Examining HIV progression mechanisms via mathematical approaches

Wenjing Zhang,Ramnath Bhagavath,Neal Madras,Jane Heffernan

doi:10.5206/mase/10774

Wenjing Zhang, Ramnath Bhagavath + Show 2 more

Open Access

https://doi.org/10.5206/mase/10774

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Abstract

   The progression of HIV infection to AIDS is unclear and under examined. Many mechanisms have been proposed, including a decline in immune response, increase in replication rate, involution of the thymus, syncytium inducing capacity, activation of the latently infected cell pool, chronic activation of the immune system, and the ability of the virus to infect other immune system cells. The significance of each mechanism in combination has not been studied. We develop a simple HIV viral dynamics model incorporating proposed mechanisms as parameters that are allowed to vary. In the entire parameter space, we derive two formulae for the basic reproduction number (R0) by considering the infection starting with a single infected CD4 T cell and a single virion, respectively. We show that both formulae are equivalent. We derive analytical conditions for the occurrence of backward and forward bifurcations. To investigate the influence of the proposed mechanisms to the HIV progression, we perform uncertainty and sensitivity analysis for all parameters and conduct a bifurcation analysis on all parameters that are shown to be significant, in combination, to explore various HIV/AIDS progression dynamics.  

Highlights

HIV can infect all cells in the immune system and the central nervous system which have a CD4 receptor on the cell surface, including T helper cells, monocytes, macrophages, and dendritic cells
Several factors such as a decline in immune response [23, 22], increase in replication rate [8, 41, 60], involution of the thymus [75, 7], syncytium inducing capacity [23, 40], activation of the latently infected cell pool [27, 20, 58, 14, 59, 10], chronic activation of the immune system [51, 38, 61, 35, 30], and the ability of the virus to infect other immune system cells [50, 70, 67, 19] have been associated with HIV progression to AIDS
The Latin hypercube sampling (LHS)-Partial Rank Correlation Coefficients (PRCC) results suggest that an increase in CD4 T-cell count and a decrease in HIV viral load are significantly influenced by the death rate of the infected cells killed by immune response (a) and the proliferation rate and addition of infected macrophages, monocytes and dendritic cells and activation of latently infected cells (r), but that HIV progression to AIDS is mostly determined by viral clearance rate (u) and the viral production rate

Summary

Introduction

HIV can infect all cells in the immune system and the central nervous system which have a CD4 receptor on the cell surface, including T helper cells, monocytes, macrophages, and dendritic cells. The model consists of three ordinary differential equations describing the uninfected and productively infected target cell populations, and the infectious HIV viral load. Similar to the basic model of virus dynamics [49], uninfected cells either die (rate d) or become infected by HIV infection (βxv). We assume that all model parameters may change slowly with progression of the infection This assumption allows us to study the key underlying mechanisms related to HIV progression to AIDS. Since the characteristic equation P (L) = 0 has one negative root and the other parameters satisfy Lemma 3.2, the proof is obvious.

Uncertainty and Sensitivity Analysis

Bifurcation Analysis and Numerical Simulations

Discussion

BT 0 subcritical Hopf