Stability Analysis of Caputo Fractional Order Viral Dynamics of Hepatitis B Cellular Infection

Opoku, Michael O.; Wiah, Eric Neebo; Okyere, Eric; Sackitey, Albert Lanor; Essel, Emmanuel Kwame; Moore, Stephen E.

doi:10.3390/mca28010024

Cited by 4 publications

(3 citation statements)

References 19 publications

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“…In this section, sensitivity analysis of the parameters of model ( 10) will be investigated.The sensitivity analysis enables us to establish a connection between a model parameter and the basic reproductive number R 0 [12,24]. Specifically, the sensitivity index guides us to compute the relative change in a state variable when there is a change in parameter.…”

Section: Sensitivity Analysismentioning

confidence: 99%

Optimal Control for Fractional Order Dynamics of Tumor Growth

Nortey,

Fellah,

Akindeinde

et al. 2023

Preprint

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This paper concerns the analysis and optimal control of fractional order model of tumor cells and the body’s immunological response using Atangana-Baleanu-Caputo derivative fractional operator. The model consists of spawning cells (S), reposing cells (R) and tumor cell (T) where we have used the Hattaf-Yousfi functional response for the activation of the reposing cells in the presence of tumor cells. We investigate the model’s existence and stability and present numerical results using a modified predict-evaluate-correct-evaluate (PECE) method of Adams-Bashforth-Moulton. We also study the Fractional optimal control problem (FOCP) in order to minimize tumor cell density. The Fractional Pontryagin maximum principle (FPMP) is used to characterize the fractional optimal control problem and we implement the forward-backward PECE method to determine the extremals of the problem. We study the optimal control dynamics of tumor growth via several numerical simulations.

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Section: Sensitivity Analysismentioning

confidence: 99%

Optimal Control for Fractional Order Dynamics of Tumor Growth

Nortey,

Fellah,

Akindeinde

et al. 2023

Preprint

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“…The generalized analysis of modern calculus has attracted a lot of interest from mathematicians and physicists during the last few years. Due to its numerous applications in the engineering and physical sciences for simulating a variety of phenomena in mathematical physics, bioengineering, and chaos theory [15][16][17][18][19][20][21]. In fractional-order calculus mathematical models, the order of the derivatives and integrals is arbitrary.…”

Section: Introductionmentioning

confidence: 99%

Investigation of Fractional Order Dynamics of Tuberculosis under Caputo Operator

2023

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In this article, a new deterministic disease system is constructed to study the influence of treatment adherence as well as awareness on the spread of tuberculosis (TB). The suggested model is composed of six various classes, whose dynamics are discussed in the sense of the Caputo fractional operator. Firstly the model existence of a solution along with a unique solution is checked to determine whether the system has a solution or not. The stability of a solution is also important, so we use the Ulam–Hyers concept of stability. The approximate solution analysis is checked by the technique of Laplace transformation using the Adomian decomposition concept. Such a solution is in series form which is decomposed into smaller terms and the next term is obtained from the previous one. The numerical simulation is established for the obtained schemes using different fractional orders along with a comparison of classical derivatives. Such an analysis will be helpful for testing more dynamics instead of only one type of integer order discussion.

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“…Fractional calculus involves the use of non-integer derivatives and integrals. The application of fractional derivatives is becoming increasingly important in many fields, including physics, engineering, finance, and biology [16,17]. In physics and engineering, fractional derivatives are used to model and analyze complex systems that exhibit nonlinear behavior, such as viscoelastic materials, signal processing, and control systems [18].…”

Section: Introductionmentioning

confidence: 99%

Qualitative and Quantitative Analysis of Fractional Dynamics of Infectious Diseases with Control Measures

Alyobi

Jan

2023

Fractal Fract

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Infectious diseases can have a significant economic impact, both in terms of healthcare costs and lost productivity. This can be particularly significant in developing countries, where infectious diseases are more prevalent, and healthcare systems may be less equipped to handle them. It is recognized that the hepatitis B virus (HBV) infection remains a critical global public health issue. In this study, we develop a comprehensive model for HBV infection that includes vaccination and hospitalization through a fractional framework. It has been shown that the solutions of the recommended system of HBV infection are positive and bounded. We examine the steady states of the model and determine the basic reproduction number; denoted by R0. The qualitative and quantitative behavior of the model is demonstrated using mathematical skills and numerical techniques. It has been proved that the infection-free steady state of the system is locally asymptotically stable if R0<1 and unstable otherwise. Furthermore, the Ulam–Hyers stability (UHS) of the recommended fractional models is investigated and the significant conditions are provided. We present an iterative technique to visualize the dynamical behavior of the system. We perform different simulations to illustrate the effect of different input factors on the solution pathways of the system of HBV infection to conceptualize the role of parameters in the control and prevention of the infection.

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Stability Analysis of Caputo Fractional Order Viral Dynamics of Hepatitis B Cellular Infection

Cited by 4 publications

References 19 publications

Optimal Control for Fractional Order Dynamics of Tumor Growth

Optimal Control for Fractional Order Dynamics of Tumor Growth

Investigation of Fractional Order Dynamics of Tuberculosis under Caputo Operator

Qualitative and Quantitative Analysis of Fractional Dynamics of Infectious Diseases with Control Measures

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