A novel within-host model of HIV and nutrition

Archana N. Timsina; Yuganthi R. Liyanage; Maia Martcheva; Necibe Tuncer; Archana N. Timsina; Yuganthi R. Liyanage; Maia Martcheva; Necibe Tuncer

doi:10.3934/mbe.2024246

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 4: 5577-5603. doi: 10.3934/mbe.2024246

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A novel within-host model of HIV and nutrition

1.
Department of Population Health and Pathobiology, North Carolina State University, Raleigh 27607, USA
2.
Department of Mathematical Sciences, Florida Atlantic University, Boca Raton 33431, USA
3.
Department of Mathematics, University of Florida, Gainesville 32611, USA

Received: 18 January 2024 Revised: 17 March 2024 Accepted: 29 March 2024 Published: 09 April 2024

In this paper we develop a four compartment within-host model of nutrition and HIV. We show that the model has two equilibria: an infection-free equilibrium and infection equilibrium. The infection free equilibrium is locally asymptotically stable when the basic reproduction number $ \mathcal{R}_0 < 1 $, and unstable when $ \mathcal{R}_0 > 1 $. The infection equilibrium is locally asymptotically stable if $ \mathcal{R}_0 > 1 $ and an additional condition holds. We show that the within-host model of HIV and nutrition is structured to reveal its parameters from the observations of viral load, CD4 cell count and total protein data. We then estimate the model parameters for these 3 data sets. We have also studied the practical identifiability of the model parameters by performing Monte Carlo simulations, and found that the rate of clearance of the virus by immunoglobulins is practically unidentifiable, and that the rest of the model parameters are only weakly identifiable given the experimental data. Furthermore, we have studied how the data frequency impacts the practical identifiability of model parameters.
- HIV,
- within-host model,
- nutrition,
- structural identifiability,
- practical identifiability
Citation: Archana N. Timsina, Yuganthi R. Liyanage, Maia Martcheva, Necibe Tuncer. A novel within-host model of HIV and nutrition[J]. Mathematical Biosciences and Engineering, 2024, 21(4): 5577-5603. doi: 10.3934/mbe.2024246

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Abstract

In this paper we develop a four compartment within-host model of nutrition and HIV. We show that the model has two equilibria: an infection-free equilibrium and infection equilibrium. The infection free equilibrium is locally asymptotically stable when the basic reproduction number $ \mathcal{R}_0 < 1 $, and unstable when $ \mathcal{R}_0 > 1 $. The infection equilibrium is locally asymptotically stable if $ \mathcal{R}_0 > 1 $ and an additional condition holds. We show that the within-host model of HIV and nutrition is structured to reveal its parameters from the observations of viral load, CD4 cell count and total protein data. We then estimate the model parameters for these 3 data sets. We have also studied the practical identifiability of the model parameters by performing Monte Carlo simulations, and found that the rate of clearance of the virus by immunoglobulins is practically unidentifiable, and that the rest of the model parameters are only weakly identifiable given the experimental data. Furthermore, we have studied how the data frequency impacts the practical identifiability of model parameters.

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