Advisors: Vladimir Minin and Ira Longini
Despite seasonal cholera outbreaks in Bangladesh, little is known about the relationship between environmental conditions and cholera cases. We seek to develop a predictive model for cholera outbreaks in Bangladesh based on environmental predictors. To do this, we estimate the contribution of environmental variables, such as water depth and water temperature, to cholera outbreaks in the context of two different disease transmission models. First, we develop a Bayesian estimation procedure that simultaneously accounts for disease dynamics and environmental variables in a Susceptible-Infected-Recovered-Susceptible (SIRS) model. The entire system is treated as a continuous-time hidden Markov model, where the hidden Markov states are the numbers of people who are susceptible, infected, or recovered at each time point, and the observed states are the numbers of cholera cases reported. We implement a particle Markov chain Monte Carlo algorithm to approximate the posterior distribution of the the hidden SIRS model parameters. We test this method using both simulated data and data from Mathbaria, Bangladesh. We use the posterior distribution of the hidden SIRS model parameters to make short-term predictions that capture the formation and decline of epidemic peaks. We demonstrate that our model can successfully predict an increase in the number of infected individuals in the population weeks before the observed number of cholera cases increases, which could allow for early notification of an epidemic and timely allocation of resources. We apply this Bayesian analysis to data from multiple geographical areas in Bangladesh to test the generalizability of our methods and results. We then expand our analysis of the Mathbaria data to include multiple environmental covariates shifted in time by multiple lags, testing estimation and prediction in the presence of multiple highly correlated predictors. Finally, we add an additional latent water compartment to the hidden SIRS model and explore the difficulties of parameter estimation and cholera outbreak prediction using this complex, but biologically more realistic model for cholera transmission.