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

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

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

Inexact restoration approaches to solve mathematical program with complementarity constraints

Mathematical Program with Complementarity Constraints (MPCC) finds application in many fields. As the complementarity constraints fail the standard Linear Independence Constraint Qualification (LICQ) or the Mangasarian-Fromovitz constraint qualification (MFCQ), at any feasible point, the nonlinear programming theory may not be directly applied to MPCC. However, the MPCC can be reformulated as NLP problem and solved by nonlinear programming techniques. One of them, the Inexact Restoration (IR) approach, performs two independent phases in each iteration - the feasibility and the optimality phases. This work presents two versions of an IR algorithm to solve MPCC. In the feasibility phase two strategies were implemented, depending on the constraints features. One gives more importance to the complementarity constraints, while the other considers the priority of equality and inequality constraints neglecting the complementarity ones. The optimality phase uses the same approach for both algorithm versions. The algorithms were implemented in MATLAB and the test problems are from MACMPEC collection