A Comparison of Measles Vaccination Regimes in a Stochastic, Spatial SIR Model

Abstract

Measles is a disease that continues to affect millions of people; however, it can now be controlled through vaccination. Using a spatial, stochastic, continuous-time SIR model, we investigate four different vaccination regimes in a "country" of 25 cities. The model was constructed using work by Bjørnstad et al. and May and Anderson as a basis for determining the spatial structure of the country and a set of appropriate parameters [May and Anderson, 1984, Bjørnstad et al., 2002]. We examine the behavior of measles under these vaccination regimes over a period of 20 years with the goal of determining an optimal regime that leads to herd immunity. All data was simulated using an Euler approximation of the continuous-time Markov chain. As vaccination rates increase and begin to induce herd immunity, on average, the same proportion of susceptible people are vaccinated across regimes. However, a closer investigation of the qualitative behavior of these regimes reveals distinct differences among them. Briefly, some regimes maintained a much lower proportion of susceptibles in the population, while others allowed the number of susceptible people in the population to fluctuate significantly. A steady, high vaccination rate across the population eliminated cases and led to herd immunity without such fluctuations.