A hybrid particle filter for simultaneous parameter and state estimation

Disease surveillance plays an important role in public health providing vital information for the detection, monitoring, and control of infectious diseases and other health threats within populations. By systematically collecting, analyzing, and interpreting data on disease occurrence, trends, and patterns, surveillance systems enable public health practitioners to identify outbreaks, track the spread of diseases, and assess the effectiveness of interventions. Timely detection of outbreaks allows for swift implementation of mitigation strategies to prevent further transmission and minimize the impact on community health. Furthermore, statistical models of infectious diseases can provide valuable insights into the distribution of diseases across different demographic groups and geographic regions, facilitating targeted interventions to address health disparities and inequities.

It is important for these models to be accurate and timely, but modeling complex, dynamic systems like disease spread can pose significant computational challenges. In this dissertation, we propose a computationally efficient algorithm that can estimate unobserved phenomena in the population such as the number of simultaneously infected individuals as well as epidemic parameters that control how and where the disease spreads. In addition, we introduce an accompanying open-source software package to facilitate use of this efficient estimation technique by other researchers. Finally, we analyze a cholera outbreak in Haiti using our software package.