  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 a disease transmission model. We implement a method
which 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 use a Bayesian framework to fit this hidden SIRS model,
implementing particle Markov chain Monte Carlo methods to sample from the
posterior distribution of the environmental and transmission parameters given
the observed data. We test this method using both simulation and data from
Mathbaria, Bangladesh. Parameter estimates are used 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.
