P. K. Sinha, S. Mukhopadhyay
Conventional mathematical models of infectious diseases often overlook the spatial spread of the disease, focusing only on local transmission. However, spatial propagation of various diseases has been observed mainly due to the movement of infectious individuals from one geographical region to another. In this work, we propose a multiregion discrete-time chain binomial framework to model the dependencies between the multiple infection time series from neighboring regions. The proposed model is based on the epidemiological principle that new infections arise from interactions between susceptible individuals and previously infected cases. To strengthen the statistical formulation, the probability of new infections within each spatial unit is modeled through an appropriate link function, by allowing it to depend on lagged local incidence, inter-regional transmission effects, and region-specific time-varying covariates. The framework also allows for higher-order temporal dependence through an AR(p) specification. To reduce the complexity of the model as the number of spatial units increases, sparsity is imposed by using spatial contiguity matrices and k-nearest-neighbor structures. For estimating these multiregion chain-binomial models, an appropriate likelihood function maximization approach is proposed. A predictive likelihood based method is used to generate short- and long term forecasts of disease counts in connected spatial units. In-depth analyses of two real world datasets and simulation studies incorporating seasonal patterns, different weight matrices across connected regions, and varying intervention strategies are used to motivate the proposed modeling framework and demonstrate its ability to reproduce realistic outbreak dynamics.