Analyzing measles spread through a Markovian SEIR model

In this study, we studied the spread of measles using the SEIR (Susceptible-Exposed-Infectious-Recovered) epidemic model, which we treated as a Markov chain. In epidemiology, a stationary distribution means that the disease will continue spreading until a vaccine is found. Our study presents a Markovian SEIR model to analyze the long-term behavior of measles transmission. Unlike deterministic models, our approach incorporates stochastic dynamics by computing the stationary distribution, offering insights into disease persistence. We employ the state reduction method to simplify complex computations and develop a Mathematica-based algorithm to efficiently determine steady-state probabilities. The findings provide a probabilistic understanding of measles spread, helping to assess vaccination strategies and long-term control measures.