Carvalho, João Maurício

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Carvalho

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João Maurício

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João Maurício de Carvalho

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João Paulo Simões Maurício de Carvalho exerce funções como docente e investigador na área de sistemas dinâmicos, integrando o Centro de Matemática da Universidade do Porto. Licenciado em Astronomia pela Faculdade de Ciências da mesma instituição, consolidou uma formação de base sólida no domínio da Física, a qual sustenta e potencia a sua abordagem analítica e o seu interesse na modelação matemática de fenómenos complexos. Prosseguiu os estudos na Universidade do Porto, onde obteve o grau de Mestre em Matemática, tendo posteriormente concluído o Doutoramento em Matemática no âmbito de um programa doutoral conjunto que envolveu a Universidade do Porto, a Universidade de Aveiro e a Universidade do Minho. A sua atividade científica tem-se centrado no desenvolvimento e análise de modelos determinísticos de sistemas dinâmicos, com especial incidência na modelação matemática da propagação de doenças infeciosas. Durante o doutoramento, aprofundou o estudo de equações diferenciais ordinárias, teoria das bifurcações, estabilidade de equilíbrios e dinâmica caótica, áreas fundamentais para a compreensão rigorosa de fenómenos epidemiológicos e para a fundamentação de estratégias de intervenção e controlo mais eficazes. A sua investigação é orientada pela convicção de que a integração entre a análise teórica e a incorporação de dados empíricos permite conceber modelos matemáticos robustos, suscetíveis de aplicação prática, capazes de identificar regiões com elevada prevalência de infeção, prever padrões de transmissão e apoiar a tomada de decisão em políticas de vacinação e medidas de saúde pública. No âmbito da docência no ensino superior, leciona unidades curriculares nas áreas de equações diferenciais ordinárias, análise numérica e modelação matemática, assim como unidades curriculares na área da física, promovendo o desenvolvimento do pensamento crítico, da autonomia intelectual e da capacidade de resolver problemas complexos em contextos reais. Valoriza de forma particular a colaboração interdisciplinar e a partilha de conhecimento com investigadores de diferentes domínios científicos, reconhecendo que é na interseção de saberes que emergem soluções inovadoras com potencial impacto social. O seu percurso profissional reflete um compromisso continuado com a investigação de excelência, a atualização permanente do conhecimento e a contribuição ativa para o progresso científico orientado para a melhoria da qualidade de vida.

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https://orcid.org/0000-0001-7709-1631
D818-32ED-1DE4
57222719456
NWH-4741-2025

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REMIT – Research on Economics, Management and Information Technologies
Centro de investigação que que tem como objetivo principal produzir e disseminar conhecimento teórico e aplicado que possibilite uma maior compreensão das dinâmicas e tendências económicas, empresariais, territoriais e tecnológicas do mundo contemporâneo e dos seus efeitos socioeconómicos. O REMIT adota uma perspetiva multidisciplinar que integra vários domínios científicos: Economia e Gestão; Ciências e Tecnologia; Turismo, Património e Cultura. Founded in 2017, REMIT – Research on Economics, Management and Information Technologies is a research unit of Portucalense University. Based on a multidisciplinary and interdisciplinary perspective it aims at responding to social challenges through a holistic approach involving a wide range of scientific fields such as Economics, Management, Science, Technology, Tourism, Heritage and Culture. Grounded on the production of advanced scientific knowledge, REMIT has a special focus on its application to the resolution of real issues and challenges, having as strategic orientations: - the understanding of local, national and international environment; - the development of activities oriented to professional practice, namely in the business world.

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A mostrar 1 - 8 de 8
  • Miniatura
    PublicaçãoAcesso Restrito
    Role of the Immune System in AIDS-defining Malignancies
    2022-01-01 - Carvalho, João Maurício; Pinto , Carla M. A.
    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 those in HIV-negative patients. It is thus compelling to further understand the dynamics of AIDS-related cancer growth. We propose a non-integer order model to describe the role of the immune system in cancer cells’ growth in a HIV-infected individual. The model incorporates anti-retroviral therapy and chemotherapy. We simulate the model for different proliferation functions of the cytotoxic T lymphocytes (CTLs), and other parameters, namely the HIV-infection rate, the elimination rate of infected T cells by CTLs, and the elimination rate of cancer cells by the immune system and discuss the results from a physiological perspective. The order of the fractional derivative completes the discussion of the results.
  • Miniatura
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    Double Hopf bifurcation and chaotic dynamics in a periodically-forced SIR model
    2025-12-24 - Carvalho, João Maurício
    We perform a qualitative analysis of a periodically-forced SIR model which incorporates the disease transmission rate by direct contact with the natural viral source, in addition to the classic disease transmission rate between individuals. We direct this work towards two main topics: (i) in the absence of seasonality, the endemic equilibrium point (and unique) undergoes both supercritical and subcritical Hopf bifurcations. We identify a specific range of values for the disease transmission rate , for which the system exhibits an attracting periodic solution while the equilibrium is unstable; (ii) in the presence of seasonality, we prove via torus-breakdown theory that the system exhibits strange attractors (observable chaos). These findings reveal that small changes in parameters can generate complex epidemic dynamics, becoming very difficult to control. All findings are derived analytically and supported by numerical simulations.
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    Fractional Model for Type 1 Diabetes
    2020-02-12 - Carvalho, Ana R. M.; Pinto, Carla M. A.; Carvalho, João Maurício
    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 involved in the onset of T1D. In this paper, we generalize an integer-order model for T1D to include a non-integer order (also known as, fractional order (FO)) derivative. We study the local and the global stabilities of the disease-free equilibrium. Then, we discuss the results of the simulations of the FO model and investigate the role of macrophages from non-obese diabetic (NOD) mice and from control (Balb/c) mice in triggering autoimmune T1D. We observe that, for a value of the order of the fractional derivative equal to 1 (α = 1), an apoptotic wave can trigger T1D in NOD but not in Balb/c mice. The apoptotic wave is cleared efficiently in Balb/c mice preventing the onset of T1D. For smaller values of α, the inflammation persists for NOD and control mice. This alludes to a specific role of the order of the fractional derivative α in disease progression.
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    PublicaçãoAcesso Restrito
    A fractional-order model for CoViD-19 dynamics with reinfection and the importance of quarantine
    2021-10-01 - Carvalho, João Maurício; Moreira-Pinto, Beatriz
    Coronavirus disease 2019 (CoViD-19) is an infectious disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Among many symptoms, cough, fever and tiredness are the most common. People over 60 years old and with associated comorbidities are most likely to develop a worsening health condition. This paper proposes a non-integer order model to describe the dynamics of CoViD-19 in a standard population. The model incorporates the reinfection rate in the individuals recovered from the disease. Numerical simulations are performed for different values of the order of the fractional derivative and of reinfection rate. The results are discussed from a biological point of view.
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    Strange attractors in a dynamical system inspired by a seasonally forced SIR model
    2022-06-01 - Carvalho, João Maurício; Rodrigues, Alexandre A.
    We analyze a multiparameter periodically-forced dynamical system inspired in the SIR endemic model. We show that the condition on the basic reproduction number is not sufficient to guarantee the elimination of Infectious individuals due to a backward bifurcation. Using the theory of rank-one attractors, for an open subset in the space of parameters where , the flow exhibits persistent strange attractors. These sets are not confined to a tubular neighborhood in the phase space, shadow the ghost of a two-dimensional invariant torus and are numerically observable. Although numerical experiments have already suggested that periodically-forced biological models may exhibit observable chaos, a rigorous proof was not given before. Our results agree well with the empirical belief that intense seasonality induces chaos.
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    SIR Model with vaccination: Bifurcation analysis
    2023-05-17 - Carvalho, João Maurício; Rodrigues , Alexandre A.
    There are few adapted SIR models in the literature that combine vaccination and logistic growth. In this article, we study bifurcations of a SIR model where the class of Susceptible individuals grows logistically and has been subject to constant vaccination. We explicitly prove that the endemic equilibrium is a codimension two singularity in the parameter space , where is the basic reproduction number and p is the proportion of Susceptible individuals successfully vaccinated at birth. We exhibit explicitly the Hopf, transcritical, Belyakov, heteroclinic and saddle-node bifurcation curves unfolding the singularity. The two parameters are written in a useful way to evaluate the proportion of vaccinated individuals necessary to eliminate the disease and to conclude how the vaccination may affect the outcome of the epidemic. We also exhibit the region in the parameter space where the disease persists and we illustrate our main result with numerical simulations, emphasizing the role of the parameters.
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    Qualitative analysis of HAART effects on HIV and SARS-CoV-2 coinfection model
    2025-07-11 - Carvalho, João Maurício
    HIV is known for causing the destruction of the immune system by affecting different types of cells, while SARS-CoV-2 is an extremely contagious virus that leads to the development of COVID-19. Understanding how these two viruses interact in coinfected individuals is essential, especially in populations under antiretroviral treatment. In this study, we develop and analyze a novel mathematical model capturing the coinfection dynamics of HIV and SARS-CoV-2 under the influence of highly active antiretroviral therapy (HAART). In contrast to previous models, our formulation includes the effect of HAART on both infections and derives the basic reproduction numbers for each virus. We prove that transcritical bifurcations occur when the basic reproduction numbers cross the threshold value of 1, and we establish the conditions for stability of the disease-free equilibria. Numerical simulations show that HAART, although designed to control HIV, also reduces SARS-CoV-2 proliferation in coinfected hosts, which, as far as we know, has not been fully addressed in previous models in the literature. These findings reveal a potentially beneficial indirect effect of antiretroviral therapy on SARS-CoV-2 dynamics, offering new theoretical insights into the control of viral coinfections.
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    PublicaçãoAcesso Aberto
    Pulse vaccination in a SIR model: Global dynamics, bifurcations and seasonality
    2024-12-01 - Carvalho, João Maurício; Rodrigues, Alexandre A.
    We analyze a periodically-forced dynamical system inspired by the SIR model with impulsive vaccination. We fully characterize its dynamics according to the proportion of vaccinated individuals and the time between doses. If the basic reproduction number is less than 1 (i.e ), then we obtain precise conditions for the existence and global stability of a disease-free -periodic solution. Otherwise, if , then a globally stable -periodic solution emerges with positive coordinates. We draw a bifurcation diagram and we describe the associated bifurcations. We also find analytically and numerically chaotic dynamics by adding seasonality to the disease transmission rate. In a realistic context, low vaccination coverage and intense seasonality may result in unpredictable dynamics. Previous experiments have suggested chaos in periodically-forced biological impulsive models, but no analytic proof has been given.