Opinion propagation in bounded medium-sized populations

We study the dynamics of opinion propagation in a medium-sized population with low population turnover. Opinion spreading is modelled by a Markovian non-standard Susceptible–Infected–Recovered (SIR) epidemic model with stochastic arrivals, departures, infections and recoveries. The system performance is evaluated by two complementary approaches: a numerical but approximate solution approach which relies on Maclaurin-series expansions of the stationary solution of the Markov process and a fluid limit approach. Both methods are evaluated numerically. Moreover, convergence to the fluid limit is proved, and explicit expressions for the fixed points of the differential equations are obtained for the case of linearly increasing infection and arrival rates.