A novel high-order multivariate Markov model for spatiotemporal analysis with application to COVID-19 outbreak.

We propose a new strategy for analyzing the evolution of random phenomena over time and space simultaneously based on the high-order multivariate Markov chains. We develop a novel Markov model of order $r$ for $m$ chains consisting of $s$ possible states to gather parsimony with realism. It can capture negative and positive associations among the chains with only a reduced number of parameters, $r{m}^2\left(s^2,+,2\right)$, remarkably lower than $m{s}^{rm+1}$ required for the full parameterized model. Our model privileges are enhanced by a Monte Carlo simulation experiment, besides application to analyze the spatial-temporal dynamics for the risk level of a recently global pandemic (COVID-19) outbreak in world health organization (WHO) regions for predicting the risk state of epidemiological prevalence and monitoring infection control.