  We address in this paper a new approach for fitting spatiotemporal models
with application in disease mapping using the interaction types 1,2,3, and 4.
When we account for the spatiotemporal interactions in disease-mapping models,
inference becomes more useful in revealing unknown patterns in the data.
However, when the number of locations and/or the number of time points is
large, the inference gets computationally challenging due to the high number of
required constraints necessary for inference, and this holds for various
inference architectures including Markov chain Monte Carlo (MCMC) and
Integrated Nested Laplace Approximations (INLA). We re-formulate INLA approach
based on dense matrices to fit the intrinsic spatiotemporal models with the
four interaction types and account for the sum-to-zero constraints, and discuss
how the new approach can be implemented in a high-performance computing
framework. The computing time using the new approach does not depend on the
number of constraints and can reach a 40-fold faster speed compared to INLA in
realistic scenarios. This approach is verified by a simulation study and a real
data application, and it is implemented in the R package INLAPLUS and the
Python header function: inla1234().
