Fractional order mathematical model of Ebola virus under Atangana–Baleanu–Caputo operator

Yadav, Pooja; Jahan, Shah; Nisar, Kottakkaran Sooppy

doi:10.1016/j.rico.2023.100332

Cited by 5 publications

(2 citation statements)

References 35 publications

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“…In this Section, Numerical simulations are carried to evaluate how accurate and dependable the method is. Recently, Mathematical modelling has been investigated with Numerical simulations [24][25][26]. The Mathematical expressions derived in this paper have been cross-referenced with a highly precise numerical solution acquired through MATLAB (pdex4) software.…”

Section: Comparison Of Analytical Results With Numerical Simulationmentioning

confidence: 99%

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Investigation of a Mathematical Model and Non-Linear Effects Based on Parallel-Substrates Biochemical Conversion

et al. 2024

Contemp. Math.

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According to the broad applicability and advancements made in addressing complex non-linear problems, Researchers have been actively involved in addressing the accurate approaches to solve non-linear problems in fields such as chemical science, material science, and image processing. In this paper, the Amperometric response of catalase-peroxidase (parallel-substrates) conversion has been discussed. The Mathematical model relies on a set of non-linear differential equations that describe the reaction and diffusion of the system. The analytical methods were extended to derive the approximate solution of the non-linear reaction-diffusion equation. The straightforward and concise analytical expressions for the concentrations and current of the Biosensor are developed. This study includes the computational resolution of the problem by utilizing a MATLAB program. A comparison between analytical outcomes and those derived numerically has been conducted. The analytical findings presented are dependable and offer an effective comprehension of the behaviour of this system.

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Section: Comparison Of Analytical Results With Numerical Simulationmentioning

confidence: 99%

“…For instance, for the particular values of parameter γ 1 = 0.1, γ 2 = 0.1 and µ = 5 . Solving Eqn (25), (26), (27). We get m = 0.3415, n = 0.1291, q = 0.1291.…”

Section: Approximate Analytical Expressions For the Concentration Of ...mentioning

confidence: 99%

Investigation of a Mathematical Model and Non-Linear Effects Based on Parallel-Substrates Biochemical Conversion

et al. 2024

Contemp. Math.

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An innovative fractional-order evolutionary game theoretical study of personal protection, quarantine, and isolation policies for combating epidemic diseases

Akter,

Nurunnahar,

Ullah

et al. 2024

Sci Rep

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This study uses imposed control techniques and vaccination game theory to study disease dynamics with transitory or diminishing immunity. Our model uses the ABC fractional-order derivative mechanism to show the effect of non-pharmaceutical interventions such as personal protection or awareness, quarantine, and isolation to simulate the essential control strategies against an infectious disease spread in an infinite and uniformly distributed population. A comprehensive evolutionary game theory study quantified the significant influence of people’s vaccination choices, with government forces participating in vaccination programs to improve obligatory control measures to reduce epidemic spread. This model uses the intervention options described above as a control strategy to reduce disease prevalence in human societies. Again, our simulated results show that a combined control strategy works exquisitely when the disease spreads even faster. A sluggish dissemination rate slows an epidemic outbreak, but modest control techniques can reestablish a disease-free equilibrium. Preventive vaccination regulates the border between the three phases, while personal protection, quarantine, and isolation methods reduce disease transmission in existing places. Thus, successfully combining these three intervention measures reduces epidemic or pandemic size, as represented by line graphs and 3D surface diagrams. For the first time, we use a fractional-order derivate to display the phase-portrayed trajectory graph to show the model’s dynamics if immunity wanes at a specific pace, considering various vaccination cost and effectiveness settings.

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Comprehending symmetry in epidemiology: A review of analytical methods and insights from models of COVID-19, Ebola, Dengue, and Monkeypox

Shanmugam,

Byeon

2024

Medicine

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The challenge of developing comprehensive mathematical models for guiding public health initiatives in disease control is varied. Creating complex models is essential to understanding the mechanics of the spread of infectious diseases. We reviewed papers that synthesized various mathematical models and analytical methods applied in epidemiological studies with a focus on infectious diseases such as Severe Acute Respiratory Syndrome Coronavirus-2, Ebola, Dengue, and Monkeypox. We address past shortcomings, including difficulties in simulating population growth, treatment efficacy and data collection dependability. We recently came up with highly specific and cost-effective diagnostic techniques for early virus detection. This research includes stability analysis, geographical modeling, fractional calculus, new techniques, and validated solvers such as validating solver for parametric ordinary differential equation. The study examines the consequences of different models, equilibrium points, and stability through a thorough qualitative analysis, highlighting the reliability of fractional order derivatives in representing the dynamics of infectious diseases. Unlike standard integer-order approaches, fractional calculus captures the memory and hereditary aspects of disease processes, resulting in a more complex and realistic representation of disease dynamics. This study underlines the impact of public health measures and the critical importance of spatial modeling in detecting transmission zones and informing targeted interventions. The results highlight the need for ongoing financing for research, especially beyond the coronavirus, and address the difficulties in converting analytically complicated findings into practical public health recommendations. Overall, this review emphasizes that further research and innovation in these areas are crucial for addressing ongoing and future public health challenges.

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Fractional order mathematical model of Ebola virus under Atangana–Baleanu–Caputo operator

Cited by 5 publications

References 35 publications

Investigation of a Mathematical Model and Non-Linear Effects Based on Parallel-Substrates Biochemical Conversion

Investigation of a Mathematical Model and Non-Linear Effects Based on Parallel-Substrates Biochemical Conversion

An innovative fractional-order evolutionary game theoretical study of personal protection, quarantine, and isolation policies for combating epidemic diseases

Comprehending symmetry in epidemiology: A review of analytical methods and insights from models of COVID-19, Ebola, Dengue, and Monkeypox

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