Abstract
We analyzed the fundamental issues related to the development of mathematical models in immunology, i.e., the structural and practical identifiability of the models in mathematical immunology. To this end, the differential algebraic techniques and Bayesian approach implemented in StructuralIdentifiability.jl and DynamicHMC.jl Julia-based packages, respectively, are used. The experimental data on kinetics of viral load and cytotoxic T lymphocyte (CTL) response characterizing an acute lymphocytic choriomeningitis virus (LCMV) infection in mice were considered. Although the models differ in terms of one to three parameters, the structural identifiability strongly depends on details of observability and initial determination of the state variables. The estimated via a Bayesian approach posterior distributions for model parameter characterize the rates of interactions underlying the acute infection development. The results of the data assimilation on LCMV-CTL kinetics suggest that a bilinear-type description of the virus-induced CTL expansion and the CTL-driven virus elimination need to be refined to a bounded-rate (e.g., Michaelis–Menten) type parameterizations.
Funding statement: The reported study was funded by the Russian Science Foundation, grant No. 23-11-00116.
References
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Articles in the same Issue
- Frontmatter
- Preface
- Algorithms of variational data assimilation for problems of ocean dynamics
- Identifiability of basic models and parameters in mathematical immunology
- Analysis of the error of difference solutions as a basis for improving accuracy
- Numerical method for hydraulic fracture propagation in a two-phase poroelastoplasticity model
- The method of adjoint equations for solving the problem of quasi-geostrophic currents in a two-layer ocean periodic channel
Articles in the same Issue
- Frontmatter
- Preface
- Algorithms of variational data assimilation for problems of ocean dynamics
- Identifiability of basic models and parameters in mathematical immunology
- Analysis of the error of difference solutions as a basis for improving accuracy
- Numerical method for hydraulic fracture propagation in a two-phase poroelastoplasticity model
- The method of adjoint equations for solving the problem of quasi-geostrophic currents in a two-layer ocean periodic channel