Some qualitative properties of the discrete models for malaria propagation

Faragó, István; Mosleh, Rahele

doi:10.1016/j.amc.2022.127628

Cited by 1 publication

(2 citation statements)

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“…However, it is not easy to establish the boundedness of this NSFD scheme comparing with (31). The NSFD scheme (34) also preserves the boundedness of solutions as the NSFD scheme (34), but x k+1 or y k+1 is not immediately utilized to compute the remaining component.…”

Section: Construction Of Positivity-preserving Nsfd Schemementioning

confidence: 99%

“…On the other hand, NSFD schemes are simple, effective and can be applied to solve a broad class of differential equations. For these reasons, NSFD schemes have been widely used in solving differential equation models arising in real-world applications nowadays [1,2,8,9,10,20,21,22,30,33,34,35,66,75,77,78]. In [23,24,25,26,43,44,45,46,47,48],…”

Section: Introductionmentioning

confidence: 99%

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Dynamical analysis and numerical simulation of a new fractional-order two-stage species model with recruitment

Hoang

2023

Preprint

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The purpose of this work is to propose and analyze a new fractional-order two-stage species model with recruitment to discover memory effects on population dynamics. This fractional-order model is constructed by incorporating a well-known integer-order two-stage species model with the Caputo fractional derivative. Firstly, the positivity and boundedness of solutions of the proposed model are investigated by using some standard comparison results for fractional differential equations. Next, a simple approach is utilized to study stability properties of the fractional-order model. This approach is based on the Lyapunov stability theory and Barbalat’s lemma in combination with some nonstandard techniques for fractional dynamical systems. More clearly, we use general quadratic Lyapunov candidate functions and combine them with characteristics of quadratic forms associated with real matrices to establish the stability properties. As an important consequence, global asymptotic stability, uniform and Mittag-Leffler stability and therefore, population dynamics of the proposed fractional-order model are analyzed rigorously. Finally, we extend the Mickens’ methodology to construct a dynamically consistent nonstandard finite difference (NSFD) scheme for the purpose of numerical simulation of the fractional-order model. It is proved that the NSFD scheme preserves the positivity and boundedness of the fractional-order model regardless of the values of the step size; moreover, it is also simple and efficient. The theoretical results and advantages of the NSFD scheme are supported by illustrative numerical experiments. The experiments provide strong evidence, which shows that the numerical results are consistent with the theoretical ones.

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Section: Construction Of Positivity-preserving Nsfd Schemementioning

confidence: 99%