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  1. Article ; Online: Fractal and fractional SIS model for syphilis data.

    Gabrick, Enrique C / Sayari, Elaheh / Souza, Diogo L M / Borges, Fernando S / Trobia, José / Lenzi, Ervin K / Batista, Antonio M

    Chaos (Woodbury, N.Y.)

    2023  Volume 33, Issue 9

    Abstract: This work studies the SIS model extended by fractional and fractal derivatives. We obtain explicit solutions for the standard and fractal formulations; for the fractional case, we study numerical solutions. As a real data example, we consider the ... ...

    Abstract This work studies the SIS model extended by fractional and fractal derivatives. We obtain explicit solutions for the standard and fractal formulations; for the fractional case, we study numerical solutions. As a real data example, we consider the Brazilian syphilis data from 2011 to 2021. We fit the data by considering the three variations of the model. Our fit suggests a recovery period of 11.6 days and a reproduction ratio (R0) equal to 6.5. By calculating the correlation coefficient (r) between the real data and the theoretical points, our results suggest that the fractal model presents a higher r compared to the standard or fractional case. The fractal formulation is improved when two different fractal orders with distinguishing weights are considered. This modification in the model provides a better description of the data and improves the correlation coefficient.
    MeSH term(s) Humans ; Epidemiological Models ; Fractals ; Syphilis ; Brazil
    Language English
    Publishing date 2023-09-15
    Publishing country United States
    Document type Journal Article
    ZDB-ID 1472677-4
    ISSN 1089-7682 ; 1054-1500
    ISSN (online) 1089-7682
    ISSN 1054-1500
    DOI 10.1063/5.0153122
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  2. Article ; Online: Adaptive exponential integrate-and-fire model with fractal extension.

    Souza, Diogo L M / Gabrick, Enrique C / Protachevicz, Paulo R / Borges, Fernando S / Trobia, José / Iarosz, Kelly C / Batista, Antonio M / Caldas, Iberê L / Lenzi, Ervin K

    Chaos (Woodbury, N.Y.)

    2024  Volume 34, Issue 2

    Abstract: The description of neuronal activity has been of great importance in neuroscience. In this field, mathematical models are useful to describe the electrophysical behavior of neurons. One successful model used for this purpose is the Adaptive Exponential ... ...

    Abstract The description of neuronal activity has been of great importance in neuroscience. In this field, mathematical models are useful to describe the electrophysical behavior of neurons. One successful model used for this purpose is the Adaptive Exponential Integrate-and-Fire (Adex), which is composed of two ordinary differential equations. Usually, this model is considered in the standard formulation, i.e., with integer order derivatives. In this work, we propose and study the fractal extension of Adex model, which in simple terms corresponds to replacing the integer derivative by non-integer. As non-integer operators, we choose the fractal derivatives. We explore the effects of equal and different orders of fractal derivatives in the firing patterns and mean frequency of the neuron described by the Adex model. Previous results suggest that fractal derivatives can provide a more realistic representation due to the fact that the standard operators are generalized. Our findings show that the fractal order influences the inter-spike intervals and changes the mean firing frequency. In addition, the firing patterns depend not only on the neuronal parameters but also on the order of respective fractal operators. As our main conclusion, the fractal order below the unit value increases the influence of the adaptation mechanism in the spike firing patterns.
    MeSH term(s) Action Potentials/physiology ; Fractals ; Models, Neurological ; Neurons/physiology
    Language English
    Publishing date 2024-02-10
    Publishing country United States
    Document type Journal Article
    ZDB-ID 1472677-4
    ISSN 1089-7682 ; 1054-1500
    ISSN (online) 1089-7682
    ISSN 1054-1500
    DOI 10.1063/5.0176455
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  3. Article: The Role of Potassium and Calcium Currents in the Bistable Firing Transition.

    Borges, Fernando S / Protachevicz, Paulo R / Souza, Diogo L M / Bittencourt, Conrado F / Gabrick, Enrique C / Bentivoglio, Lucas E / Szezech, José D / Batista, Antonio M / Caldas, Iberê L / Dura-Bernal, Salvador / Pena, Rodrigo F O

    bioRxiv : the preprint server for biology

    2023  

    Abstract: Healthy brains display a wide range of firing patterns, from synchronized oscillations during slowwave sleep to desynchronized firing during movement. These physiological activities coexist with periods of pathological hyperactivity in the epileptic ... ...

    Abstract Healthy brains display a wide range of firing patterns, from synchronized oscillations during slowwave sleep to desynchronized firing during movement. These physiological activities coexist with periods of pathological hyperactivity in the epileptic brain, where neurons can fire in synchronized bursts. Most cortical neurons are pyramidal regular spiking cells (RS) with frequency adaptation and do not exhibit bursts in current-clamp experiments (
    Language English
    Publishing date 2023-08-17
    Publishing country United States
    Document type Preprint
    DOI 10.1101/2023.08.16.553625
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  4. Article: The Roles of Potassium and Calcium Currents in the Bistable Firing Transition.

    Borges, Fernando S / Protachevicz, Paulo R / Souza, Diogo L M / Bittencourt, Conrado F / Gabrick, Enrique C / Bentivoglio, Lucas E / Szezech, José D / Batista, Antonio M / Caldas, Iberê L / Dura-Bernal, Salvador / Pena, Rodrigo F O

    Brain sciences

    2023  Volume 13, Issue 9

    Abstract: Healthy brains display a wide range of firing patterns, from synchronized oscillations during slow-wave sleep to desynchronized firing during movement. These physiological activities coexist with periods of pathological hyperactivity in the epileptic ... ...

    Abstract Healthy brains display a wide range of firing patterns, from synchronized oscillations during slow-wave sleep to desynchronized firing during movement. These physiological activities coexist with periods of pathological hyperactivity in the epileptic brain, where neurons can fire in synchronized bursts. Most cortical neurons are pyramidal regular spiking (RS) cells with frequency adaptation and do not exhibit bursts in current-clamp experiments (in vitro). In this work, we investigate the transition mechanism of spike-to-burst patterns due to slow potassium and calcium currents, considering a conductance-based model of a cortical RS cell. The joint influence of potassium and calcium ion channels on high synchronous patterns is investigated for different synaptic couplings (gsyn) and external current inputs (
    Language English
    Publishing date 2023-09-20
    Publishing country Switzerland
    Document type Journal Article
    ZDB-ID 2651993-8
    ISSN 2076-3425
    ISSN 2076-3425
    DOI 10.3390/brainsci13091347
    Database MEDical Literature Analysis and Retrieval System OnLINE

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