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2021 Stability and Dynamic of HIV-1 Mathematical Model with Logistic Target Cell Growth, Treatment Rate, Cure Rate and Cell-to-cell Spread
Najmeh Akbari, Rasoul Asheghi, Maryam Nasirian
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Taiwanese J. Math. Advance Publication 1-31 (2021). DOI: 10.11650/tjm/211102

Abstract

One way of HIV infection spreading is through the cell division of infected cells by mitosis‎ ‎expressed in mathematical models as a logistic process‎. ‎Cell-to-cell transmission is another factor in the spread and speed of disease‎. ‎In this work‎, ‎we present a five-dimensional Ordinary Differential Equation model (ODE) with the logistic form for proliferation of uninfected cells‎, ‎cell-to-cell and virus-to-cell transmission rate‎, ‎two types of cellular and humoral immune responses‎, ‎the cure rate for returning infected cells to non-infectious cells‎, ‎and two treatment rates‎, ‎one for reducing infectious cells and the other for blocking free viruses‎. ‎We discuss the positivity and boundedness of solutions‎, ‎free-equilibrium points‎, ‎steady-state equilibrium points‎, ‎and stability by the Routh Hurwitz criterion‎. ‎The rate of reproduction is analyzed, ‎and the useful parameters for increasing or decreasing it are identified‎. ‎Numerical simulations are performed to investigate the dynamic behavior of model responses to treatment effects on disease.

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Najmeh Akbari. Rasoul Asheghi. Maryam Nasirian. "Stability and Dynamic of HIV-1 Mathematical Model with Logistic Target Cell Growth, Treatment Rate, Cure Rate and Cell-to-cell Spread." Taiwanese J. Math. Advance Publication 1 - 31, 2021. https://doi.org/10.11650/tjm/211102

Information

Published: 2021
First available in Project Euclid: 2 December 2021

Digital Object Identifier: 10.11650/tjm/211102

Subjects:
Primary: 34A34, 34C11, 34D20

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

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