Epidemic fade-out in the Markovian SIR-with-demography infection model

Abstract

“Epidemic fade-out” refers to the situation in which an infection is eliminated after an initial major wave of infection. This thesis by publication contains three papers (two published, the third submitted and under review) on the subject of epidemic fade-out in the Markovian SIR-with-demography infection model. The first paper [6] surveys previous work containing methods for approximating the probability of epidemic fade-out, then proposes a numerical method which is more accurate. Using this method, it surveys trends over a range of parameters, and observes that the probability of epidemic fade-out has a non-monotonic relationship with respect to β, the transmission rate parameter. It shows that this probability often has a local maximum where R0, the basic reproduction number, is about 2; and gives an explanation for this phenomenon. The second paper [7] examines the possibility of controlling β, in order to maximise the probability of epidemic fade-out. An optimal policy may be found using Markov decision theory, but this requires very large data structures, meaning this is impractical for all but very small population sizes. So the paper also derives a simple formula for an almost-optimal policy, which can be applied for any population size, and is independent of the values of β. The third paper [8] extends the Markovian SIR-with-demography infection model to allow β to be time dependent, as the transmission rate may vary with the time of year. It also extends the work to the Markovian SIRS model. It presents an algorithm for calculating the probability of epidemic fade-out for these models, and considers parameters appropriate to influenza-like and measles-like infections. It concludes that the local maximum in the probability of epidemic fade-out is at a value of R0 somewhat greater than 2, when β is time-dependent.