problem in a continuous planar region considering the interaction between the facility and the existing demand points. A facility can be defined as semi-desirable if it has both undesirable and desirable effects to the people living in the vicinity. Our aim is to maximize the weighted distance of the facility from the closest demand point as well as to minimize the service cost of the facility. The distance between the facility and the demand poi...
Citation Formats
S. Belen, E. Kropat, and G. W. Weber, “On the classical Maki-Thompson rumour model in continuous time,” CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH, pp. 1–17, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/57044.