Optimal control of a dengue epidemic model with vaccination

We present a SIR+ASI epidemic model to describe the interaction between human and dengue fever mosquito populations. A control strategy in the form of vaccination, to decrease the number of infected individuals, is used. An optimal control approach is applied in order to find the best way to fight the disease.Comment: This is a preprint of a paper accepted for presentation at ICNAAM 2011, Halkidiki, Greece, 19-25 September 2011, and to appear in AIP Conference Proceedings, volume 138

Modeling and Optimal Control Applied to a Vector Borne Disease

A model with six mutually-exclusive compartments related to Dengue disease is presented. In this model there are three vector control tools: insecticides (larvicide and adulticide) and mechanical control. The problem is studied using an Optimal Control (OC) approach. The human data for the model is based on the Cape Verde Dengue outbreak. Some control measures are simulated and their consequences analyzed

Insecticide control in a Dengue epidemics model

A model for the transmission of dengue disease is presented. It consists of eight mutually-exclusive compartments representing the human and vector dynamics. It also includes a control parameter (insecticide) in order to fight the mosquitoes. The main goal of this work is to investigate the best way to apply the control in order to effectively reduce the number of infected humans and mosquitoes. A case study, using data of the outbreak that occurred in 2009 in Cape Verde, is presented.Comment: Accepted 28/07/2010 in the special session "Numerical Optimization" of the 8th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2010), Rhodes, Greece, 19-25 September 201

Geodesic regression on spheres : a numerical optimization approach

In this paper we address the problem of finding a geodesic curve that best fits a given set of time-labeled points on a sphere. Since the corresponding normal equations are highly non-linear, we formulate the problem as a constrained nonlinear optimization problem and solve it using the routine fmincon from MATLAB with the SQP (Sequential Quadratic Programming) algorithm.Foundation for Science and Technology in Projects scope: FCOMP-01-0124-FEDER-022674 and PTDC/EEACRO/ 122812/201

Solving mathematical programs with complementarity constraints with nonlinear solvers

MPCC can be solved with specific MPCC codes or in its nonlinear equivalent formulation (NLP) using NLP solvers. Two NLP solvers - NPSOL and the line search filter SQP - are used to solve a collection of test problems in AMPL. Both are based on SQP (Sequential Quadratic Programming) philosophy but the second one uses a line search filter scheme.(undefined

Mathematical program with complementarity constraints as nonlinear program

XXVIII Congreso Nacional de Estadística e Investigación OperativaLos problemas de optimización con restricciones de complementariedad, MPCC, se pueden resolver en su formulación no lineal equivalente (NLP) por solvers NLP (MATLAB, NPSOL e LOQO). En este trabajo se ha seleccionado un conjunto de problemas en AMPL y se hace un análisis del comportamiento de los varios solvers.Fundação para a Ciência e a Tecnologia (FCT

A fractional Malthusian growth model with variable order using an optimization approach

The goal of this work is to show, based on concrete data, that fractional differential equations with variable fractional order are more efficient to model the world population growth than the classical differential equation, or even a fractional differential equation with constant order. With these new models, we can predict more efficiently the population growth based on the present data.The first and second authors were supported by Portuguese funds through the CIDMA Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (FCT-Fundação para a Ciência e a Tecnologia), within project UID/MAT/04106/2013; third author by the ALGORITMI R&D Center and project COMPETE: POCI-01-0145-FEDER-007043 and FCT Fundação para a Ciência e a Tecnologia within the Project Scope: UID/CEC/00319/2013

Solving a signalized traffic intersection problem with NLP solvers

Mathematical Programs with Complementarity Constraints (MPCC) finds many applications in areas such engineering design, economic equilibrium and mathematical theory itself. In this work we consider a queuing system model resulting from a single signalized traffic intersection regulated by pre-timed control in an urban traffic network. The model is formulated as an MPCC problem and may be used to ascertain the optimal cycle and the green split allocation. This MPCC problem is also formulated as its NLP equivalent reformulation. The goal of this work is to solve the problem, using both MPCC and NLP formulations, minimizing two objective functions: the average queue length over all queues and the average waiting time over the worst queue. The problem was codified in AMPL and solved using some optimization software packages.Fundação para a Ciência e a Tecnologia (FCT) FCOMP-01-0124-FEDER-022674 (R&D unit Algoritmi)PEst-OE/MAT/UI4080/201

Innovating to improve – An experience in a computer engineering programme

This paper presents a pedagogical experience carried out in a course unit of a master’s programme in Computer Engineering at the University of Minho. The course unit, Numerical Methods and Nonlinear Optimization, is placed in the first semester of the third year and the experience took place with 184 students in the academic year 2020-2021. Until then, it had been taught in a traditional way, with theoretical lectures and practical classes for solving exercises. There were several reasons to innovate, namely the need to move to online teaching due to COVID-19, which was an opportunity to introduce new methodologies and technologies, but also the need to foster students’ engagement and performance. A b-learning approach was implemented through a combination of strategies and resources, aiming to enhance motivation, interaction and participation in learning. Assessment was more diversified and distributed over time to foster ongoing study and progress. It included mini-tests and two MatLab projects carried out in teams with the main challenge of finding a real-world phenomenon for the application of a course concept, which implied connecting conceptual learning with reality and creating bridges with other areas of knowledge. The experience was evaluated on the basis of students’ assessment results and their perceptions collected in a survey. The new approach resulted in high levels of student engagement and satisfaction, promoting cooperation and the personal construction of knowledge, which are essential competences for lifelong learning. Nevertheless, the development of MatLab projects requires further improvements, not only as regards support to students but also the evaluation of their impact on learning.This work has been supported by FCT – Fundação para a Ciência e Tecnologia within the R&D Units Project Scope: UIDB/00319/2020

Engaging with real-world phenomena through Matlab programming projects

This presentation aims to report a pedagogical experience carried out in a course unit of a graduate programme in Computer Engineering at the University of Minho. The course unit, Numerical Methods and NonLinear Optimization (NMNO), integrates the first semester of the third year. The experience took place in 2021-2022 with 146 students, and it was supported by Centre IDEA-UMinho within the project 2Be-Learning. The classes were taught face-to-face (theoretical lectures and lab practice) and several strategies were implemented to support learning: ARS, padlet, videos, storytelling, and projects. Assessment was diversified and distributed over time to foster ongoing study and progress. It included two face-to-face written tests, four online multiple choice mini-tests (one per month, lasting about 10 minutes, based on extensive question banks), and one Matlab project. The focus of the presentation is on the impact of Matlab projects in the learning process. The projects were carried out by teams of 4 students. Each team could choose one of five proposed topics. The main challenge was to search for and select a real-world phenomenon where the chosen topic could be applied and solve a problem that should have an adequate level of complexity. The experience was evaluated on the basis of the quality of projects, students’ grades and their perceptions collected in a survey at the end of the course unit. Results show that students developed their creativity through building bridges with other scientific areas and solving problems in innovative ways. Projects promoted their involvement in learning, autonomy, cooperation and the personal construction of knowledge, which are essential competences for lifelong learning. Overall, it can be considered that engaging with real-world phenomena creates conditions for students to connect course-based learning with authentic situations, analyse and solve problems from a multidisciplinary perspective, mediated by digital technologies, and become pro-active learners.This work has been supported the Centre IDEA-UMinho and by FCT – Fundação para a Ciência e Tecnologia within the R&D Units Project Scope: UIDB/00319/2020. The authors are grateful to the reviewers for their valuable comment