Ghana Numerical Analysis Day

A special issue of Mathematical and Computational Applications (ISSN 2297-8747).

Deadline for manuscript submissions: closed (15 March 2023) | Viewed by 6532

Special Issue Editors

Department of Mathematics, University of Cape Coast, Cape Coast, Ghana
Interests: space-time methods; partial differential equations; finite element methods; surface partial differential equations; numerical linear algebra
Department of Mathematics, University of Cape Coast, Cape Coast, Ghana
Interests: homogenization
Department of Data Science, Ramapo College of New Jersey, Mahwah, NJ 07430, USA
Interests: stochastic analysis; machine learning and scientific computing with applications to finance, health sciences and geophysics
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Special Issue Information

Dear Colleagues,

This Special Issue will collect contributions from the Ghana Numerical Analysis Day (https://bit.ly/3zwtpdu). Papers considered to fit the scope of the journal (Mathematical and Computational Applications) and to be of exceptional quality after evaluation by the reviewers will be published free of charge.

Dr. Stephen Moore
Prof. Dr. Emmanuel K. Essel
Dr. Osei K. Tweneboah
Guest Editors

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Published Papers (4 papers)

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Research

23 pages, 939 KiB  
Article
Stability Analysis of Caputo Fractional Order Viral Dynamics of Hepatitis B Cellular Infection
by Michael O. Opoku, Eric N. Wiah, Eric Okyere, Albert L. Sackitey, Emmanuel K. Essel and Stephen E. Moore
Math. Comput. Appl. 2023, 28(1), 24; https://doi.org/10.3390/mca28010024 - 09 Feb 2023
Cited by 2 | Viewed by 1248
Abstract
We present a Caputo fractional order mathematical model that describes the cellular infection of the Hepatitis B virus and the immune response of the body with Holling type II functional response. We study the existence of unique positive solutions and the local and [...] Read more.
We present a Caputo fractional order mathematical model that describes the cellular infection of the Hepatitis B virus and the immune response of the body with Holling type II functional response. We study the existence of unique positive solutions and the local and global stability of virus-free and endemic equilibria. Finally, we present numerical results using the Adam-type predictor–corrector iterative scheme. Full article
(This article belongs to the Special Issue Ghana Numerical Analysis Day)
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18 pages, 579 KiB  
Article
Global Stability of Multi-Strain SEIR Epidemic Model with Vaccination Strategy
by Zakaria Yaagoub and Karam Allali
Math. Comput. Appl. 2023, 28(1), 9; https://doi.org/10.3390/mca28010009 - 07 Jan 2023
Cited by 5 | Viewed by 1682
Abstract
A three-strain SEIR epidemic model with a vaccination strategy is suggested and studied in this work. This model is represented by a system of nine nonlinear ordinary differential equations that describe the interaction between susceptible individuals, strain-1-vaccinated individuals, strain-1-exposed individuals, strain-2-exposed individuals, strain-3-exposed [...] Read more.
A three-strain SEIR epidemic model with a vaccination strategy is suggested and studied in this work. This model is represented by a system of nine nonlinear ordinary differential equations that describe the interaction between susceptible individuals, strain-1-vaccinated individuals, strain-1-exposed individuals, strain-2-exposed individuals, strain-3-exposed individuals, strain-1-infected individuals, strain-2-infected individuals, strain-3-infected individuals, and recovered individuals. We start our analysis of this model by establishing the existence, positivity, and boundedness of all the solutions. In order to show global stability, the model has five equilibrium points: The first one stands for the disease-free equilibrium, the second stands for the strain-1 endemic equilibrium, the third one describes the strain-2 equilibrium, the fourth one represents the strain-3 equilibrium point, and the last one is called the total endemic equilibrium. We establish the global stability of each equilibrium point using some suitable Lyapunov function. This stability depends on the strain-1 reproduction number R01, the strain-2 basic reproduction number R02, and the strain-3 reproduction number R03. Numerical simulations are given to confirm our theoretical results. It is shown that in order to eradicate the infection, the basic reproduction numbers of all the strains must be less than unity. Full article
(This article belongs to the Special Issue Ghana Numerical Analysis Day)
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20 pages, 1031 KiB  
Article
Stochastic Capital–Labor Lévy Jump Model with the Precariat Labor Force
by Jaouad Danane
Math. Comput. Appl. 2022, 27(6), 93; https://doi.org/10.3390/mca27060093 - 10 Nov 2022
Cited by 1 | Viewed by 1044
Abstract
In this work, we study a capital–labor model by considering the interaction between the new proposed and the confirmed free jobs, the precariat labor force, and the mature labor force by introducing Brownian motion and Lévy noise. Moreover, we illustrate the well-posedness of [...] Read more.
In this work, we study a capital–labor model by considering the interaction between the new proposed and the confirmed free jobs, the precariat labor force, and the mature labor force by introducing Brownian motion and Lévy noise. Moreover, we illustrate the well-posedness of the solution. In addition, we establish the conditions of the extinction of both the free jobs and labor force; subsequently, we prove the persistence of only the free jobs, and we also show the conditions of the persistence of both the free jobs and labor force. Finally, we validate our theoretical finding by numerical simulation by building a new stochastic Runge–Kutta method. Full article
(This article belongs to the Special Issue Ghana Numerical Analysis Day)
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13 pages, 530 KiB  
Article
HIV Dynamics with a Trilinear Antibody Growth Function and Saturated Infection Rate
by Fatima Ezzahra Fikri and Karam Allali
Math. Comput. Appl. 2022, 27(5), 85; https://doi.org/10.3390/mca27050085 - 08 Oct 2022
Cited by 1 | Viewed by 1102
Abstract
The objective of this paper is to study a new mathematical model describing the human immunodeficiency virus (HIV). The model incorporates the impacts of cytotoxic T lymphocyte (CTL) immunity and antibodies with trilinear growth functions. The boundedness and positivity of solutions for non-negative [...] Read more.
The objective of this paper is to study a new mathematical model describing the human immunodeficiency virus (HIV). The model incorporates the impacts of cytotoxic T lymphocyte (CTL) immunity and antibodies with trilinear growth functions. The boundedness and positivity of solutions for non-negative initial data are proved, which is consistent with biological studies. The local stability of the equilibrium is established. Finally, numerical simulations are presented to support our theoretical findings. Full article
(This article belongs to the Special Issue Ghana Numerical Analysis Day)
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