caa a22 4500 445359552 CHVBK 20180317142911.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s10100-009-0120-4 doi (NATIONALLICENCE)springer-10.1007/s10100-009-0120-4 On the classical Maki-Thompson rumour model in continuous time [Elektronische Daten] [Selma Belen, Erik Kropat, Gerhard-Wilhelm Weber] 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. Springer-Verlag, 2009 Rumours nationallicence Maki-Thompson model nationallicence Stochastic process nationallicence Dynamical systems nationallicence Lambert- w function nationallicence Operations research nationallicence Belen Selma Department of Mathematics and Computer, CAG University, 33800, Yenice-Tarsus, Mersin, Turkey aut Kropat Erik Institute for Theoretical Computer Science, Mathematics, and Operations Research, Universität der Bundeswehr München, 85577, Neubiberg, Germany aut Weber Gerhard-Wilhelm Institute of Applied Mathematics, Middle East Technical University, 06531, Ankara, Turkey aut Central European Journal of Operations Research Springer-Verlag 19/1(2011-03-01), 1-17 1435-246X 19:1<1 2011 19 10100 https://doi.org/10.1007/s10100-009-0120-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10100-009-0120-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Belen Selma Department of Mathematics and Computer, CAG University, 33800, Yenice-Tarsus, Mersin, Turkey aut NATIONALLICENCE 700 1- Kropat Erik Institute for Theoretical Computer Science, Mathematics, and Operations Research, Universität der Bundeswehr München, 85577, Neubiberg, Germany aut NATIONALLICENCE 700 1- Weber Gerhard-Wilhelm Institute of Applied Mathematics, Middle East Technical University, 06531, Ankara, Turkey aut NATIONALLICENCE 773 0- Central European Journal of Operations Research Springer-Verlag 19/1(2011-03-01), 1-17 1435-246X 19:1<1 2011 19 10100 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer