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The objective of this thesis is to study the e ect of under-reporting in epidemics. In particular, there are two broad questions we investigate: In the situation of under-reporting in epidemics, what would happen if the data were treated as if no under-reporting were occurring? Such assumption leads to an under-estimation of the contact rate, implying an under-estimation of the reproduction number. By allowing for the fact that under-reporting is occurring, how and how well can we estimate the reporting rate and other parameters of the model? We explore the above questions by considering the stochastic Markovian SIR epidemic in which various reporting processes are incorporated. We consider cases of constant reporting probability and move on to more realistic assumptions such as the reporting probability depending on time, the number of reported cases and the dependence on the source of infection for each infected individual. We develop various methodologies, based on temporal data, to account for underreporting in the Bayesian framework using MCMC to sample from the posterior distributions of the model parameters. An introduction to the spatial aspect is also considered with the SIR model with reporting process on Z. |
