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HIV-1 infection dynamics and optimal control with Crowley-Martin function response
Muhammad Naeem Jan1, Nigar Ali1, Gul Zaman1
1Department of Mathematics, University of Malakand, Chakdara, Dir(Lower), Khyber Pakhtunkhwa, Pakistan.
Computer Methods and Programs in Biomedicine
|May 11, 2020
Summary
This study models human immunodeficiency virus type-1 (HIV-1) infection dynamics. Mathematical analysis confirms that a basic reproductive number (R0) below 1 eradicates HIV-1, while R0 above 1 indicates persistent infection, guiding treatment strategies.
Area of Science:
- Mathematical Biology
- Virology
- Epidemiology
Background:
- Mathematical models are crucial for understanding Human Immunodeficiency Virus type-1 (HIV-1) infection dynamics.
- This study incorporates a Crowley-Martin function to represent the contact rate in the HIV-1 model.
Purpose of the Study:
- To analyze the local and global stability of the HIV-1 infection model.
- To develop strategies for preventing HIV-1 outbreaks in the community.
Main Methods:
- Numerical simulation using the Runge-Kutta fourth-order method for the nonlinear differential equations.
- Application of the Lyapunov-LaSalle invariance principle for global stability analysis.
- Utilization of Pontryagin's maximum principle for optimal control strategy development.
Main Results:
- The basic reproductive number (R0) is a critical threshold for HIV-1 eradication or persistence.
- Treatment significantly reduces infected cell density and viral load, preventing further virus production.
- Optimal control strategies effectively minimize infected cells and viruses while maximizing healthy cells.
Conclusions:
- HIV-1 infection is eradicated when R0 < 1 and persists when R0 > 1, with the chronic state being globally stable.
- The study validates the model's stability properties, including boundedness, positivity, and permanence.
- Developed optimal control strategies offer a pathway to manage HIV-1 infection by reducing viral load and infected cells.
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