Markovian SIR model for opinion propagation

In this work, we propose a new model for the dynamics of single opinion propagation at a size-limited location with a low population turnover. This means that a maximum number of individuals can be supported by the location and that the allowed individuals have a long sojourn time before leaving the location. The individuals can have either no opinion (S), a strong opinion that they want to spread (I), or an opinion that they keep for themselves (R); the letters stem from the popular Susceptible-Infectious-Recovered (SIR) epidemic model. Furthermore, we consider a variable opinion transmission rate. Hence, the opinion spreading is modelled as a Markovian non-standard SIR epidemic model with stochastic arrivals, departures, infections and recoveries. We evaluate the system performance by two complementary approaches: we apply a numerical but approximate solution approach which relies on Maclaurin series expansions and we investigate the fluid limit of the system at hand. Finally, we illustrate our approach by some numerical examples.