An Evaluation of Propagation of the HIV-Infected Cells via Optimization Problem

Granata, Donatella; Lorenzi, Luca

doi:10.3390/math10122021

Cited by 2 publications

(5 citation statements)

References 30 publications

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“…Proof. In this part, we have proven the existence and smoothness of the defined functions in Equation ( 25), the existence of a system of solutions for the model in Equation (11), and Equation ( 12) has been illustrated. It has been assumed that N(t),T(t),I(t) and C(t) are bounded N(t) ≤ θ 1 , T(t) ≤ θ 2 , I(t) ≤ θ 3 and C(t) ≤ θ 4 .…”

Section: Existence and Uniqueness Of Solutions Of The Cancer Chemothe...mentioning

confidence: 92%

“…This section is devoted to the investigation of the uniqueness and existence of the solutions of our Caputo-Fabrizio fraction model of cancer chemotherapy in Equation (11) with the initial conditions mentioned in Equation (12). To seek this goal, the fix-point theory has been used [88,89].…”

Section: Existence and Uniqueness Of Solutions Of The Cancer Chemothe...mentioning

confidence: 99%

“…It is noteworthy to mention that the proposed control method can be exerted by clinicians to find the optimal amount of drug based on the patient's state to eradicate tumor cells. To this aim, clinicians must first obtain the patients' parameters by measuring the patient's state and fit the logged data to the mathematical model of the patient given in Equation (11). Then, using the mathematical model, the control agent should be pre-trained.…”

Section: Scenario Cmentioning

confidence: 99%

“…Mathematical models have been used as valuable tools in understanding the transmission dynamics of cancers [10]. Actually, mathematical modeling could play a pivotal role in the understanding of the disease's dynamics [11][12][13][14][15]. One common approach to modeling cancer is to use ordinary differential equations (ODEs), which are used to describe the time evolution of a system.…”

Section: Introductionmentioning

confidence: 99%

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A New Fuzzy Reinforcement Learning Method for Effective Chemotherapy

et al. 2023

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A key challenge for drug dosing schedules is the ability to learn an optimal control policy even when there is a paucity of accurate information about the systems. Artificial intelligence has great potential for shaping a smart control policy for the dosage of drugs for any treatment. Motivated by this issue, in the present research paper a Caputo–Fabrizio fractional-order model of cancer chemotherapy treatment was elaborated and analyzed. A fix-point theorem and an iterative method were implemented to prove the existence and uniqueness of the solutions of the proposed model. Afterward, in order to control cancer through chemotherapy treatment, a fuzzy-reinforcement learning-based control method that uses the State-Action-Reward-State-Action (SARSA) algorithm was proposed. Finally, so as to assess the performance of the proposed control method, the simulations were conducted for young and elderly patients and for ten simulated patients with different parameters. Then, the results of the proposed control method were compared with Watkins’s Q-learning control method for cancer chemotherapy drug dosing. The results of the simulations demonstrate the superiority of the proposed control method in terms of mean squared error, mean variance of the error, and the mean squared of the control action—in other words, in terms of the eradication of tumor cells, keeping normal cells, and the amount of usage of the drug during chemotherapy treatment.

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Section: Existence and Uniqueness Of Solutions Of The Cancer Chemothe...mentioning

confidence: 92%

Section: Existence and Uniqueness Of Solutions Of The Cancer Chemothe...mentioning

confidence: 99%

Section: Scenario Cmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A New Fuzzy Reinforcement Learning Method for Effective Chemotherapy

et al. 2023

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“…Wang et al 9 explored the dynamics of an age-structured hybrid HIV/AIDS model with self-protection and media coverage. Granata et al 10 used an optimization technique to investigate the propagation of HIV-infected cells. Yuzbasi and Karacayir 11 used the Galerkin scheme in order to solve the HIV transmission model.…”

Section: Introductionmentioning

confidence: 99%

Transmission dynamics of a novel HIV/AIDS model through a higher-order Galerkin time discretization scheme

Attaullah

Zeb

Khan

et al. 2023

Sci Rep

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There are numerous contagious diseases caused by pathogenic microorganisms, including bacteria, viruses, fungi, and parasites, that have the propensity to culminate in fatal consequences. A communicable disease is an illness caused by a contagion agent or its toxins and spread directly or indirectly to a susceptible animal or human host by an infected person, animal, vector, or immaterial environment. Human immunodeficiency virus (HIV) infection, hepatitis A, B, and C, and measles are all examples of communicable diseases. Acquired immunodeficiency syndrome (AIDS) is a communicable disease caused by HIV infection that has become the most severe issue facing humanity. The research work in this paper is to numerically explore a mathematical model and demonstrate the dynamics of HIV/AIDS disease transmission using a continuous Galerkin–Petrov time discretization of a higher-order scheme, specifically the cGP(2)-scheme. Depict a graphical and tabular comparison between the outcomes of the mentioned scheme and those obtained through other classical schemes that exist in the literature. Further, a comparison is performed relative to the well-known fourth-order Ruge–Kutta (RK4) method with different step sizes. By contrast, the suggested approach provided more accurate results with a larger step size than RK4 with a smaller step size. After validation and confirmation of the suggested scheme and code, we implement the method to the extended model by introducing a treatment rate and show the impact of various non-linear source terms for the generation of new cells. We also determined the basic reproduction number and use the Routh-Hurwitz criterion to assess the stability of disease-free and unique endemic equilibrium states of the HIV model.

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An Evaluation of Propagation of the HIV-Infected Cells via Optimization Problem

Cited by 2 publications

References 30 publications

A New Fuzzy Reinforcement Learning Method for Effective Chemotherapy

A New Fuzzy Reinforcement Learning Method for Effective Chemotherapy

Transmission dynamics of a novel HIV/AIDS model through a higher-order Galerkin time discretization scheme

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