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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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

A set of female individuals with the above criteria were considered. Further demographic and diet considerations (in order to select similar patients) led to selecting 11 different individuals’ one day of intake as the initial dataset for the model. In another setting, we only considered people that have consumed a reasonable amount of sodium and water. We consider these two nutrients as the main constraints in the DASH diet. 



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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. 

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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.  

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To design a high-quality treatment, we select the beams sizes, positions, and shapes using optimization models and approximation algorithms. The optimization models are designed to deliver an appropriate amount of dose to the tumor volume while simultaneously avoiding sensitive healthy tissues. In this project, we work on finding the best beam positions for the radiation focal points for Gamma Knife® Perfexion™, using quadratic programming and algorithms such as grassfire and sphere-packing.

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This work was performed with the MIT/MGH Collaboration.

In many healthcare services, care is provided continuously, however, the care providers, e.g., doctors and nurses, work in shifts that are discrete. Hence, hand-offs between care providers is inevitable. Hand-offs are generally thought to effect patient care, although it is often hard to quantify the effects due to reverse causal effects between patients’ duration of stay and the number of hand-off events. We use a natural randomized control experiment, induced by physicians’ schedules, in teaching general medicine teams. We employ statistical tools to show that between the two randomly assigned groups of patients, a subset who experiences hand-off experience a different length of stay compared to the other group.

This work was performed with the MIT/MGH Collaboration.

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We developed a real-time scheduling framework to address the problem, specifically for infusion clinics. The algorithm assumes no knowledge of future appointments and does not change past appointments. Operational constraints are taken into account, and the algorithm can offer multiple choices to patients.

We generalize this framework to a new scheduling model and analyze its performance through competitive ratio. The resource utilization of the real-time algorithm is compared with an optimal algorithm, which knows the entire future. It can be proved that the competitive ratio of the scheduling algorithm is between 3/2 and 5/3 of an optimal algorithm.

This work was performed with the MIT/MGH Collaboration.

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