Study of solutions of a continuous-discrete model of HIV infection spread

2016 ◽  
Vol 31 (5) ◽  
Author(s):  
Nikolay V. Pertsev
Keyword(s):  
Hiv Infection ◽  
Existence Of Solutions ◽  
Social Groups ◽  
Monotone Operators ◽  
Model Parameters ◽  
Risk Of Infection ◽  
Model Equations ◽  
And Migration ◽  
Discrete Mathematical Model ◽  
Number Of Individuals

AbstractEquations of a continuous-discrete mathematical model describing the propagation of HIV infection among the population of several regions are presented. The model equations take into account the reproduction and migration of the population, the risk of infection of individuals from different social groups, an impulse change in the number of individuals at discrete time moments under the action of various factors. The results of the study of the model solutions are also presented. We obtain conditions for the model parameters and initial data that provide the existence of solutions interpreted as full eradication of HIV infection in all considered regions or maintenance of sizes of groups of infected individuals at some acceptable level. The solutions analysis uses the monotone operators method and properties of nonsingular M-matrices.

scholarly journals A Banach space mixed formulation for the unsteady Brinkman–Forchheimer equations

2020 ◽  
Author(s):  
Sergio Caucao ◽  
Ivan Yotov
Keyword(s):  
Banach Space ◽  
Time Discretization ◽  
Monotone Operators ◽  
Rates Of Convergence ◽  
Mixed Formulation ◽  
Model Parameters ◽  
Weak Formulation ◽  
Finite Element Approximations ◽  
Backward Euler ◽  
Discrete Finite Element

Abstract We propose and analyse a mixed formulation for the Brinkman–Forchheimer equations for unsteady flows. Our approach is based on the introduction of a pseudostress tensor related to the velocity gradient and pressure, leading to a mixed formulation where the pseudostress tensor and the velocity are the main unknowns of the system. We establish existence and uniqueness of a solution to the weak formulation in a Banach space setting, employing classical results on nonlinear monotone operators and a regularization technique. We then present well posedness and error analysis for semidiscrete continuous-in-time and fully discrete finite element approximations on simplicial grids with spatial discretization based on the Raviart–Thomas spaces of degree $k$ for the pseudostress tensor and discontinuous piecewise polynomial elements of degree $k$ for the velocity and backward Euler time discretization. We provide several numerical results to confirm the theoretical rates of convergence and illustrate the performance and flexibility of the method for a range of model parameters.

scholarly journals Existence of solutions for the Eulerian flamelet model equations

2013 ◽  
Vol 57 (9-10) ◽  
pp. 2196-2206
Author(s):  
Greice S. Lorenzzetti ◽  
Álvaro L. de Bortoli ◽  
Lígia D.F. Marczak
Keyword(s):  
Existence Of Solutions ◽  
Flamelet Model ◽  
Model Equations

Implications of Using Dual Number Derivatives With a Numerical Solution

2013 ◽  
Author(s):  
Suryanarayana R. Pakalapati ◽  
Hayri Sezer ◽  
Ismail B. Celik
Keyword(s):  
Automatic Differentiation ◽  
Numerical Solutions ◽  
Computer Code ◽  
Model Parameters ◽  
Model Parameter ◽  
Systematic Assessment ◽  
Dual Number ◽  
Advection Diffusion Equation ◽  
Model Equations ◽  
Derivatives Of

Dual number arithmetic is a well-known strategy for automatic differentiation of computer codes which gives exact derivatives, to the machine accuracy, of the computed quantities with respect to any of the involved variables. A common application of this concept in Computational Fluid Dynamics, or numerical modeling in general, is to assess the sensitivity of mathematical models to the model parameters. However, dual number arithmetic, in theory, finds the derivatives of the actual mathematical expressions evaluated by the computer code. Thus the sensitivity to a model parameter found by dual number automatic differentiation is essentially that of the combination of the actual mathematical equations, the numerical scheme and the grid used to solve the equations not just that of the model equations alone as implied by some studies. This aspect of the sensitivity analysis of numerical simulations using dual number auto derivation is explored in the current study. A simple one-dimensional advection diffusion equation is discretized using different schemes of finite volume method and the resulting systems of equations are solved numerically. Derivatives of the numerical solutions with respect to parameters are evaluated automatically using dual number automatic differentiation. In addition the derivatives are also estimated using finite differencing for comparison. The analytical solution was also found for the original PDE and derivatives of this solution are also computed analytically. It is shown that a mathematical model could potentially show different sensitivity to a model parameter depending on the numerical method employed to solve the equations and the grid resolution used. This distinction is important since such inter-dependence needs to be carefully addressed to avoid confusion when reporting the sensitivity of predictions to a model parameter using a computer code. A systematic assessment of numerical uncertainty in the sensitivities computed using automatic differentiation is presented.

scholarly journals Features of choosing the tactics and method of treatment of external joint frequencies of long external bones in people living with HIV

2020 ◽  
Vol 12 (1) ◽  
pp. 65-72
Author(s):  
N. G. Doronin ◽  
S. N. Khoroshkov ◽  
S. L. Maksimov
Keyword(s):  
Hiv Infection ◽  
Infectious Complications ◽  
Antiretroviral Drugs ◽  
People Living With Hiv ◽  
Long Bones ◽  
Treatment Results ◽  
Improve Treatment ◽  
Articular Fractures ◽  
And Migration ◽  
Living With Hiv

Objective. Develop an algorithm for determining tactics and parameters of their treatment to improve treatment outcomes. Methodology. Material and research methods. A statistical analysis of the treatment results of 90 HIV-infected patients aged from 23 to 54 years with extra-articular fractures of long bones of the extremities was carried out. When determining the tactics and method of treatment, the peculiarities of the effect of HIV infection, antiretroviral drugs, and opportunistic diseases on the patient’s body were not taken into account. Results. Non-infectious complications are characteristic of HIV-infected patients: sides of the postoperative wound (seromas, hematomas, discrepancy of wound edges, delayed crushing), aseptic loosening and migration of fixatives, delayed consolidation of fractures. The presence of a statistically significant relationship between the objective factors characterizing the course of HIV infection: the stage of the disease, the number of CD lymphocytes, the ratio of CD4 / CD8 lymphocytes, viral load and the risk of postoperative complications was revealed.Conclusion. The application of the developed algorithm allows you to objectify the procedure and provide an individual approach in determining the tactics and method of treatment for HIV-infected patients with extraarticular fractures of long bones of the extremities

scholarly journals Immediate Antiretroviral Therapy Reduces Risk of Infection-Related Cancer During Early HIV Infection

2016 ◽  
Vol 63 (12) ◽  
pp. 1668-1676 ◽  
Author(s):  
Álvaro H. Borges ◽  
Jacqueline Neuhaus ◽  
Abdel G. Babiker ◽  
Keith Henry ◽  
Mamta K. Jain ◽  
...  
Keyword(s):  
Antiretroviral Therapy ◽  
Hiv Infection ◽  
Risk Of Infection

HIV testing in Acute Care

2018 ◽  
Vol 17 (2) ◽  
pp. 61-61
Author(s):  
Pippa J Newton ◽  
Keyword(s):  
Health Care ◽  
Hiv Infection ◽  
Hiv Testing ◽  
Health Care Services ◽  
Hiv Infections ◽  
Late Presentation ◽  
Care Services ◽  
Undiagnosed Hiv ◽  
The Usa ◽  
Number Of Individuals

Readers may be aware of the need to improve uptake of HIV testing in health care-settings to reduce the number of individuals with undiagnosed infection who later present with advanced disease. Late presentation of HIV infection is associated with a poorer immune response to antiretroviral therapy, an increased morbidity and mortality with a resultant higher cost burden to health-care services. Individuals with undiagnosed HIV infection who inadvertently transmit their infection to others are thought to be responsible for more than half of new HIV infections in the USA.

A study on the effects of electrical and thermal stresses on void formation and migration lifetime of Sn3.0Ag0.5Cu solder joints

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Yanruoyue Li ◽  
Guicui Fu ◽  
Bo Wan ◽  
Zhaoxi Wu ◽  
Xiaojun Yan ◽  
...  
Keyword(s):  
Solder Joint ◽  
Thermal Stresses ◽  
Solder Joints ◽  
Void Formation ◽  
Model Parameters ◽  
Time To Failure ◽  
Current Crowding ◽  
Theoretical Derivation ◽  
Content Type ◽  
And Migration

Purpose The purpose of this study is to investigate the effect of electrical and thermal stresses on the void formation of the Sn3.0Ag0.5Cu (SAC305) lead-free ball grid array (BGA) solder joints and to propose a modified mean-time-to-failure (MTTF) equation when joints are subjected to coupling stress. Design/methodology/approach The samples of the BGA package were subjected to a migration test at different currents and temperatures. Voltage variation was recorded for analysis. Scanning electron microscope and electron back-scattered diffraction were applied to achieve the micromorphological observations. Additionally, the experimental and simulation results were combined to fit the modified model parameters. Findings Voids appeared at the corner of the cathode. The resistance of the daisy chain increased. Two stages of resistance variation were confirmed. The crystal lattice orientation rotated and became consistent and ordered. Electrical and thermal stresses had an impact on the void formation. As the current density and temperature increased, the void increased. The lifetime of the solder joint decreased as the electrical and thermal stresses increased. A modified MTTF model was proposed and its parameters were confirmed by theoretical derivation and test data fitting. Originality/value This study focuses on the effects of coupling stress on the void formation of the SAC305 BGA solder joint. The microstructure and macroscopic performance were studied to identify the effects of different stresses with the use of a variety of analytical methods. The modified MTTF model was constructed for application to SAC305 BGA solder joints. It was found suitable for larger current densities and larger influences of Joule heating and for the welding ball structure with current crowding.

scholarly journals SEIR Modeling of the Italian Epidemic of SARS-CoV-2 Using Computational Swarm Intelligence

2020 ◽  
Vol 17 (10) ◽  
pp. 3535 ◽  
Author(s):  
Alberto Godio ◽  
Francesca Pace ◽  
Andrea Vergnano
Keyword(s):  
Particle Swarm Optimization ◽  
Stochastic Approach ◽  
Model Parameters ◽  
Medium Term ◽  
Swarm Optimization ◽  
Community Mobility ◽  
Italian Regions ◽  
The World ◽  
Model Equations ◽  
Official Data

We applied a generalized SEIR epidemiological model to the recent SARS-CoV-2 outbreak in the world, with a focus on Italy and its Lombardy, Piedmont, and Veneto regions. We focused on the application of a stochastic approach in fitting the model parameters using a Particle Swarm Optimization (PSO) solver, to improve the reliability of predictions in the medium term (30 days). We analyzed the official data and the predicted evolution of the epidemic in the Italian regions, and we compared the results with the data and predictions of Spain and South Korea. We linked the model equations to the changes in people’s mobility, with reference to Google’s COVID-19 Community Mobility Reports. We discussed the effectiveness of policies taken by different regions and countries and how they have an impact on past and future infection scenarios.

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