My main research area, from the mathematical viewpoint, is the modeling and application of optimization and control tools for problems in the management of renewable natural resources, from both theoretical and applied approaches. The areas on which I have developed my research include (but are not limited to):
Bioremediation of water resources and bioprocesses
Control of deterministic and stochastic population dynamics
Epidemiological models for prison populations
Numerical simulation methods for control problems
Stochastic optimal control of time continuous Itô diffusions
My areas of interest are those on which engineering, mathematics, and computer sciences can contribute to the management and decision making, improving processes. I am interested in:
Data visualization and mathematical simulation.
Machine learning methods (shallow and deep methods).
Methods of signal processing, time series, and statistical analysis.
I have extensively used these techniques in several projects that involve healthcare management during the last years:
Project: "Estimation of I.C.U. bed demand for severe acute respiratory infections" (Hosp. Luis Calvo Mackenna)
We use signal processing tools and statistical methods to predict the demand of hospitalizations (occupation of I.C.U. beds) due to severe acute respiratory infections, and develop a system of early alerts, based on emergency service’s current and historical data.
Project: "Technological solutions, based on advanced mathematical tools and machine learning, to increase efficiency in hospital management" (FONDEF IDeA, Hosp. Luis Calvo Mackenna, CRS. Cordillera Oriente, Hosp. Regional de Talca).
We identify the reasons and main features that influence the not attendance of a patient to a medical appointment. We train machine learning models, using historical appointment and personal data, to predict the attendance status of a specific patient to a specific appointment, in order for the hospital scheduling staff to take action on those with high risk of missing the appointment (telephonic reminder, etc.). We develop a web platform on which the hospital staff can process the daily data of patients, to get the alerts on the patients that are likely to no show to the appointment.
Project: "Operating room management in Hospital Luis Calvo Mackenna" (Hosp. Luis Calvo Mackenna).
We aim to optimize the patient’s allocation to operating room, reducing the length (number of patients) and the mean and median waiting time of the surgical waiting list. We develop a two-stage procedure, based on MILP approaches, that assigns medical specialties to hourly blocks (under an offered and demanded time balance), and then assigns patients to the blocks. We develop a web platform on which the nurse that creates the weekly operating schedule can introduce the waiting list, to obtain the optimized weekly schedule.