Real systems are often small in size and observed at finite times, while the modelling techniques presuppose infinite time and size. In data we might not be able to distinguish all classes, as for example, we might observe post-symptomatic cases only. Finally, our model might not capture all key processes. In spite of these difficulties we are still trying to find parameters and predict the spread of epidemics and the outcome of control measures. A suite of models is constructed and fitted to the data and we discuss the reliability of the predictions by comparing the results with separate experiments targeting individual interactions.
Users communicate by sending messages to the channel.
When multiple messages are sent simultaneously, these messages collide and are not delivered successfully. Messages arrive according to a Poisson process. The key question is whether a given protocol is stable, for example, whether the corresponding Markov chain is recurrent. I will survey recent work in this area, including joint work with Jerrum, Kannan and Paterson. In the first I consider a population in which both males and females differ in quality.