Bayesian approach to infer changes in disease transmission

Compartmental models are popular in epidemic modeling because they help to understand and predict the spread of infectious diseases. Existing compartmental models for modeling epidemics such as COVID-19 include SIR, SEIR, and numerous variations of each of these. However, few of these models incorporate mobility data to determine changes in disease transmission rates. In this dissertation, I will build a statistical model to infer whether there is a change in the transmission rate of a compartmental model, given that there is a change in human mobility. I propose a model which allows different transmission rates for different time periods so that a model comparison approach can be used to test if a change-point in disease transmission should be present in the model. In order to achieve that, parameter estimation using partial epidemic data is done using a Bayesian approach. In particular, a Bayesian state-space model is specified and inference is made through a particle filter and the Metropolis Hastings method. Model comparison for testing the change is done using the deviance information criterion (DIC). Replicability of the algorithm is assessed using a simulation study where I calculated the average bias and average mean squared error for the parameter estimation. I also performed a simulation study to assess the DIC approach. The simulation study revealed that the algorithm was able to accurately estimate the parameters. Further, whenever there is a large enough change in the transmission rate from one period to the next, then the DIC would select the model that incorporated a change-point in the disease transmission.