A numerical algorithm for constructing an individual mathematical model of HIV dynamics at cellular level
Abstract
In this paper a problem of specifying HIV-infection parameters and immune response using additional measurements of the concentrations of the T-lymphocytes, the free virus and the immune effectors at fixed times for a mathematical model of HIV dynamics is investigated numerically. The problem of the parameter specifying of the mathematical model (an inverse problem) is reduced to a problem of minimizing an objective function describing the deviation of the simulation results from the experimental data. A genetic algorithm for solving the least squares function minimization problem is implemented and investigated. The results of a numerical solution of the inverse problem are analyzed.
Funding statement: The stability investigation (Section 3) was supported by the grant No. MK-1214.2017.1 of the President of Russian Federation, the analysis of numerical solving of the inverse problem (Section 4) was supported by the grant No. 18-71-10044 of Russian Science Foundation, the investigation of confidence intervals (Section 5) was supported by the grant No. AFOSR FA9550-15-1-0298 of U.S. Air Force Office of Scientific Research.
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- TGV-based multiplicative noise removal approach: Models and algorithms
- Design criteria for geometrical calibration phantoms in fan and cone beam CT systems
- Under-relaxed quasi-Newton acceleration for an inverse fixed-point problem coming from Positron Emission Tomography
- An adaptive iteration reconstruction method for limited-angle CT image reconstruction
- Accuracy estimates of regularization methods and conditional well-posedness of nonlinear optimization problems
- A non-smooth and non-convex regularization method for limited-angle CT image reconstruction
- Optimization analysis of the inverse coefficient problem for the nonlinear convection-diffusion-reaction equation
- A finite difference method for the very weak solution to a Cauchy problem for an elliptic equation
- A numerical algorithm for constructing an individual mathematical model of HIV dynamics at cellular level
Artikel in diesem Heft
- Frontmatter
- TGV-based multiplicative noise removal approach: Models and algorithms
- Design criteria for geometrical calibration phantoms in fan and cone beam CT systems
- Under-relaxed quasi-Newton acceleration for an inverse fixed-point problem coming from Positron Emission Tomography
- An adaptive iteration reconstruction method for limited-angle CT image reconstruction
- Accuracy estimates of regularization methods and conditional well-posedness of nonlinear optimization problems
- A non-smooth and non-convex regularization method for limited-angle CT image reconstruction
- Optimization analysis of the inverse coefficient problem for the nonlinear convection-diffusion-reaction equation
- A finite difference method for the very weak solution to a Cauchy problem for an elliptic equation
- A numerical algorithm for constructing an individual mathematical model of HIV dynamics at cellular level