Результаты поиска по 'forward bifurcation':
Найдено статей: 2
  1. Kazymov B.I., Limareva M.J., Lobanov A.I., Fisher J.V., Yaremin B.I.
    Numerical simulation of flow inversion in the portal vein
    Computer Research and Modeling, 2026, v. 18, no. 3, pp. 659-674

    A mathematical model of fluid movement in the portal vein is considered. The fundamental circumstance determining the whole variety of portal hemodynamic phenomena is the absence of a valve apparatus. The flow direction is solely a function of the pressure gradient, and, therefore, it is fundamentally reversible when the boundary conditions of the system change.

    Calculations were performed in the area representing a CT image fragment of the portal vein of a particular patient, which does not contain vascular bifurcations. The interpolation of patient Dopplerography data published in the press was used as boundary conditions for the flow. The calculations were carried out using the FlowVision industrial hydrodynamics software package. A comparison of calculations using the ideal fluid model and the Kuemada model of viscoplastic flow is carried out.

    Calculations were performed for different values of the resistance coefficient corresponding to the physiological norm and with an increased value of the resistance coefficient.

    At a normal value of the resistance coefficient, the flow in the portal vein is characterized by strong convective mixing.

    As a result of calculations, it was found that when using the Kuemada model, the flow in the portal vein is stratified. The nature of the stratification depends on the hematocrit. At a normal value of the resistance coefficient, a plastic core of the flow is formed as the velocity decreases. With an increased value of the resistance coefficient during flow inversion, the flow core is also formed. When the flow is inverted, the plastic core continues to move in the forward direction, while the wall layers of the liquid begin to move in the opposite direction.

    It is noted that in order to obtain correct modeling results, it is necessary to refine the blood composition of the portal vein and, possibly, refine the rheological model. Such information can be obtained both from comparing simulation data with clinical data, and by laboratory examination of portal vein blood.

    Keywords: portal vein, flow inversion, mathematical modeling, Quemada liquid model, FlowVision software package.
  2. Zevika M.Z., Triska A.T., Puspita J.W.
    The dynamics of monkeypox transmission with an optimal vaccination strategy through a mathematical modelling approach
    Computer Research and Modeling, 2023, v. 15, no. 6, pp. 1635-1651

    Monkeypox is a disease reemerging in 2022 which is caused by the monkeypox virus (MPV). This disease can be transmitted not only from rodents to humans, but also from humans to other humans, and even from the environment to humans. In this work, we propose a mathematical model to capture the dynamics of monkeypox transmission which involve three modes of transmission, namely, from rodents to rodents, rodents to humans, and from humans to other humans. In addition to the basic reproduction number, we investigate the stability of all equilibrium points analytically, including an implicit endemic equilibrium by applying the center manifold theorem. Moreover, the vaccination as an alternative solution to eradicate the monkeypox transmission is discussed and solved as an optimal control problem. The results of this study show that the transmission of monkeypox is directly affected by the internal infection rates of each population, i. e., the infection rate of the susceptible human by an infected human and the infection rate of the susceptible rodent by an infected rodent. Furthermore, the external infection rates, i. e., the infection rate of the susceptible human by an infected rodent also affects the transmission of monkeypox although it does not affect the basic reproduction number directly.

    Keywords: SEIR-SEIR model, monkeypox, vaccination, optimal control, forward bifurcation.

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