Towards Bayesian Estimation of Compartmental Models for COVID-19
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This thesis explores concept of compartmental modelling of infectious disease particularly like COVID-19. The world is still under siege by COVID-19. I have discussed two such fundamental mathematical models SIR and SEIR model that form the basis in epidemiological modelling and how they help predict the dynamics of current pandemic, COVID-19. My research is principally based upon SIR model and ‘rstan’ codes developed by (Grinsztajn, Semenova, Margossian, & Riou, 2020). The main aim of my thesis is to show how MCMC algorithm is used to estimate the model (SIR) parameter and draw much needed inference about the dynamics of such infectious disease. For this purpose, we tried to use real COVID-19 data from various cities within Norway and started off accordingly. However, the model we used i.e. SIR model did not work perfectly with the data as MCMC algorithm could not sample from huge population size (5.3m) and our sample being too small. We had some glitch in our inference table as clearly evidenced by much variation in the value of R̂ implying our Markov chains are not in sync with one another. So, we decided to show the same estimation process with different data. While my focus is on SIR and SEIR model, I have also tried to give the basic concept behind Bayesian thinking and some important MCMC algorithms that are an integral part of such models. I have tried not to digress from COVID-19 to other diseases. The main objective of all the infectious models that statisticians currently use or will use in future is to predict the dynamics of such disease so that public health officials make informed decisions to save as many lives as they can. I am trying to present how such process works. As more complex mathematical models are being developed around the globe, it is still very useful to understand the SIR and SEIR model as most of the newly developed models are derivatives of these models.