TITLE:
On Quantitative Approach to Parametric Identifiability of Dual HIV-Parasitoid Infectivity Model
AUTHORS:
Bassey E. Bassey, Lebedev K. Andreyevich
KEYWORDS:
Parametric-Identifiability, Algebraic-Identifiability, Observed-State-Variable, Stratified-Trend, Validation
JOURNAL NAME:
Open Access Library Journal,
Vol.3 No.8,
August
19,
2016
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.