Measles

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How International Travel and Vaccine Resistance have led to a resurgence of Measles in the U.S.

By Lauren Gardner
US Measles Risk Dashboard

This resurgence of measles cases is due to two main risk factors. The first, as previously noted by Olive et. al. and reiterated by Hotez, is a fall in vaccination rates fueled by anti-vaccination movements in both the U.S. and Europe. In the U.S. in particular there has been an upsurge of non-medical exemptions (NMEs) in the 18 states which allow it. Compounding the decrease in vaccination rates is the increase in international travel into these localities (where measles is supposed to have been eliminated through vaccination) from regions where measles remains endemic, and outbreaks are ongoing. The fact that measles is a highly contagious virus capable of airborne spread further increases the seriousness of this threat.

Olive et al. previously presented a “heat map” of measles risk based on NMEs for vaccination in U.S. counties. In collaboration with Sahotra Sarkar at UT Austin and others (Aleksa Zlojutro at UNSW Sydney and Kamran Khan at University of Toronto), we further investigated how this “heat map” of measles risk in the US might shift geographically when county level NME rates (that reveal pockets of low vaccination) were compounded with incoming international air travel volume weighted by the size of measles outbreaks abroad.

To do so, we performed an analysis that compounds four factors: 1) international air travel volume arriving from measles affected countries into each U.S. county, 2) county NME rates, 3) county population, and 4) the size (incidence rate) of the measles outbreak at travel origin country.  The analysis was conducted for each year between 2011 and 2019. The detailed methods and results of the analysis are soon to be published in Lancet Infectious Diseases. An interactive map illustrating the results of our analysis and corresponding data is available here. Additionally, the figures below illustrate the U.S. measles risk for 2019 computed by the model, and the corresponding global level measles outbreak data from WHO. (NOTE: the 2019 analysis uses WHO reported cases from each country up to April 19.)

Results from the 2019 analysis reveal the U.S. counties at highest risk of a measles outbreak at present, and are spatially consistent with the U.S. measles cases reported to date (April 19): either the counties we identify or those immediately adjacent to them are the ones that have reported measles cases.

Critically, the results correctly predict the areas in Washington, Oregon, and New York that have seen major measles outbreaks. The risk analysis also reveals U.S. localities that have not experienced a measles outbreak in 2019 but are at risk of imported measles cases resulting in a local outbreak because they lie adjacent to a county that has and/or is served by a major international airport. These include Travis (TX), Maricopa (AZ), Clayton (GA), Honolulu County (HI), Wayne (MI), Salt Lake (UT), Hennepin (MN), Suffolk (MA), Loudon (VA), San Diego (CA) and multiple counties in Florida. Additional surveillance should also target Cook (IL) and Los Angeles (CA), which have seen only one case so far, but due to the presence of major international airports, they may serve as the fulcrum of continuous importation of measles into the United States.

Lastly, this analysis also reveals the set of countries that contribute most to measles risk across the U.S. in 2019. The top countries ordered by risk posed are: Ukraine, Mexico, Cuba, Israel, Japan, Thailand and Philippines. Therefore, we recommend that surveillance should also be directed towards those U.S. counties with the high incoming passenger volume from these countries, which should themselves be targeted for vaccination efforts. Prof. Sarkar suggests additional actions for prevention in his blog.

For further information please see our publication in Lancet Infectious Diseases (Published Online May 9, 2019).

Figure 1: Top 25 U.S. Counties Predicted to be at Highest Risk for Measles in 2019.

This results in this figure correspond to our publication in Lancet Infectious Diseases (Published Online May 9, 2019).  Risk is measured by the expected relative size of a measles outbreak in a county.

Figure 2: Annual Measles Cases by Country as reported by WHO
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Assume that a decision-maker’s uncertain behavior is observed. We develop a an inverse optimization framework to impute an objective function that is robust against misspecifications of the behavior. In our model, instead of considering multiple data points, we consider an uncertainty set that encapsulates all possible realizations of the input data. We adopt this idea from robust optimization, which has been widely used for solving optimization problems with uncertain parameters. By bringing robust and inverse optimization together, we propose a robust inverse linear optimization model for uncertain input observations. We aim to find a cost vector for the underlying forward problem such that the associated error is minimized for the worst-case realization of the uncertainty in the observed solutions. That is, such a cost vector is robust in the sense that it protects against the worst misspecification of a decision-maker’s behavior. 

As an example, we consider a diet recommendation problem. Suppose we want to learn the diet patterns and preferences of a specific person and make personalized recommendations in the future. The person’s choice, even if restricted by nutritional and budgetary constraints, may be inconsistent and vary over time. Assuming the person’s behavior can be represented by an uncertainty set, it is important to find a cost vector that renders the worst-case behavior within the uncertainty set as close to optimal as possible. Note that the cost vector can have a general meaning and may be interpreted differently depending on the application (e.g., monetary cost, utility function, or preferences). Under such a cost vector, any non-worst-case diet will thus have a smaller deviation from optimality.  

We introduce a new approach that combines inverse optimization with conventional data analytics to recover the utility function of a human operator. In this approach, a set of final decisions of the operator is observed. For instance, the final treatment plans that a clinician chose for a patient or the dietary choices that a patient made to control their disease while also considering her own personal preferences. Based on these observations, we develop a new framework that uses inverse optimization to infer how the operator prioritized different trade-offs to arrive at her decision. 

We develop a new inverse optimization framework to infer the constraint parameters of a linear (forward) optimization based on multiple observations of the system. The goal is to find a feasible region for the forward problem such that all given observations become feasible and the preferred observations become optimal. We explore the theoretical properties of the model and develop computationally efficient equivalent models. We consider an array of functions to capture various desirable properties of the inferred feasible region. We apply our method to radiation therapy treatment planning—a complex optimization problem in itself—to understand the clinical guidelines that in practice are used by oncologists. These guidelines (constraints) will standardize the practice, increase planning efficiency and automation, and make high-quality personalized treatment plans for cancer patients possible.

Inverse optimization is an area of study where the purpose is to infer the unknown parameters of an optimization problem when a set of observations is available on the previous decisions made in the settings of the problem. We develop a framework to effectively and efficiently infer the cost vector of a linear optimization problem based on multiple observations on the decisions made previously. 

We then test our models in the setting of a diet problem on a data-set obtained from NHANES; The data-set is accessible via the link bellow:

https://github.com/CSSEHealthcare/Dietary-Behavior-Dataset