Advancements in Bayesian Disease Mapping and Infectious Disease Modeling

In many epidemic systems, the disease can be prone to spread in some directions more than others. This can be due to migration and behavior patterns or due to prevailing wind patterns. Individual-level models (ILMs) are commonly used for modelling spatial risk in infectious disease transmission but have not traditionally considered these directional tendencies. A class of ILMs that allow for the directional dynamics of disease transmission is introduced. In these directionally dependent ILMs, the probability of an individual being infected depends on both the direction and distance between susceptible and infectious individuals. The characteristics of these directionally dependent ILMs are discussed, and how they can be fitted in a Bayesian Markov chain Monte Carlo (MCMC) framework are shown. Results will be illustrated with both simulated data and real data from outbreaks of seasonal influenza and foot-and-mouth disease in livestock. 

Epidemic models are invaluable tools to understand and implement strategies to control the spread of infectious diseases, as well as to inform public health policies and resource allocation. However, current modeling approaches have limitations that reduce their practical utility, such as the exclusion of human behavioral change in response to the epidemic or oversimplifying the disease transmission process. These limitations became particularly evident during the COVID-19 pandemic, underscoring the need for more accurate and informative models. Motivated by these challenges, we develop a novel Bayesian epidemic modeling framework to better capture the complexities of disease spread by incorporating behavioral responses. In particular, our framework makes two contributions: 1) leveraging additional data on hospitalizations and deaths in modeling the disease dynamics and 2) allowing the population behavioral change to be dynamically influenced by multiple data sources (cases and deaths). Given the large presence of asymptomatic infections and lack of testing during the COVID-19 pandemic, we also evaluate incorporating data uncertainty from undetected infections. We thoroughly investigate the properties of the proposed model via simulation and illustrate its utility on COVID-19 data from Montréal and Miami. 

During the Covid-19 pandemic many attempts were made to model state or national level time series of case counts or mortality. To a much lesser extent, some effort was focused on spatial aspects of the pandemic and there are a few examples of spatio-temporal modeling at finer spatial scales. It is clear that spatial aspects are important in pandemic spread at a variety of scales (both spatial and temporal). Usually, the different scales are modelled separately. However there could easily be shared impact of linkages between levels. In this talk we outline the basic linkage models which can be set up across spatial scales and their potential linkages (mainly ) via random effects.
We give an example of modeling Covid19 mortality where weekly data is available now for 173 week periods at county level and state level in the US. A simple example of one state with associated counties is given. At the state level we have time series models and at the county level spatio-temporal modeling. Linkage is by shared effects. In principal, spatio-temporal models at state level can also be used. Comparison of models with and without linkage is made.
The approach can be extended to multivariate multiscale modeling for Covid19 data whereby case incidence, mortality and hopitalizations could be examined, or indeed the distribution of related infectious disease synchronous with Covid-19 such as RSV and influenza.
 

Despite multivariate spatio-temporal counts often containing many zeroes, zero-inflated multinomial models for space-time data have not been considered. We are interested in comparing the transmission dynamics of several co-circulating infectious diseases across space and time where some can be absent for long periods. We first
assume there is a baseline disease that is well-established and always present in the region. The other diseases
switch between periods of presence and absence in each area through a series of coupled Markov chains, which
account for long periods of disease absence, disease interactions and disease spread from neighboring areas.
Since we are mainly interested in comparing the diseases, we assume the cases of the present diseases in an area
jointly follow an autoregressive multinomial model. We use the multinomial model to investigate whether there
are associations between certain factors, such as temperature, and differences in the transmission intensity
of the diseases. Inference is performed using efficient Bayesian Markov chain Monte Carlo methods based on
jointly sampling all presence indicators. We apply the model to spatio-temporal counts of dengue, Zika and chikungunya cases in Rio de Janeiro, during the first triple epidemic.