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- International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended AbstractsPublication . Pinto, C.M.A.; Mendonça, Jorge; Babo, Lurdes; Baleanu, DumitruThe present volume on Mathematical Analysis and Applications in Science and Engineering - Book of Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days). Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering, industry, and technology, to discuss the development of new mathematical models, theories, and applications that contribute to the advancement of scientific knowledge and practice. Authors proposed research in topics including partial and ordinary differential equations, integer and fractional order equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization, control, probability, computational mathematics, amongst others. The conference was designed to maximize the involvement of all participants and will present the state-of- the-art research and the latest achievements.
- International Conference Mathematical Analysis and Applications in Science and Engineering, ISEP, Porto, Portugal, June 20-22, 2024: Book of abstractsPublication . Golubitsky, Martin; Lacarnobara, Walter; Pinto, Carla M.A.; Babo, Lurdes; Mendonça, Jorge; Carvalho, Fernando; Rocha, Rui
- Power law and entropy analysis of catastrophic phenomenaPublication . Machado, J.A.Tenreiro; Pinto, Carla M.A.; Lopes, António M.Catastrophic events, such as wars and terrorist attacks, tornadoes and hurricanes, earthquakes, tsunamis, floods and landslides, are always accompanied by a large number of casualties. The size distribution of these casualties has separately been shown to follow approximate power law (PL) distributions. In this paper, we analyze the statistical distributions of the number of victims of catastrophic phenomena, in particular, terrorism, and find double PL behavior. This means that the data sets are better approximated by two PLs instead of a single one. We plot the PL parameters, corresponding to several events, and observe an interesting pattern in the charts, where the lines that connect each pair of points defining the double PLs are almost parallel to each other. A complementary data analysis is performed by means of the computation of the entropy. The results reveal relationships hidden in the data that may trigger a future comprehensive explanation of this type of phenomena.
- Effects of treatment, awareness and condom use in a coinfection model for HIV and HCV in MSMPublication . Pinto, Carla M.A.; Carvalho, Ana R.M.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 HIV only submodels). We sketch bifurcation diagrams for different parameters, such as the probabilities that a contact will result in a HIV or an HCV infection. We present numerical simulations of the full model where the HIV, HCV and double endemic equilibria can be observed. We also show numerically the qualitative changes of the dynamical behavior of the full model for variation of relevant parameters. We extrapolate the results from the model for actual measures that could be implemented in order to reduce the number of infected individuals.
- Fractional model for malaria transmission under control strategiesPublication . Pinto, Carla M.A.; Machado, J.A.TenreiroWe study a fractional model for malaria transmission under control strategies.Weconsider the integer order model proposed by Chiyaka et al. (2008) in [15] and modify it to become a fractional order model. We study numerically the model for variation of the values of the fractional derivative and of the parameter that models personal protection, b. From observation of the figures we conclude that as b is increased from 0 to 1 there is a corresponding decrease in the number of infectious humans and infectious mosquitoes, for all values of α. This means that this result is invariant for variation of fractional derivative, in the values tested. These results are in agreement with those obtained in Chiyaka et al.(2008) [15] for α = 1.0 and suggest that our fractional model is epidemiologically wellposed.
- Fractional Dynamics of Computer Virus PropagationPublication . Pinto, Carla M.A.; Machado, J.A.TenreiroWe 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 richer dynamics than the classical integer order counterpart. Therefore, fractional dynamics leads to time responses with super-fast transients and super-slow evolutions towards the steady-state, effects not easily captured by the integer order models.
- Book of Abstracts of the First International Conference - Building Bridges in STEAM Education in the 21st CenturyPublication . Soares, Filomena Baptista; Lopes, Ana Paula; Pinto, Carla; Mendonça, JorgeThe 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.
- A latency fractional order model for HIV dynamicsPublication . Pinto, Carla M.A.; Carvalho, Ana R.M.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 α. In terms of epidemics, this suggests that varying α induces a change in the patients’ epidemic status. Moreover, we simulate the variation of relevant parameters, such as the fraction of uninfected CD4+ T cells that become latently infected, and the CTLs proliferation rate due to infected CD4+ T cells. The model produces biologically reasonable results.
- Modified SIQR model for the COVID‐19 outbreak in several countriesPublication . Pinto, Carla M. A.; Tenreiro Machado, J. A.; Burgos‐Simón, ClaraIn 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 contact rate, the proportion of unknown infectious, and the recovering rate. The mSIQR model is simulated, and the outputs are fit to COVID-19 pandemic data from several countries, including France, US, UK, and Portugal. We discuss the epidemiological relevance of the results and provide insights on future patterns, subjected to health policies.
- Emergence of drug-resistance in HIV dynamics under distinct HAARTregimesPublication . Pinto, Carla M.A.; Carvalho, Ana R.M.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 two distinct HIV patients, the rapid progressors and the long-term non-progressors. We study the effects of equal RTI and PI efficacies, as well as distinct drug efficacies, namely RTI-based and PI-based therapeutics. Treatment is initiated when the CD4+ T cells count is less than 350 cells mm−3. The PI-based drugs seem to produce better outcomes, with respect to disease progression, than RTI-based regimes.