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# The Influence of Saturated and Bilinear Incidence Functions on the Dynamical Behavior of HIV Model Using Galerkin Scheme Having a Polynomial of Order Two

Attaullah1,*, Kamil Zeb1, Abdullah Mohamed2

1 Department of Mathematics & Statistics, Bacha Khan University, Charsadda, 24461, Pakistan
2 Research Centre, Future University in Egypt, New Cairo, 11835, Egypt

* Corresponding Author: Attaullah. Email:

(This article belongs to the Special Issue: Differential Equations and New Methods in Mathematical Biology)

Computer Modeling in Engineering & Sciences 2023, 136(2), 1661-1685. https://doi.org/10.32604/cmes.2023.023059

## Abstract

Mathematical modelling has been extensively used to measure intervention strategies for the control of contagious conditions. Alignment between different models is pivotal for furnishing strong substantiation for policymakers because the differences in model features can impact their prognostications. Mathematical modelling has been widely used in order to better understand the transmission, treatment, and prevention of infectious diseases. Herein, we study the dynamics of a human immunodeficiency virus (HIV) infection model with four variables: S (t), I (t), C (t), and A (t) the susceptible individuals; HIV infected individuals (with no clinical symptoms of AIDS); HIV infected individuals (under ART with a viral load remaining low), and HIV infected individuals (with two different incidence functions (bilinear and saturated incidence functions). A novel numerical scheme called the continuous Galerkin-Petrov method is implemented for the solution of the model. The influence of different clinical parameters on the dynamical behavior of S (t), I (t), C (t) and A (t) is described and analyzed. All the results are depicted graphically. On the other hand, we explore the time-dependent movement of nanofluid in porous media on an extending sheet under the influence of thermal radiation, heat flux, hall impact, variable heat source, and nanomaterial. The flow is considered to be 2D, boundary layer, viscous, incompressible, laminar, and unsteady. Sufficient transformations turn governing connected PDEs into ODEs, which are solved using the proposed scheme. To justify the envisaged problem, a comparison of the current work with previous literature is presented.

## Keywords

APA Style
Attaullah, , Zeb, K., Mohamed, A. (2023). The influence of saturated and bilinear incidence functions on the dynamical behavior of HIV model using galerkin scheme having a polynomial of order two. Computer Modeling in Engineering & Sciences, 136(2), 1661-1685. https://doi.org/10.32604/cmes.2023.023059
Vancouver Style
Attaullah , Zeb K, Mohamed A. The influence of saturated and bilinear incidence functions on the dynamical behavior of HIV model using galerkin scheme having a polynomial of order two. Comput Model Eng Sci. 2023;136(2):1661-1685 https://doi.org/10.32604/cmes.2023.023059
IEEE Style
Attaullah, K. Zeb, and A. Mohamed "The Influence of Saturated and Bilinear Incidence Functions on the Dynamical Behavior of HIV Model Using Galerkin Scheme Having a Polynomial of Order Two," Comput. Model. Eng. Sci., vol. 136, no. 2, pp. 1661-1685. 2023. https://doi.org/10.32604/cmes.2023.023059

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