On Quantitative Approach to Parametric Identifiability of Dual HIV-Parasitoid Infectivity Model - Open Access Library Journal

OALibJ > Vol.3 No.8, August 2016

On Quantitative Approach to Parametric Identifiability of Dual HIV-Parasitoid Infectivity Model ()

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DOI: 10.4236/oalib.1102931 1,071 Downloads 1,636 Views Citations

Author(s)

Bassey E. Bassey^1*, Lebedev K. Andreyevich²

Affiliation(s)

¹Department of Mathematical and Computer Methods, Kuban State University, Krasnodar, Russia.
²Department of Computational Mathematics and Informatics, Kuban State University, Krasnodar, Russia.

ABSTRACT

In this present paper, we proposed and formulated a quantitative approach to parametric identifiability of dual HIV-parasitoid-pathogen infectivity in a novel 5-dimensional algebraic identifiability HIV dynamic model, as against popular 3-dimensional HIV/AIDS models. In this study, ordinary differential equations were explored with analysis conducted via two improved developed techniques—the method of higher-order derivatives (MHOD) and method of multiple time point (MMTP), with the later proven to be more compatible and less intensive. Identifiability function was introduced to these techniques, which led to the derivation of the model identifiability equations. The derived model consists of twelve identifiable parameters from two observable state variables (viral load and parasitoid-pathogen), as against popular six identifiable parameters from single variable; also, the minimal number of measurements required for the determination of the complete identifiable parameters was established. Analysis of the model indicated that, of the twelve parameters, ten are independently identifiable, while only the products of two pairs of the remaining parameters (

and

) are identifiable. Validation and simulations of the model outcome were examined using well-known Runge-Kutter of order of precision 4, in Mathcad surface, with each parameter viewed as unknown and results discussed in stratified trend, which simplified the sequence of magnitude of the identifiable parameters. By the result, identifiable parameters were established which were core to a 5-D dual HIV dynamic model. Therefore, the study though centered on dual HIV-pathogen infectivity, its adoption for other nonlinear dynamic models was readily achievable.

KEYWORDS

Parametric-Identifiability, Algebraic-Identifiability, Observed-State-Variable, Stratified-Trend, Validation

Share and Cite:

Bassey, B. and Andreyevich, L. (2016) On Quantitative Approach to Parametric Identifiability of Dual HIV-Parasitoid Infectivity Model. Open Access Library Journal, 3, 1-14. doi: 10.4236/oalib.1102931.

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