Applying particle filtering in both aggregated and age-structured population compartmental models of pre-vaccination measles
Authors: Li Xiaoyan , Doroshenko Alexander , Osgood Nathaniel D. 
Published: June 2018

Measles is a highly transmissible disease and is one of the leading causes of death among young children under 5 globally. While the use of ongoing surveillance data and – recently – dynamic models offer insight on measles dynamics, both suffer notable shortcomings when applied to measles outbreak prediction. In this paper, we apply the Sequential Monte Carlo approach of particle filtering, incorporating reported measles incidence for Saskatchewan during the pre-vaccination era, using an adaptation of a previously contributed measles compartmental model. To secure further insight, we also perform particle filtering on an age structured adaptation of the model in which the population is divided into two interacting age groups – children and adults. The results indicate that, when used with a suitable dynamic model, particle filtering can offer high predictive capacity for measles dynamics and outbreak occurrence in a low vaccination context. We have investigated five particle filtering models in this project. Based on the most competitive model as evaluated by predictive accuracy, we have performed prediction and outbreak classification analysis. The prediction results demonstrated that this model could predict the measles transmission patterns and classify whether there will be an outbreak or not in the next month (Area under the ROC Curve of 0.89). We conclude that anticipating the outbreak dynamics of measles in low vaccination regions by applying particle filtering with simple measles transmission models, and incorporating time series of reported case counts, is a valuable technique to assist public health authorities in estimating risk and magnitude of measles outbreaks. Such approach offer particularly strong value proposition for other pathogens with little-known dynamics, critical latent drivers, and in the context of the growing number of high-velocity electronic data sources. Strong additional benefits are also likely to be realized from extending the application of this technique to highly vaccinated populations.

Author summary

Measles is a highly infectious disease and is one of the leading causes of death among young children globally. In 2016, close to 90,000 people died from measles. Measles can cause outbreaks particularly in people who did not receive protective vaccine. Understanding how measles outbreaks unfold can help public health agencies to design intervention strategies to prevent and control this potentially deadly infection. Although traditional methods – including the use of ongoing monitoring of infectious diseases trends by public health agencies and simulation of such trends using scientific technique of mathematical modeling – offer insight on measles dynamics, both have shortcomings when applied to our ability to predict measles outbreaks. We seek to enhance the accuracy with which we can understand the current measles disease burden as well as number of individuals who may develop measles because of lack of protection and predict future measles trends. We do this by applying a machine learning technique that combines the best features of insights from ongoing observations and mathematical models while minimizing important weaknesses of each. Our results indicate that, coupled with a suitable mathematical model, this technique can predict future measles trends and measles outbreaks in areas with low vaccination coverage.