  Gaussian process (GP) based statistical surrogates are popular, inexpensive
substitutes for emulating the outputs of expensive computer models that
simulate real-world phenomena or complex systems. Here, we discuss the
evolution of dynamic GP model - a computationally efficient statistical
surrogate for a computer simulator with time series outputs. The main idea is
to use a convolution of standard GP models, where the weights are guided by a
singular value decomposition (SVD) of the response matrix over the time
component. The dynamic GP model also adopts a localized modeling approach for
building a statistical model for large datasets.
  In this chapter, we use several popular test function based computer
simulators to illustrate the evolution of dynamic GP models. We also use this
model for predicting the coverage of Malaria vaccine worldwide. Malaria is
still affecting more than eighty countries concentrated in the tropical belt.
In 2019 alone, it was the cause of more than 435,000 deaths worldwide. The
malice is easy to cure if diagnosed in time, but the common symptoms make it
difficult. We focus on a recently discovered reliable vaccine called Mos-Quirix
(RTS,S) which is currently going under human trials. With the help of publicly
available data on dosages, efficacy, disease incidence and communicability of
other vaccines obtained from the World Health Organisation, we predict vaccine
coverage for 78 Malaria-prone countries.
