ABSTRACT
The goal of this chapter is to use matrices to explore the behavior of systems as they change, or transition, throughout time. Perron is also credited with a slightly different theorem that relies on a matrix being primitive rather than irreducible. There are a few ways that the people can initially start to analyze the long-term behavior of the states given a transition matrix. Markov chains are extremely helpful when the people wish to determine a sequence of events based on probabilities of observed behaviors. In both the likelihood and the decoding problems, the model was assumed and fixed. In 2019, the world broke out into an international pandemic which led many to start to think more closely about the mathematics behind the spread of infectious diseases. Many diseases, like COVID-19, in simple terms would be modeled with SIR models, with humans in three categories, S (Susceptible), I (Infectious), and R (Recovered).
