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Universidad EAFIT
Carrera 49 # 7 sur -50 Medellín Antioquia Colombia
Carrera 12 # 96-23, oficina 304 Bogotá Cundinamarca Colombia
(57)(4) 2619500 contacto@eafit.edu.co

Optimization

​Optimization in Epidemiology​

Definition of mathematical models of disease transmission and an estimation of its parameters with biological significance, through mathematical methods of optimization and the use of additional necessary information.

Many of the mathematical models of disease transmission that are available in literature fail to respond to the dynamics of a disease; this issue, in fact, has caused many problems dealing with diseases that circulate the country. Therefore, this subject requires a group of people with a mathematical formulation and the capability to work together in interdisciplinary teams, in order to achieve and implement the respective mathematical ideas. This subject has been part of the research project currently underway, titled “Design and Computational Implementation of a Predictive Mathematical Model of Dengue Occurrences”, which has been funded by Colciencias, Universidad de Antioquia &  Universidad EAFIT, and it includes, as a result, the consolidation of an interdisciplinary working group in the area of mathematical epidemiology. A natural consequence of research projects is that they generate questions that can potentially be thesis topics for undergraduate students. Some of them linked with the area of optimization, are:
Parameter estimation techniques from Interval Valued Optimization theory, implemented in disease transmission models.
Diffusion models of disease by means of networks.
Sensitivity analysis of parameters in disease transmission models within the framework of Interval Valued Optimization.
Parameter identification techniques, with related biological conditions, of disease transmission models.
Given that Interval Valued Optimization is a relatively new area in the world of optimization, since its initiation began with some work done in 1968, it is a topic of work where there’s a lot to do and has shown advantages in the little information that is required for applications. Another part of this topic is the application of the methods in sectors such as Health and Mass Transport. 

It should be noted that the above two topics are part of the consolidation process in the area of Optimization of the Department of Mathematical Sciences of Universidad EAFIT, which aims, among other things, to meet a necessity of the country in terms of training scientific personnel in cross-sectional areas of knowledge, such as optimization. Additionally, the sustainability of it depends largely on the continuity of the research processes and the possibility of increasing its critical mass. 

Optimization

 Models and solution methods in optimal route designs and definition frequencies of integrated multi-modal transportation system in Colombia

This grand topic can be articulated in a "pyramid research" undergraduate thesis, masters and doctoral degrees, considering the following aspects:

 

  • Data mining to analyze passenger demands and travel times of buses.
  • Optimization models for the design of routes, considering various variants of integrated transport systems and passenger assignation models.
  • Optimization models for defining frequencies to a system of designed routes
  • Integrated model of optimization for route designs and definition of frequencies.
  • Multi-objective location models for defining multimodal transfer points in mass transit systems.
  • Heuristic methods in solving models for the design of routes and/or frequencies.

Data of passenger demands and the displacement of buses transiting through multi-use lanes, are uncertain, depending on the time and type of day (business day, Saturday, Sunday). Proposed models are generally multi-objective, with contradictory objectives considering the perspective of the operators and users. Heuristic solving methods should cover the different variants of these types of models. It can be summarized that this issue relates expert method techniques for defining models, using data mining to discover new knowledge in data, mathematical modeling, heuristic and meta-heuristic solution methods, and Fuzzy Optimization.

 

Models and solving methods for problems dealing with programming schedules for real-life cases, emphasizing in the health and education sector.  These programming schedule problems are generally difficult to solve (NP - Hard). There are a variety of them, both dealing strictly with its definition and in areas of application. For example, assigning nurses to shifts in hospitals and class schedule, exam and classroom assignments under a faculty and/or university. Also, programming courses to the students while considering fundamental preferences and restrictions of course credits per semester. Considering the wide range of application of this problem, this issue is currently being addressed in international conferences and journals indexed by the wide variety of models and solving methods for different case studies that are continuously being presented. ​


Última modificación: 07/03/2016 13:18