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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.

Multiplicity of new cases of HIV/AIDS and its allied infectious diseases daunted by lack of proper parametric estimation necessitated this present work. Formulated using ordinary differential equation was a five-dimensional (5D) differential mathematical model with which compatibility of optimal control strategy for dual (viral load and parasitoid-pathogen) infectivity in the blood plasma was investigated. Discretization method indicated the incompatibility of the model due to large error derivatives. The study using numerical method established treatment set point with which we explored the variation of predominant model parameters and thereof investigated the maximization of uninfected healthy CD4 T cell count as well as the de-replication of viruses following the consistent administration of reverse transcriptase inhibitor from set point. Presented was a series of numerical calculations obtained using well-known Runge-Kutter of order of precision 4, in Mathcad platform. Analysis of simulated parameters showed that distortion of replication viruses and de-transmutation of susceptible CD4 T cells by viruses via chemotherapy led to restoration and gradual increase of healthy blood plasma, with near zero declination of both viral load and parasitoid-pathogen within chemotherapy validity time frame. The model was worthy in the study of treatment analysis of dual HIV—pathogen infection and thereof recommended for other related dual infectious diseases.