Identifiability and Parameter Estimation of Within-Host Model of HIV with Immune Response

This study examines the interactions between healthy target cells, infected target cells, virus particles, and immune cells within an HIV model. The model exhibits two equilibrium points: an infection-free equilibrium and an infection equilibrium. Stability analysis shows that the infection-free equilibrium is locally asymptotically stable when ${\mathcal{R}}_0<1$. Further, it is unstable when ${\mathcal{R}}_0>1$. The infection equilibrium is locally asymptotically stable when ${\mathcal{R}}_0>1$. The structural and practical identifiabilities of the within-host model for HIV infection dynamics were investigated using differential algebra techniques and Monte Carlo simulations. The HIV model was structurally identifiable by observing the total uninfected and infected target cells, immune cells, and viral load. Monte Carlo simulations assessed the practical identifiability of parameters. The production rate of target cells $\left(\lambda \right)$, the death rate of healthy target cells $\left(d\right)$, the death rate of infected target cells $\left(\delta \right)$, and the viral production rate by infected cells $\left(\pi \right)$ were practically identifiable. The rate of infection of target cells by the virus $\left(\beta \right)$, the death rate of infected cells by immune cells $\left(\Psi \right)$, and antigen-driven proliferation rate of immune cells $\left(b\right)$ were not practically identifiable. Practical identifiability was constrained by the noise and sparsity of the data. Analysis shows that increasing the frequency of data collection can significantly improve the identifiability of all parameters. This highlights the importance of optimal data sampling in HIV clinical studies, as it determines the best time points, frequency, and the number of sample points required to accurately capture the dynamics of the HIV infection within a host.