Open Access Library Journal
How to cite this paper: Bassey, B.E. and Andreyevich, L.K. (2016) On Quantitative Approach to Parametric Identifiability of
Dual HIV-Parasitoid Infectivity Model. Open Access Library Journal, 3: e2931. http://dx.doi.org/10.4236/oalib.1102931
On Quantitative Approach to Parametric
Identifiability of Dual HIV-Parasitoid
Infectivity Model
Bassey E. Bassey
1*
, Lebedev K. Andreyevich
2
1
Department of Mathematical and Computer Methods, Kuban State University, Krasnodar, Russia
2
Department of Computational Mathematics and Informatics, Kuban State University, Krasnodar, Russia
Received 28 July 2016; accepted 16 August 2016; published 19 August 2016
Copyright © 2016 by authors and OALib.
This work is licensed under the Creative Commons Attribution International License (CC BY).
http://creativecommons.org/licenses/by/4.0/
Abstract
In this present paper, we proposed and formulated a quantitative approach to parametric identi-
fiability of dual HIV-parasitoid-pathogen infectivity in a novel 5-dimensional algebraic identifia-
bility HIV dynamic model, as against popular 3-dimensional HIV/AIDS models. In this study, ordi-
nary 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 equa-
tions. The derived model consists of twelve identifiable parameters from two observable state va-
riables (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 ( k β and dδ ) are identifiable. Validation and simulations of the model
outcome were examined using well-known Runge-Kutter of order of precision 4, in Mathcad sur-
face, 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,
*
Corresponding author.