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Sensitivity analysis in a dengue epidemiological model
Rodrigues, Helena Sofia; Monteiro, M. Teresa T.; Torres, Delfim F. M.Epidemiological models may give some basic guidelines for public health practitioners, allowing the analysis of issues that can influence the strategies to prevent and fight a disease. To be used in decision making, however, a mathematical model must be carefully parameterized and validated with epidemiological and entomological data. Here an SIR (S for susceptible, I for infectious, and R for recovered individ...
Bioeconomic perspectives to an optimal control dengue model
Rodrigues, Helena Sofia; Monteiro, M. Teresa T.; Torres, Delfim F. M.A model with six mutually exclusive compartments related to dengue is studied. Three vector control tools are considered: insecticides (larvicide and adulticide) and mechanical control. The basic reproduction number associated to the model is presented. The problem is studied using an optimal control approach. The human data are based on the dengue outbreak that occurred in Cape Verde. Control measures are simu...
Dengue in Cape Verde : vector control and vaccination
Rodrigues, Helena Sofia; Monteiro, M. Teresa T.; Torres, Delfim F. M.In 2009, for the rst time in Cape Verde, an outbreak of dengue was reported and over twenty thousand people were infected. Only a few prophylactic measures were taken. The e ects of vector control on disease spreading, such as insecticide (larvicide and adulticide) and mechanical control, as well as an hypothetical vaccine, are estimated through simulations with the Cape Verde data.
Vaccination models and optimal control strategies to dengue
Rodrigues, Helena Sofia; Monteiro, M. Teresa T.; Torres, Delfim F. M."accepted 16-Oct-2013" ; As the development of a dengue vaccine is ongoing, we simulate an hypothetical vaccine as an extra protection to the population. In a rst phase, the vaccination process is studied as a new compartment in the model, and di erent ways of distributing the vaccines investigated: pediatric and random mass vaccines, with distinct levels of e cacy and durability. In a second step, the vaccin...
Higher-order Hahn's quantum variational calculus
Cruz, Artur M. C. Brito da; Martins, Natália; Torres, Delfim F. M.We prove a necessary optimality condition of Euler-Lagrange type for quantum variational problems involving Hahn's derivatives of higher-order. (C) 2011 Elsevier Ltd. All rights reserved.
Discrete Direct Methods in the Fractional Calculus of Variations
Pooseh, Shakoor; Almeida, Ricardo; Torres, Delfim F. M.Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the same idea for fractional variational problems. We consider a minimization problem with a Lagrangian that depends on the left Riemann– Liouville fractional derivative. Using the...
Isoperimetric problems of the calculus of variations with fractional derivatives
Almeida, Ricardo; Ferreira, Rui A. C.; Torres, Delfim F. M.In this article, we study isoperimetric problems of the calculus of variations with left and right Riemann-Liouville fractional derivatives. Both situations when the lower bound of the variational integrals coincide and do not coincide with the lower bound of the fractional derivatives are considered.
Dengue disease, basic reproduction number and control
Monteiro, M. Teresa T.; Torres, Delfim F. M.; Zinober, Alan; Rodrigues, Helena SofiaDengue is one of the major international public health concerns.Although progress is underway, developing a vaccine against the disease is challenging. Thus, the main approach to fight the disease is vector control. 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 ...
Modeling and Optimal Control applied to a vector borne disease
Rodrigues, Helena Sofia; Monteiro, M. Teresa T.; Torres, Delfim F. M.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.
Discrete and continuous dynamical systems: preface
Pinho, Maria do Rosário; Ferreira, M. Margarida Amorim Ferreira; Fontes, Fernando A. C. C.; Pereira, Fernando L.; Smirnov, G.; Torres, Delfim F. M.These preface words, quoted in Francis Clarke's 1983 book, stroke a sensitive chord and set the tone for a vision fueling the construction of an extremely rich body of intertwined developments in nonsmooth analysis, optimization and control by a carefully networked community. This special issue comprises post-conference articles from a selection of works presented at the Workshop on Control, Nonsmooth Analys...
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