Analyzing measles spread through a Markovian SEIR model.

Area of Science:

• Epidemiology
• Mathematical Biology
• Stochastic Processes

Background:

• Measles transmission dynamics are complex and require robust modeling approaches.
• Deterministic models often overlook stochastic elements crucial for understanding disease persistence.
• The concept of stationary distribution in epidemiological models signifies ongoing disease spread without intervention.

Purpose of the Study:

• To analyze the long-term behavior of measles transmission using a stochastic SEIR model.
• To incorporate stochastic dynamics by computing the stationary distribution of the Markovian SEIR model.
• To provide a probabilistic understanding of measles spread for assessing control measures.

Main Methods:

• Utilized the Susceptible-Exposed-Infectious-Recovered (SEIR) model, treating it as a Markov chain.
• Employed the state reduction method to simplify computational complexity.
• Developed a Mathematica-based algorithm for efficient determination of steady-state probabilities.

Main Results:

• Computed the stationary distribution to understand the long-term measles transmission dynamics.
• Demonstrated the utility of a Markovian SEIR model in capturing stochastic elements of disease spread.
• Provided probabilistic insights into disease persistence under various scenarios.

Conclusions:

• The Markovian SEIR model offers a valuable probabilistic framework for understanding measles transmission.
• Stationary distribution analysis reveals insights into disease persistence, guiding the need for interventions.
• Findings support the assessment of vaccination strategies and long-term measles control measures.