Stochastic Modeling of a Measles Outbreak in Brazil

ABSTRACT

Development of mathematical models and its numerical implementations are essential tools in epidemiological modeling. Susceptible-Infected-Recovered (SIR) compartmental model, proposed by Kermack and McKendrick in 1927, is a widely used deterministic model which serves as a basis for more involved mathematical models. In this work, we consider two stochastic versions of the SIR model for analysing a measles outbreak in Ilha Grande, Rio de Janeiro, in 1976; Continuous Time Markov Chain and Stochastic Differential Equations. The SIR Continuous Time Markov Chain model is used to extract specific information from the measles outbreak. The outbreak probability, final size distribution and expected duration of the epidemic were computed, obtaining results in excellent agreement with the reported epidemic values. Numerical simulations are performed in Python.

Keywords:
stochastic epidemiological models; SIR model; measles outbreak