I am an applied mathematician and physicist with expertise in mathematical modeling and scientific computing. I specialize in the analysis of big data sets in multiple contexts to understand and predict the behavior of complex systems. I also have expertise in the design and analysis of numerical methods to solve partial differential equations (PDEs) for a diverse array of applications. 

Implementing and validating methodologies to solve challenging problems, in real-life computational applications, has been central to my research, and has exposed me to the use of high–performance computing environments. 

I am interested in designing and implementing novel ways to track epidemics in real-time using data from Google, Twitter, Facebook, UpToDate (digital disease detection). I am conducting research to understand the impact of climate change on disease burden in Africa and Mexico. I have also conducted research in atmospheric pollution transport modeling, climate modeling, modeling of floods due to hurricanes,and population dynamics modeling. The following paragraphs summarize my research contributions.

1. Design and implementation of Digital Disease Detection tools as decision-support tools to help public health officials make timely decisions and prevent epidemic outbreaks.

We are working towards the development of the next generation of digital epidemiolgy tools aimed at monitoring disease outbreaks in real-time. We are constantly developing methodologies that leverage information from multiple data-sources including Google search query patterns, Twitter microblogs, cloud-based electronic health records, weather, and human mobility, to produce real-time and short-term forecast estimates of endemic disease outbreaks of dengue, flu and emerging disease outbreaks such as the COVID-19 Pandemic, the 2014 West African Ebola outbreak, the 2014 Latin American Zika outbreak, and the ongoing 2019-nCoV outbreak originated in Wuhan, China. Our real-time estimates are typically available 1-4 weeks earlier than the official CDC-reported flu activity in the US. The Machine Intelligence Lab at Boston Children's Hospital / Harvard Medical School is our computational laboratory.


Figure. We are constantly striving to improve our real-time disease estimates with the goal of assisting public health officials make informed decisions to mitigate the effects of disease outbreaks. Our platform will soon display disease estimates for Dengue, Flu, and a diverse arrray of emrging outbreaks throughout the world.


2. Understanding the role of environmental factors on the timing of outbreaks of infectious diseases (Dengue, Antibiotic Resistance)

The availability of on-line and real-time sources of big data sets gives us the opportunity to monitor how climate variables (among many other factors) influence the spread of Dengue, Antibiotic Resistance, and other outbreaks around the world


Figure. Antibiotic Resistant outbreaks across pathogens shown on the left panel and Minimum Air Temeprature on the right panel. 
From: MacFadden DR, McGough SF, Fisman D, Santillana M, Brownstein JS. Antibiotic Resistance Increases with Local Temperature Nature Climate Change 8 (2018), pp 510-514. (PDF)


3. Intensive Care Unit Research

My research utilizes mathematical concepts of machine learning to improve patient outcomes and reduce hospital costs in Critical Care Medicine. This includes the development of algorithms aimed at improving (a) compliance in the intensive care unit (ICU), (b) patient outcome, and (c) bedside care. For example, in collaboration with medical doctors from the pediatric ICU, we have developed a math-based patient respiratory index that functions as a good predictor of patient outcome upon extubation/discharge (future need for non-invasive ventilation, future need of re-intubation, no need of respiratory assistance). This index is built using the last 2 - 6 hours of a patient's’ vital signs and respiratory variables recorded by the mechanical ventilator. Future development of patient "stability" indices will enable us to track, in real-time, milestones of patient's path to recovery and/or health deterioration.

Figure: Stronger and more accurate prediction of how long a patient will stay in the Intensive Care Unit are obtained if you combine vital sign information with static clinical information. 

Figure. Real-time monitoring of potassium levels in Cardiac Intensive Care Units. Plot produced by Mathieu Molina


4. Global atmospheric chemistry

Understanding the global-scale dynamics of the chemical composition of our atmosphere is essential for addressing a wide range of environmental issues from air quality to climate change. Understanding this phenomenon enables us to evaluate and devise appropriate environmental policies, such as the Kyoto Protocol on global greenhouse gases emissions. Numerical modeling of global atmospheric chemical dynamics presents an enormous challenge associated with simulating hundreds of chemical species with time scales varying from milliseconds to years. 

In my research, I have worked on the implementation of computationally efficient algorithms for calculating the time evolution of the concentration of chemical species in global 3-D models of atmospheric chemistry. I have also investigated the efficacy of adjoint based inverse modeling techniques for source attribution problems.

Assessing model errors and uncertainties: I am very interested in understanding the large dependence of the results of Global Atmospheric Chemistry Models on spatial resolution, time stepping, and spatial averaging of meteorological fields, and the impact of these on the contaminant plume propagation. 


Figure. Percentage of fast species in the GEOS-Chem chemical mechanism at different altitudes using a threshold of d 1⁄4 102 molecules cm 3 s 1. White boxes in the bottom right panel are in the stratosphere. Results are for July 8, 2004 at 00 GMT. The full GEOS-Chem chemical mechanism includes 111 species to describe tropospheric ozone-NOx-VOC- aerosol chemistry.
From: M. Santillana, P. Le Sager, D. J. Jacob, and M. P. Brenner. An adaptive reduction algorithm for efficient chemical calculations in global atmospheric chemistry models. Atmospheric Environment. Volume 44, Issue 35, pp 4426-4431, Nov 2010. (PDF))


5. Shallow water modeling

As a consequence of our changing climate, large efforts have been made to understand the social risks of storm surges (hypothesized to increase in frequency in warmer climate scenarios) and sea level rise in coastal areas. Of particular interest is the role that wetlands and coastal marshes play in storm surges and flooding events. 

For example, coastal marshes and swamps act as a buffer zone between the Gulf of Mexico and inhabited inland areas in Louisiana, where an estimated 60-75 % of residents live within 50 miles of the coast (1993) and where, between 1899 and 1995, over a dozen major hurricanes (class 3-5) have hit (with the two most recent hits being the category 5 hurricanes Katrina and Rita in 2005). Understanding the role of these rich biological ecosystems in our changing climate requires the development of appropriate mathematical models. 

 In my research,  I have studied analytically and numerically an effective equation often referred to in the literature as the diffusive wave approximation of the shallow water system of equations (DSW), used to simulate overland flow in wetlands and open channels. This equation is obtained by approximating the depth averaged continuity equations by empirical laws such as Manning’s or Chezy’s formulas and then combining the resulting expression with the free surface boundary condition. 

 I have studied the properties of approximate (weak) solutions to the DSW using the continuous and discontinuous (LDG) Galerkin method, developing error estimates and implementing a 2-D code aimed at simulating water flow on experimental settings as well as real environments. I have also investigated inverse modeling approaches to estimate friction coefficients using the DSW as a physical model.

Dam break numerical simulation
Dam break numerical simulation