Focus point: cancer and HIV/AIDS dynamics—from optimality to modelling

Debbouche, Amar; Nieto, Juan J.; Torres, Delfim F. M.

doi:10.1140/epjp/s13360-021-01154-z

Cited by 9 publications

(4 citation statements)

References 15 publications

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“…where d k = 0 for k < 0 or k > n. Therefore, the matrix element index is greater than n, or the negative index must be replaced by zero. The k-level Hurwitz determinant, denoted by detH k ; k = 1, 2, • • • , n, formed from the Hurwitz matrix (9), is defined as follows: 46]). The polynomial root (7) has a real part of its root that is negative if and only if the inequality (3) is fulfilled and…”

Section: Preliminariesmentioning

confidence: 99%

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The Stability of Solutions of the Variable-Order Fractional Optimal Control Model for the COVID-19 Epidemic in Discrete Time

Boukhobza,

Debbouche,

Shangerganesh

et al. 2024

Mathematics

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This article introduces a discrete-time fractional variable order over a SEIQR model, incorporated for COVID-19. Initially, we establish the well-possedness of solution. Further, the disease-free and the endemic equilibrium points are determined. Moreover, the local asymptotic stability of the model is analyzed. We develop a novel discrete fractional optimal control problem tailored for COVID-19, utilizing a discrete mathematical model featuring a variable order fractional derivative. Finally, we validate the reliability of these analytical findings through numerical simulations and offer insights from a biological perspective.

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Section: Preliminariesmentioning

confidence: 99%

“…Mathematical models that depict infectious diseases are pivotal in both theoretical understanding and practical application [8][9][10][11][12][13]. Developing and scrutinizing models of this nature aids in comprehending the mechanisms of transmission and disease characteristics.…”

Section: Introductionmentioning

confidence: 99%

The Stability of Solutions of the Variable-Order Fractional Optimal Control Model for the COVID-19 Epidemic in Discrete Time

Boukhobza,

Debbouche,

Shangerganesh

et al. 2024

Mathematics

Self Cite

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“…Different types of models have been presented for this kind of circumstance. For more than two decades, mathematical models of virus and cell interactions have been developed, see for instance [6][7][8][9][10]. There are several sorts of diseases, and compartmental models range from the straightforward SIR model to more complicated ones.…”

Section: Introductionmentioning

confidence: 99%

Solvability and Ulam-Hyers stability analysis for nonlinear piecewise fractional cancer dynamic systems

Khan,

Shah,

Debbouche

et al. 2024

Phys. Scr.

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We examine a nonlinear dynamical model that depicts the interaction between cancerous cells and an oncolytic virus. For best modelling the disease, we use the Caputo fractional derivative in piecewise approaches. By employing piecemeal techniques, we treat a compartment in the body that contains infectious and non-infectious cells. More precisely, the solvability and Ulam-Hyers (U-H) stability results are considered using standard concepts. Further, to support our investigation with numerical results, we apply the Euler method to develop an approximation solution. It connected with numerous graphical representations of the system using various arbitrary ordering and varying values of the isolation parameters. Here we remark that the multi-step behavior that certain problems exhibit, is one of important issues naturally. This paper introduces the idea of piecewise derivative with the goal of modeling real-world issues that follow multiples processes. With the help of the used approach, we investigate the cancer disease model and its transmission dynamical behavior with crossover effect.

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“…The estimation of this type of sets is important in the field of control for cancer dynamics, since it provides the set of possible initial health indicators, for which a treatment protocol exists allowing to heal the patient. The paper 14 summarizes shortly approach of optimality tools and modeling of cancer by ODE systems. Lastly, appear two different types of tools used to study growth of cancer.…”

Section: Introductionmentioning

confidence: 99%

Control of tumor growth modeled by system of PDE, numerical analysis of optimality conditions

Nowakowski

Krawczyk

2022

Math Methods in App Sciences

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We analyze a mathematical model of a tumor that includes the interactions among tumor cells (live or dead), macrophages, endothelial cells, and the cytokines based on a system of partial differential equations which describes inhibition of tumor growth by granulocyte‐macrophage colony‐stimulating factor (GM‐CSF) treatment. The aim of the model is to predict the growth of the tumor volume under partial blocking of hypoxia‐inducible factor (HIF)‐1 or stabilization of HIF‐2, with injection of GM‐CSF. It was assumed that tumor is a spherical and the treatment by GM‐CSF is not optimized. In this paper, we do not assume that tumor is a spherical model and we develop a dual dynamic programming approach to formulate a verification condition of an approximate treatment for an injection of GM‐CSF. Next, we analyze numerically an ε$$ \varepsilon $$‐optimal treatment.

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Focus point: cancer and HIV/AIDS dynamics—from optimality to modelling

Cited by 9 publications

References 15 publications

The Stability of Solutions of the Variable-Order Fractional Optimal Control Model for the COVID-19 Epidemic in Discrete Time

The Stability of Solutions of the Variable-Order Fractional Optimal Control Model for the COVID-19 Epidemic in Discrete Time

Solvability and Ulam-Hyers stability analysis for nonlinear piecewise fractional cancer dynamic systems

Control of tumor growth modeled by system of PDE, numerical analysis of optimality conditions

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