Carla M. A. Pinto

Polytechnic Institute of Porto | IPP · Department of Mathematics

The Higher Professional Technical Courses (CTeSP) at P.PORTO are organized around four school semesters. These include one semester for vocational work placement in the second year. Having succeeded, the students will be awarded a Senior Technical Officer Certificate, corresponding to a level 5 in the National Qualifications Framework. Then, studen...

The International Conference BBC'22 aims to provide an opportunity for all academic and non-academics to share their personal experiences and projects, presenting their contributions and getting feedback from other attendees. We hope that BBC'22 will offer an open and lean discussion space for all participants, around the main conference theme: ST...

A number of relevant models in Classical Mechanics are formulated by means of the differential equation y′′(t)+Atβy(t)=0. In this paper, we improve the results recently established for a randomized reformulation of this model that includes a generalized derivative. The stochastic analysis permits solving that generalized model by computing reliable...

The community of inquiry (CoI) framework has been developed to achieve optimal design of online learning environments, to reinforce critical thinking, critical inquiry, and discourse among students and teachers [1]. Social, teaching, and cognitive presences are defined as vital pieces to promote successful educational experiences. In the literature...

The mass production paradigm on which much of the industry was based has changed. The market is increasingly demanding, requesting diversity and products that are more and more adapted to personal wishes and requirements. This implies producing a greater diversity of products in smaller quantities. Competitiveness is enormous, which forces most com...

Type 1 diabetes (T1D), previously known as juvenile diabetes or insulin-dependent diabetes, is an autoimmune disease characterized by the insufficient (or lack of) production of insulin by the pancreas. Insulin is crucial to maintain blood sugar at healthy levels. High blood sugar damages the body and causes a variety of symptoms, ranging from seve...

The School of Engineering of the Polytechnic of Porto (ISEP) has embraced the DrIVE-MATH project, since September 2017. Active-learning (AL) techniques were implemented in several Math courses, namely Linear Algebra and Analytic Geometry, Probability and Statistics, Statistical Models, Computational Mathematics, and Differential and Integral Calcul...

In this paper we provide a description of the project DrIVE-MATH, highlighting the main goals, intellectual outputs, outcomes, the involved partners, and activities and reports from the three-years’ project. At the end we discuss the impact of the new proposed Education models at various levels, from students, to HEIs, to stakeholders.

In this paper, we propose a modified Susceptible-Infected-Quarantine-Recovered (mSIQR) model, for the COVID-19 pandemic. We start by proving the well-posedness of the model and then compute its reproduction number and the corresponding sensitivity indices. We discuss the values of these indices for epidemiological relevant parameters, namely, the c...

The Center for Disease Control and Prevention considers AIDS-defining illnesses Kaposi’s sarcoma, non-Hodgkin’s lymphoma and cervical cancer. These cancers have higher incidence in HIV-infected individuals than in the general population. Additionally, cancers’ clinical courses in HIV-positive individuals are increasingly aggressive when compared to...

Este livro foi pensado para proporcionar aos alunos dos cursos de Engenharia uma abordagem simples, organizada e direcionada para os principais temas e conceitos necessários à preparação da disciplina de Probabilidades e Estatística, comum a todos os cursos de Engenharia. Os conceitos teóricos serão apresentados de forma rigorosa mas o mais intuit...

This special issue was conceived to explore the latest advancements in the field of computational techniques for solving forward and inverse problems [...]

The COVID-19 pandemic has shaken the whole Educational framework, at all learning levels. In particular, it disrupted the higher education system. Universities acquiesced in adapting their courses to the fully online regime, and, in a very narrow window of time, teachers and students had to dramatically change the teaching archetype and become onli...

Scope: This special issue addresses a wide range of fractional operators, and their implementations in mathematical modeling of problems arising in engineering, finance and social sciences. In this special issue, we invite and welcome reviews, expository and original research articles dealing with the recent advances on the topics in fractional cal...

Generation Z – iGen, students are the next generation surging to higher education. They are technology natives, used to easy access to social media, exchanging tweets, posts, shares, snaps. This high tech environment is thus powerfully changing their communication habits and education. iGen students are eager to be given opportunities to fully imme...

This study analyses second year Baccalaureate Level Engineering students’ awareness of the development of the skills described in the Criterion 3 – Student Outcomes, of the Criteria for Accrediting Engineering Programs, of the Accreditation Board for Engineering and Technology, Inc. (ABET), for the 2020-2021 Accreditation Cycle [1]. Our main goal w...

solve real problems in engineering practice. Critical thinking is the one of the most important nontechnical skills, essential to solve complex problems emerging in today’s ever-changing world. In Industry 5.0 will be increased collaboration between humans and smart systems taking advantage of the high-speed accuracy of industrial automation and th...

The purpose of this paper is to analyse and to summarize the state-of-the-art of the publications related to active-learning (AL) techniques in the period of 2015-2019. We focus preferentially in the application of these novel and active teaching methodologies in Engineering Education. As coordinators of the Erasmus+ project DrIVE-MATH [1] which is...

We focus on Bachelor Engineering degrees students’ skills while taking actively taught Math courses. The applied active-learning techniques were Jigsaw, eduScrum, Think-Pair-Share, and Challenge-based-learning. Students were asked to fulfil a questionnaire at the end of the semester, to provide their perceptions of the learning environment and of t...

Type 1 diabetes (T1D) is an autoimmune disease characterized by the destruction of β-cells, which are responsible for the production of insulin. T1D develops from an abnormal immune response, where specific clones of cytotoxic T-cells invade the pancreatic islets of Langerhans. Other immune cells, such as macrophages and dendritic cells, are also i...

Advances in computing techniques, data acquisition technology, hardware, and networks have mutually promoted the development of multimedia analysis approaches. Many machine learning, signal/image processing, and data mining algorithms have been successfully developed for multimedia analysis. Within the multimedia domain, medical data analysis has a...

We propose a non-integer order model for the dynamics of the coinfection of HIV and HSV-2. We calculate the reproduction number of the model and study the local stability of the disease-free equilibrium. Simulations of the model for the variation of epidemiologically relevant parameters and the order of the non-integer order derivative, α , reveal...

Viral load values and CD4\(^{+}\)T cells count are markers currently evaluated in the clinical follow-up of HIV/AIDS patients. In this context, it is relevant to develop methods that provide a more complete temporal description of these markers, e.g. in between clinical appointments. To this end, we combine a mathematical model and a Bayesian metho...

The Fourth Industrial Revolution era has arrived, according to the World Economic Forum. Everything is changing (viz., artificial intelligence, automation, intelligent robots, self-driving cars and genetic editing) and exciting opportunities accompanied with major challenges come to the surface. On the other hand, major difficulties may also rise,...

We focus on the importance of pyroptosis and superinfection on the maintenance of the human immunodeficiency virus (HIV) latent reservoir on infected patients. The latent reservoir has been found to be crucial to the persistence of low levels of viral loads found in HIV-infected patients, after many years of successfully suppressive anti-retroviral...

We propose a fractional order model to study the efficacy of the Post-Exposure Prophylaxis (PEP) in human immunodeficiency virus (HIV) within-host dynamics, in the presence of the HIV latent reservoir. Latent reservoirs harbor infected cells that contain a transcriptionally silent but reactivatable provirus. The latter constitutes a major difficult...

This work proposes an estimation method to obtain the optimal parameter estimates of a mathematical model, from a set of CD4+T values collected in a HIV patient. To this end, the following scheme is adopted: the first step consists in selecting an initial estimate for the model’s parameters as that having minimum square error, from a set of uniform...

In this paper, we study the immune response in a fractional order model for HIV dynamics, for distinct disease transmission rates and saturated cytotoxic T-lymphocyte (CTL) response. Our goal is twofold: (i) to analyze the role of the order of the fractional derivative, α , on the efficacy of the immune response, (ii) to examine the immune response...

Patients infected with the human immunodeficiency virus (HIV) are more vulnerable to develop various types of cancer, in particular, Hodgkin's lymphoma, Kaposi's sarcoma and vulvar cancer. Moreover, cancers progression tend to be more aggressive in HIV-positive individuals than in HIV-negative ones. In this work, we develop an impulsive mathematica...

We introduce a fractional-order model for the coinfection of the immunodeficiency virus and tuberculosis, in the presence of drug resistant tuberculosis strains and treatment for both diseases. We compute the reproduction number of the model. Numerical simulations show the different dynamics of the model for variation of relevant parameters. Moreov...

In this paper we study the effect of time-varying drug exposure in the dynamics of a fractional order model for the human immunodeficiency virus infection. We compute the reproduction number of the model and verify the stability of the disease-free equilibrium. The model is simulated for parameters directly modelling the pharmacodynamics of HIV, na...

Diabetes mellitus (DM) affects the epidemiology of tuberculosis (TB), being associated with higher risk of treatment failure and TB incidence. DM increase in low- and middle-income countries can impair TB control worldwide. Thus, understanding the mechanisms behind the coexistence of DM and TB infection is useful to devise better health policies. I...

https://www.mdpi.com/journal/applsci/special_issues/Signals_Care Dear Colleagues, Biomedical signals enjoy a place of privilege in our daily life. Disease risk evaluation and diagnostics are often based in the analysis of biomedical signals. Frequently, these diagnostic tools are non-invasive and simple to perform in hospitals and health centres....

Advances in Difference Equations welcomes submissions to the thematic series titled 'Advances in Differential Equations and Their Real World Applications (Part Two)'. The content of this thematic series will contain the latest and the most significant results in fractional differential equations and their real-world applications. The main aim is to...

Viral load values and CD4+T cells count are markers currently evaluated in the clinical follow-up of HIV/AIDS patients. In this context, it is relevant to develop methods that provide a more complete temporal description of these markers, e.g. in between clinical appointments. To this end, we combine a mathematical model and a Bayesian methodology...

Meaningful learning is proven to occur when it is done in a practical, relevant and participated way. Thus, there is an urgent need to develop innovative pedagogical methods which promote this type of learning process. A growing body of research has been presenting an increased awareness of the critical role of active learning methodologies in fost...

This work introduces an estimation method to obtain the optimal parameter estimates of a mathematical model from a set of CD4+T values from a HIV patient. To this end, the following scheme is adopted: the �rst step consists of selecting the candidate with minimum square error, from a set of randomly generated candidates. In the second step, the sel...

The project e-GYM - Matheletes' Gym consists of a brain-training site, for students attending undergraduate courses on Engineering, where logic & thinking & math meet best learning and teaching practices. Students have the opportunity to learn geometry, algebra, differential and integral calculus, graph theory, amongst others, in an environment whe...

We study the impact of diabetes and multi-drug resistant strains in a non-integer order model for tuberculosis (TB) infection in a community. We compute the reproduction number, R0, of the model and analyse its behaviour numerically for variation of epidemiologically relevant parameters. Namely, the increased susceptibility to TB due to diabetes, t...

We study the burden of the HIV viremia and of treatment efficacy in the severity of the patterns of the HIV/HCV coinfection. For this, we derive a simple non-integer-order (fractional-order) model for the coinfection dynamics. Fractional-order models have been proved in the literature to provide good fits to real data from patients suffering from s...

We study the burden of the HIV viral load and of the cell-to-cell transmission on the dynamics of a fractional model for HIV/HCV coinfection. The model includes treatment for HCV. We calculate the reproduction number of the model and the local stability of the disease-free equilibrium. Simulations of the model reveal the effect of the HIV viral loa...

We introduce a fractional order model for the human immunodeficiency virus (HIV) dynamics, where time-varying drug exposure and drug resistance are assumed. We derive conditions for the local and global asymptotic stability of the disease-free equilibrium. We find periodic stable endemic states for certain parameter values, for sinusoidal drug effi...

We introduce a novel fractional-order model for the coinfection of HIV and tuberculosis (TB), in the presence of multi-drug resistant TB strains (MDR-TB) and treatment for both diseases. We compute the reproduction number of the HIV and TB submodels and of the full model and the local and global stabilities of the disease-free equilibria. Numerical...

We propose a simple delay mathematical model for the dynamics of AIDS-related cancers with treatment of HIV and chemotherapy. The main goals are to study the effects of the delay and of treatment (HAART and chemotherapy) in cancer cells growth. The model was simulated for several biologically reasonable values of the delay, of HAART efficacies and...

We analyse the impact of pre-exposure prophylaxis (PrEP) and screening effects on HIV dynamics in infected patients. Our model incorporates condom use, the number of sexual partners, and treatment for HIV. Numerical simulations are performed and the model is fitted to data on the cumulative HIV and AIDS cases in Portugal. Moreover, critical epidemi...

Introduction: The laboratory diagnosis of chronic kidney disease (CKD) is a simple and cost-effective procedure that allows the detection of early stages of the disease, which is essential to avoid kidney damage and a life threateaning event. It consists of measuring serum creatinine concentration, urinary albumin concentration and calculating the...

We consider a fractional-order model of two asymmetrically coupled spiking neurons. The dynamical behavior of the two neurons is modeled by the fractional-order Hodgkin-Huxley equations. Simulations of the model for distinct values of the order of the fractional derivative, α, and of the coupling constants, k1,2, show interesting features, such as...

We propose a delay fractional order model for the co-infection of malaria and the human immunodeficiency virus, where personal protection and vaccination against malaria are considered. We compute the reproduction number of the model and study the stability of the disease free equilibrium. The numerical simulations of the model are performed for di...

No seguimento hospitalar de um indivíduo com HIV/SIDA, os valores da Carga Viral (CV) e da contagem de células CD4+T observados ao longo do tempo constituem um conjunto de observações não-igualmente espaçadas, não existindo informação entre consultas. É neste contexto que o trabalho proposto irá contribuir de forma relevante, combinando um modelo m...

We propose a mathematical model with memory for the dynamics of HIV epidemics, where two transmission modes, cell-to-cell and virus-to-cell, and drug resistance are considered. Systems with memory, or fractional order systems, have largely been applied to the modeling of several real life phenomena. Here, we consider a fractional model where the or...

Este trabalho tem como objetivo a caracterização da evolução temporal do vírus da imunodeficiência humana (VIH) em pacientes infetados, combinando um modelo baseado em sistemas de equações diferenciais ordinárias (EDO) e técnicas estatísticas para estimação dos seus parâmetros. A estimação é desenvolvida segundo a abordagem Bayesiana, possibili...

Low levels of viral load are found in HIV-infected patients, after many years under successful suppressive anti-retroviral therapy (ART). The factors leading to this persistence are still under debate, but it is now more or less accepted that the latent reservoir may be crucial to the maintenance of this residual viremia. In this paper, we study th...

We study a fractional order model for HIV infection where latent T helper cells are included. We compute the reproduction number of the model and study the stability of the disease free equilibrium. We observe that the reproduction number varies with the order of the fractional derivative . In terms of epidemics, this suggests that varying induces...

We study the contributions of within-host (virus-to-cell) and synaptic (cell-to-cell) transmissions in a mathematical model for human immunodeficiency virus epidemics. The model also includes drug resistance. We prove the local and global stability of the disease-free equilibrium and the local stability of the endemic equilibrium. We analyse the ef...

We simulate a fractional feed-forward network. This network consists of three coupled identical ‘cells’ (aka, oscillators). We study the behaviour of the associated coupled cell system for variation of the order of the fractional derivative, 0 < α < 1. We consider the Caputo derivative, approximated by the Grünwald–Letnikov approach, using finite d...

In this paper we propose a model for the dynamics of HIV epidemics under distinct HAART regimes, and study the emergence of drug-resistance. The model predicts HIV dynamics of untreated HIV patients for all stages of the infection. We compute the local and the global stability of the disease-free equilibrium of the model. We simulate the model for...

We study the dynamic of HIV epidemics in the three stages of infection. The proposed mathematical model includes macrophages, CD4+ T cells and CTLs, and drug-resistance. Numerical simulations of the model show the disease free equilibrium. Future work will focus on the analyses of the equilibria of the model and on the dynamics of the model in the...

In this paper, we analyze a stochastic model for the dynamics of CD4+ T cells in immunodeficienvy virus (HIV) transmission. The model includes antiretroviral therapy (ART), combining the reverse transcriptase inhibitors (RTIS) and the protease inhibitors (PI), and drug resistance. The stochastic terms are placed in the mortality rates of the CD4+ T...

In this paper, we analyse a mathematical model for the dynamics of CD4+ T cells in human immunodeficiency virus (HIV) transmission. The model includes antiretroviral therapy (ART), combining reverse transcriptase inhibitors (RTIs) and protease inhibitors (PIs), and drug resistance. We modify a deterministic model proposed in the literature to inclu...

We study a fractional complex-order (FO) model for drug-resistance in HIV infection during therapy. We simulate the model for different values of the fractional derivative of complex order (FD) Dα ± ȷβ, where α,β ∈ R+. The FD is a generalization of the integer order derivative where α = 1 and β = 0. The FO system reveals rich dynamics. The novelty...

We develop a new a coinfection model for hepatitis C virus (HCV) and the human immunodeficiency virus (HIV). We consider treatment for both diseases, screening, unawareness and awareness of HIV infection, and the use of condoms. We study the local stability of the disease-free equilibria for the full model and for the two submodels (HCV only and HI...

In this paper it is studied a fractional order model for the three stages of HIV epidemics with drug-resistance. The model includes CD4⁺ T cells, CTLs, macrophages, and the virus populations. We simulate the model for different values of the fractional derivative α ∈ [0.5,1.0]. The fractional order system untangles generous dynamical characteristic...

In this paper we present a coupled SIQR model for computer and a SI model for removable devices viruses dynamics, with impulse quarantine. We simulate the model for two initial conditions. We observe that the model approaches either the stable disease-free equilibrium or the stable endemic equilibrium. Moreover, we observe the dithering phenomenon.

We propose a new model for computer worms propagation, using dynamic quarantine and a nonlinear infection rate. The dynamic quarantine is based in epidemic disease control methods and in the principle ‘assume guilty before proven inocent’. This means that the host is blocked whenever its behavior looks suspicious. After a short time, the quarantin...

We develop a mathematical model for the dynamics of coinfection of HIV and tuberculosis (TB), that includes treatment for both diseases and exogeneous reinfection in the case of TB. In the numerical simulations, we vary the exogeneous reinfection level, p, and observe that for increasing values of p there is a bifurcation from the disease free equi...

We study curious dynamical patterns appearing in a network of a unidirectional ring of Chen oscillators coupled to a ‘buffer’ cell. The network has Z 3 exact symmetry group. We simulate the coupled cell systems associated to the two networks and obtain steady-states, rotating waves, quasiperiodic behavior, and chaos. The different patterns appear t...

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We propose a fractional complex-order model for drug resistance in HIV infection. We consider three distinct growth rates for the CD4+ T helper cells. We simulate the model for different values of the fractional derivative of complex order D α±jβ, where α,β ∈ R +, and for distinct growth rates. The fractional derivative of complex order is a genera...

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z(3) x Z(5) cyclic symmetry group. The complex derivative D-alpha +/- j beta, with alpha,beta is an element of R+ is a generalization of the co...

In this paper we study a fractional order model for HIV and TB coinfection. We consider vertical transmission for HIV and treatment for both diseases. We analyze numerical results of the proposed model for different values of the order of the fractional derivative. The results are in agreement with the integer order model and reveal that we can ext...

We study curious dynamical patterns appearing in networks of one ring of cells coupled to a ‘buffer’ cell. Depending on how the cells in the ring are coupled to the ‘buffer’ cell, the full network may have a nontrivial group of symmetries or a nontrivial group of ‘interior’ symmetries. This group is Z3 in the unidirectional case and D3 in the bidir...

We study exotic patterns appearing in a network of coupled Chen oscillators. Namely, we consider a network of two rings coupled through a "buffer" cell, with symmetry group. Numerical simulations of the network reveal steady states, rotating waves in one ring and quasiperiodic behavior in the other, and chaotic states in the two rings, to name a fe...

We study a mathematical model for the human immunodeficiency virus (HIV) and hepatites C virus (HCV) coinfection. The model predicts four distinct equilibria: the disease free, the HIV endemic, the HCV endemic, and the full endemic equilibria. The local and global stability of the disease free equilibrium was calculated for the full model and the H...

Bipedal gaits have been classified on the basis of the group symmetry of the minimal network of identical differential equations (alias cells) required to model them. Primary bipedal gaits (e.g., walk, run) are characterized by dihedral symmetry, whereas secondary bipedal gaits (e.g., gallop-walk, gallop-run) are characterized by a lower, cyclic sy...

In this paper we study a model for HIV and TB coinfection. We consider the integer order and the fractional order versions of the model. Let α∈[0.78,1.0]α∈[0.78,1.0] be the order of the fractional derivative, then the integer order model is obtained for α=1.0α=1.0. The model includes vertical transmission for HIV and treatment for both diseases. We...

Catastrophic events, such as wars and terrorist attacks, big tornadoes and hurricanes, huge earthquakes, tsunamis, floods, and landslides, are always accompanied by a large number of casualties. The size distribution of these casualties have separately been shown to follow approximate power law (PL) distributions. In this paper, we analyze the numb...

Power law (PL) distributions have been largely reported in the modeling of distinct real phenomena and have been associated with fractal structures and self-similar systems. In this paper, we analyze real data that follows a PL and a double PL behavior and verify the relation between the PL coefficient and the capacity dimension of known fractals....

We propose a fractional model for computer virus propagation. The model includes the interaction between computers and removable devices. We simulate numerically the model for distinct values of the order of the fractional derivative and for two sets of initial conditions adopted in the literature. We conclude that fractional order systems reveal r...