Existence and Uniqueness of Positive Periodic Solution of an Extended Rosenzweig-MacArthur Model via Brouwer's Topological Degree

Joshua, Enobong E.; Akpan, Ekemini T.; Adebimpe, Olukayode; Madubueze, Chinwendu Emilian

doi:10.9734/bjmcs/2017/31342

Cited by 3 publications

(3 citation statements)

References 13 publications

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“…Mathematical modelling becomes a suitable tool to study the qualitative and quantitative dynamical behaviour of physical systems. The notion of Mathematical modelling has become a trans-disciplinary research tool, to investigate complexities and nonlinear behaviour in several disciplines and subject including population dynamics of ecological species [13,14], neuronal dynamics and cognition [15,16], romantic love [17], drug abuse and alcohol [18,19,20] , terrorism and insurgency [20], finance and management sciences [21], and infectious diseases and control [22,23]. Mathematical modelling has been used to study the spread, and control measure of infectious diseases, to facilitate sound, critical decision and policy making by the government, and other stakeholders.…”

Section: Introductionmentioning

confidence: 99%

Computational Nonlinear Dynamics: Analysis and Assessment in Optimal Control of COVID-19 in Akwa Ibom State, Nigeria

Joshua,

Akpan,

Inyang

2024

JAMCS

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World Health Organization(WHO) instigates a continuous alertness and preparation to contain re emergence of other variants of corona viruses. In the same vein, public welfare managements in allocating health related resources require predictive decision making, made possible through the assessment of existing health challenges. Therefore it is imperative to carryout an efficiency analysis to prioritize and determine an optimal control strategy that curtailed the transmission of COVID19 in Akwa Ibom state. In this paper, a deterministic epidemic model has been formulated using principles of Mathematical modelling of infectious diseases. This is a nonlinear system of differential equations coupled with three (3) time-varying control functionals. The control functionals are exible educational programmes, vaccination and treatment of COVID-19. The usual fuzzy-like characterization of infection severity (0 \(\le\) R0, Rc \(\le\) 1) and ( R0 , Rc > 1) were achieved using the Next Generation Matrix Operator. An optimality system was derived using Pontryagin's Maximum principle, with some propositions on controllability criteria. Some forward-backward numerical solutions was executed in maple16 using validated datasets published by the Nigeria Centre for Disease Control(NCDC), peculiar to Akwa Ibom State. The efficiency analysis predicted that Strategy I (a combination of educational intervention programmes and vaccinations of the exposed and susceptible individual) as the most efficacious and optimal control strategy. Comparatively, Strategy I with 96% efficiency on reducing the infected sub-population is more effective than Strategy IV (a combination of the three control states) with efficiency index of 91%. A continuous vaccination and educational awareness programme has been recommended for community health practitioners, and compliance to these policies by the citizens can eradicate the dreaded pandemic with minimal intervention cost in the state.

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Section: Introductionmentioning

confidence: 99%

Computational Nonlinear Dynamics: Analysis and Assessment in Optimal Control of COVID-19 in Akwa Ibom State, Nigeria

Joshua,

Akpan,

Inyang

2024

JAMCS

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“…Thus, more realistic mathematical models in ecological population dynamics needs to incorporate a time lag or history between the moment in which an action takes place and the moment its effect is actually observed in the dynamical system. There are recent studies in dynamical behaviors of a 3-D Rosenzweig-MacArthur Model (1963) such as uniform boundedness, local and global asymptotic stabilities, local Hopf-bifurcation/limit cycles, persistence and permanence, global attractors, existence and uniqueness of positive periodic solution (see, Feng, Freeze, Lu & Rocco, 2014;Joshua, Akpan, Adebimpe & Madubueze, 2016;Joshua & Akpan, 2017). However, to the best of the authors' knowledge little emphasis has been placed on the effects of time-delay parameter on the model.…”

Section: Introductionmentioning

confidence: 99%

Global Stability and Hopf-bifurcation Analysis of Biological Systems using Delayed Extended Rosenzweig-MacArthur Model

Joshua¹,

Akpan²

2018

MAS

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This paper investigates the global asymptotic stability of a Delayed Extended Rosenzweig-MacArthur Model via Lyapunov-Krasovskii functionals. Frequency sweeping technique ensures stability switches as the delay parameter increases and passes the critical bifurcating threshold.The model exhibits a local Hopf-bifurcation from asymptotically stable oscillatory behaviors to unstable strange chaotic behaviors dependent of the delay parameter values. Hyper-chaotic fluctuations were observed for large delay values far away from the critical delay margin. Numerical simulations of experimental data obtained via non-dimensionalization have shown the applications of theoretical results in ecological population dynamics.

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“…The model shows dynamical behaviors such as stability, limit cycles, hopf-bifurcation, persistence and global stability,periodic solutions, and stability dynamics with deviated arguments or delays. (see., Joshua, Akpan, & Madubueze 2016;Joshua, Akpan, Madubueze, Adebimpe, 2017, Joshua, & Akpan, 2018. In this article, system (4)is modified with a ratio-dependent functional response and its dynamical complexity is studied.…”

Section: Introductionmentioning

confidence: 99%

Spirals and Cycles of Biological Systems via Extended Rosenzweig-MacArthur Model with Ratio-dependent Functional Response

Joshua¹,

Akpa²

2018

MAS

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This paper investigates stable proper nodes, stable spiral sinks and stable ω−limit cycles of Extended Rosenzweig-MacAthur Model, which incorporates ratio-dependent functional response on predation mechanism. The ultimate bound-edness condition has been used to predict extinction, co-existence, and exponential convergence scenarios of the model. The Poincare-Bendixson results guarantee existence of periodic cycles of the models. The system degenerate from stable spiral sinks to stable ω−limit cycles as control parameter varies. Numerical simulations are provided to support the va-lidity of theoretical findings.

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Existence and Uniqueness of Positive Periodic Solution of an Extended Rosenzweig-MacArthur Model via Brouwer's Topological Degree

Cited by 3 publications

References 13 publications

Computational Nonlinear Dynamics: Analysis and Assessment in Optimal Control of COVID-19 in Akwa Ibom State, Nigeria

Computational Nonlinear Dynamics: Analysis and Assessment in Optimal Control of COVID-19 in Akwa Ibom State, Nigeria

Global Stability and Hopf-bifurcation Analysis of Biological Systems using Delayed Extended Rosenzweig-MacArthur Model

Spirals and Cycles of Biological Systems via Extended Rosenzweig-MacArthur Model with Ratio-dependent Functional Response

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