Dynamical Study of Fractional Model of Allelopathic Stimulatory Phytoplankton Species

Abbas, Syed; Mahto, Lakshman; Favini, Angelo; Hafayed, Mokhtar

doi:10.1007/s12591-014-0219-5

Cited by 24 publications

(6 citation statements)

References 15 publications

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“…Abbas et al [45] presented a fractional model and performed some simulations, which validated their analytical findings using a discritization method. [46] presented and discussed some approaches used in modeling and surveillance of infectious diseases dynamics, by considering asymptomatic and symptomatic stages of infections.…”

Section: Related Workmentioning

confidence: 86%

Optimal control of the coronavirus pandemic with both pharmaceutical and non-pharmaceutical interventions

Oke

Ekum

Akintande

et al. 2023

Int. J. Dynam. Control

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Coronaviruses are types of viruses that are widely spread in humans, birds, and other mammals, leading to hepatic, respiratory, neurologic, and enteric diseases. The disease is presently a pandemic with great medical, economical, and political impacts, and it is mostly spread through physical contact. To extinct the virus, keeping physical distance and taking vaccine are key. In this study, a dynamical transmission compartment model for coronavirus (COVID-19) is designed and rigorously analyzed using Routh–Hurwitz condition for the stability analysis. A global dynamics of mathematical formulation was investigated with the help of a constructed Lyapunov function. We further examined parameter sensitivities (local and global) to identify terms with greater impact or influence on the dynamics of the disease. Our approach is data driven to test the efficacy of the proposed model. The formulation was incorporated with available confirmed cases from January 22, 2020, to December 20, 2021, and parameterized using real-time series data that were collected on a daily basis for the first 705 days for fourteen countries, out of which the model was simulated using four selected countries: USA, Italy, South Africa, and Nigeria. A least square technique was adopted for the estimation of parameters. The simulated solutions of the model were analyzed using MAPLE-18 with Runge–Kutta–Felberg method (RKF45 solver). The model entrenched parameters analysis revealed that there are both disease-free and endemic equilibrium points. The solutions depicted that the free equilibrium point for COVID-19 is asymptotic locally stable, when the epidemiological reproduction number condition $$(R_{0}<1)$$ ( R 0 < 1 ) . The simulation results unveiled that the pandemic can be controlled if other control measures, such as face mask wearing in public areas and washing of hands, are combined with high level of compliance to physical distancing. Furthermore, an autonomous derivative equation for the five-dimensional deterministic was done with two control terms and constant rates for the pharmaceutical and non-pharmaceutical strategies. The Lagrangian and Hamilton were formulated to study the model optimal control existence, using Pontryagin’s Maximum Principle describing the optimal control terms. The designed objective functional reduced the intervention costs and infections. We concluded that the COVID-19 curve can be flattened through strict compliance to both pharmaceutical and non-pharmaceutical strategies. The more the compliance level to physical distance and taking of vaccine, the earlier the curve is flattened and the earlier the economy will be bounce-back.

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Section: Related Workmentioning

confidence: 86%

Optimal control of the coronavirus pandemic with both pharmaceutical and non-pharmaceutical interventions

Oke

Ekum

Akintande

et al. 2023

Int. J. Dynam. Control

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“…GAS of interior equilibrium point and predator-extinction point are established by defining a suitable Lyapunov function. In the paper addressed by Abbas et al, [70] Lipschitz condition helps find conditions for existence and uniqueness of solutions. With the help of limit superior and limit inferior, permanence of the fractional model has been tackled.…”

Section: Approach On Ecological Modelsmentioning

confidence: 99%

A comprehensive review article on fractional models involving ecology and eco-epidemiology

Pramanik,

Das,

Karmakar

et al. 2023

J. Appl. Math.

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This paper deals with the various definitions involved in the very old yet novel topic called fractional calculus. This survey intends to report some of the major works carried out in the arena of fractional calculus that took place since 2010. Fractional calculus is a prominent topic for research within the discipline of applied mathematics doe to its usefulness in solving problems in several different branches of science, engineering, medicine, finance, economics and the likes. With the various definitions involved in this field, we explore the various models taken into consideration to study the effect and impact of fractional calculus to understand how the dynamics of such models change.

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“…13 More specifically, some novel fractional-order studies to define the dynamics of Covid-19 epidemic are given in Atangana and Araz. [14][15][16] Varieties of numerical algorithms have been produced in several years to simulate fractional order systems (for interest, see Abbas et al and Kumar et al [17][18][19][20][21] ). Non-classical-type differential equations are very important due to their non-local properties and useful to simulate the hereditary feature of materials.…”

Section: Introductionmentioning

confidence: 99%

Stability and bifurcation analysis of a fractional‐order model of cell‐to‐cell spread of HIV‐1 with a discrete time delay

Abbas

Tyagi

Kumar

et al. 2022

Math Methods in App Sciences

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In this manuscript, fractional order is introduced onto a time‐delay differential equation model of cell‐to‐cell spread of HIV‐1. The fractional derivative of Caputo type is considered. We deal with the local stability of the resulting system and derive some necessary and sufficient conditions ensuring Hopf bifurcation to occur for this system. Explicit expressions for determining stability of critical surfaces are also given. An Adams‐type predictor–corrector technique is applied to illustrate the numerical results. The main target of this study is to describe the structure of HIV‐1 by using a fractional‐order mathematical model, and the motivation of using fractional derivatives is the ability of these operators to capture memory effects in the system.

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Dynamical Study of Fractional Model of Allelopathic Stimulatory Phytoplankton Species

Cited by 24 publications

References 15 publications

Optimal control of the coronavirus pandemic with both pharmaceutical and non-pharmaceutical interventions

Optimal control of the coronavirus pandemic with both pharmaceutical and non-pharmaceutical interventions

A comprehensive review article on fractional models involving ecology and eco-epidemiology

Stability and bifurcation analysis of a fractional‐order model of cell‐to‐cell spread of HIV‐1 with a discrete time delay

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