Piecewise fractional analysis of the migration effect in plant-pathogen-herbivore interactions

Rahman, Mati ur; Arfan, Muhammad; Băleanu, Dumitru

doi:10.59292/bulletinbiomath.2023001

Cited by 14 publications

(6 citation statements)

References 28 publications

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“…However, MERS-CoV and SARS-CoV-2 can cause pandemics or sporadic epidemics with ongoing human-tohuman transmission. Several researchers have suggested mathematical models by applying different approaches to an infectious disease and studying its dynamics from different angles [33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Predictive Modeling and Control Strategies for the Transmission of Middle East Respiratory Syndrome Coronavirus

Fatima,

Yavuz,

ur Rahman

et al. 2023

MCA

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The Middle East respiratory syndrome coronavirus (MERS-CoV) is a highly infectious respiratory illness that poses a significant threat to public health. Understanding the transmission dynamics of MERS-CoV is crucial for effective control and prevention strategies. In this study, we develop a precise mathematical model to capture the transmission dynamics of MERS-CoV. We incorporate some novel parameters related to birth and mortality rates, which are essential factors influencing the spread of the virus. We obtain epidemiological data from reliable sources to estimate the model parameters. We compute its basic reproduction number (R0). Stability theory is employed to analyze the local and global properties of the model, providing insights into the system’s equilibrium states and their stability. Sensitivity analysis is conducted to identify the most critical parameter affecting the transmission dynamics. Our findings revealed important insights into the transmission dynamics of MERS-CoV. The stability analysis demonstrated the existence of stable equilibrium points, indicating the long-term behavior of the epidemic. Through the evaluation of optimal control strategies, we identify effective intervention measures to mitigate the spread of MERS-CoV. Our simulations demonstrate the impact of time-dependent control variables, such as supportive care and treatment, in reducing the number of infected individuals and controlling the epidemic. The model can serve as a valuable tool for public health authorities in designing effective control and prevention strategies, ultimately reducing the burden of MERS-CoV on global health.

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Section: Introductionmentioning

confidence: 99%

Predictive Modeling and Control Strategies for the Transmission of Middle East Respiratory Syndrome Coronavirus

Fatima,

Yavuz,

ur Rahman

et al. 2023

MCA

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“…In recent studies researchers have explored various aspects of fractional analysis in different contexts. The examination of the migration effect in plant-pathogen-herbivore interactions was specifically conducted through the utilization of piecewise fractional analysis [ 13 ]. Another study examined the fractional model of COVID-19 by means of piecewise global operators [ 14 ].…”

Section: Introductionmentioning

confidence: 99%

Computational and stability analysis of Ebola virus epidemic model with piecewise hybrid fractional operator

Nisar,

Farman,

Jamil

et al. 2024

PLoS ONE

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In this manuscript, we developed a nonlinear fractional order Ebola virus with a novel piecewise hybrid technique to observe the dynamical transmission having eight compartments. The existence and uniqueness of a solution of piecewise derivative is treated for a system with Arzel’a-Ascoli and Schauder conditions. We investigate the effects of classical and modified fractional calculus operators, specifically the classical Caputo piecewise operator, on the behavior of the model. A model shows that a completely continuous operator is uniformly continuous, and bounded according to the equilibrium points. The reproductive number R0 is derived for the biological feasibility of the model with sensitivity analysis with different parameters impact on the model. Sensitivity analysis is an essential tool for comprehending how various model parameters affect the spread of illness. Through a methodical manipulation of important parameters and an assessment of their impact on Ro, we are able to learn more about the resiliency and susceptibility of the model. Local stability is established with next Matignon method and global stability is conducted with the Lyapunov function for a feasible solution of the proposed model. In the end, a numerical solution is derived with Newton’s polynomial technique for a piecewise Caputo operator through simulations of the compartments at various fractional orders by using real data. Our findings highlight the importance of fractional operators in enhancing the accuracy of the model in capturing the intricate dynamics of the disease. This research contributes to a deeper understanding of Ebola virus dynamics and provides valuable insights for improving disease modeling and public health strategies.

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“…However, it is noteworthy that existing models utilize classical reaction-diffusion approaches, particularly in the context of glioblastoma growth. To the best of our knowledge, fractional reaction-diffusion modeling for glioblastoma growth has not been reported in the literature, despite the increasing prevalence of fractional models for disease modeling [25][26][27][28][29]. In this work, we propose a fractional tumor growth model at a macroscopic scale, rooted in a mathematical problem known as the quenching problem [30], which incorporates a type of reaction-diffusion equation.…”

Section: Introductionmentioning

confidence: 99%

A fractional mathematical model approach on glioblastoma growth: tumor visibility timing and patient survival

Kar,

Özalp

2024

Mathematical Modelling and Numerical Simulation With Applications

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In this paper, we introduce a mathematical model given by \begin{equation} { }^c \mathfrak{D}_t^\alpha u = \nabla \cdot \mathrm{D} \nabla u + \rho f(u) \quad \text{in } \Omega, \end{equation} where $f(u)=\frac{1}{1-u/\mathrm{K}}, \, u/\mathrm{K} \neq 1, \, \mathrm{K} > 0$, to enhance established mathematical methodologies for better understanding glioblastoma dynamics at the macroscopic scale. The tumor growth model exhibits an innovative structure even within the conventional framework, including a proliferation term, $f(u)$, presented in a different form compared to existing macroscopic glioblastoma models. Moreover, it represents a further refined model by incorporating a calibration criterion based on the integration of a fractional derivative, $\alpha$, which differs from the existing models for glioblastoma. Throughout this study, we initially discuss the modeling dynamics of the tumor growth model. Given the frequent recurrence observed in glioblastoma cases, we then track tumor mass formation and provide predictions for tumor visibility timing on medical imaging to elucidate the recurrence periods. Furthermore, we investigate the correlation between tumor growth speed and survival duration to uncover the relationship between these two variables through an experimental approach. To conduct these patient-specific analyses, we employ glioblastoma patient data and present the results via numerical simulations. In conclusion, the findings on tumor visibility timing align with empirical observations, and the investigations into patient survival further corroborate the well-established inter-patient variability for glioblastoma cases.

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Piecewise fractional analysis of the migration effect in plant-pathogen-herbivore interactions

Cited by 14 publications

References 28 publications

Predictive Modeling and Control Strategies for the Transmission of Middle East Respiratory Syndrome Coronavirus

Predictive Modeling and Control Strategies for the Transmission of Middle East Respiratory Syndrome Coronavirus

Computational and stability analysis of Ebola virus epidemic model with piecewise hybrid fractional operator

A fractional mathematical model approach on glioblastoma growth: tumor visibility timing and patient survival

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