A boundedness and monotonicity preserving method for a generalized population model

Qin, Wendi; Ma, Qiang; Man, Zhenyong; Ding, Xiaohua

doi:10.1080/10236198.2020.1832088

Cited by 3 publications

(1 citation statement)

References 22 publications

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“…Hence, NSFD schemes are effective to simulate dynamics of dynamical differential models over long time periods. Because of this, nowadays NSFD schemes have been recognized as one of the effective approaches to solve differential equation equations arising in theory and practice [1,5,10,13,23,25,26,39,53,56,57,62,63]. In recent works [15,16,17,18,19,20,31,32], we have successfully developed the Mickens's methodology to construct NSFD schemes for some mathematical models arising in biology and epidemiology.…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of a generalized hepatitis B epidemic model and its dynamically consistent discrete model

Hoang¹

2021

Preprint

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The aim of this work is to study qualitative dynamical properties of a generalized hepatitis B epidemic model and its dynamically consistent discrete model. Positivity, boundedness, the basic reproduction number and asymptotic stability properties of the model are analyzed rigorously. By the Lyapunov stability theory and the Poincare-Bendixson theorem in combination with the Bendixson-Dulac criterion, we show that a disease-free equilibrium point is globally asymptotically stable if the basic reproduction number R 0 ≤ 1 and a diseaseendemic equilibrium point is globally asymptotically stable whenever R 0 > 1. Next, we apply the Mickens' methodology to propose a dynamically consistent nonstandard finite difference (NSFD) scheme for the continuous model. By rigorously mathematical analyses, it is proved that the constructed NSFD scheme preserves essential mathematical features of the continuous model for all finite step sizes. Finally, numerical experiments are conducted to illustrate the theoretical findings and to demonstrate advantages of the NSFD scheme over standard ones. The obtained results in this work not only improve but also generalize some existing recognized works.

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Section: Introductionmentioning

confidence: 99%

Dynamical analysis of a generalized hepatitis B epidemic model and its dynamically consistent discrete model

Hoang¹

2021

Preprint

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Dynamically consistent nonstandard finite difference schemes for a virus-patch dynamic model

Hoang

2021

J. Appl. Math. Comput.

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Dynamical analysis of a generalized hepatitis B epidemic model and its dynamically consistent discrete model

Hoang

2023

Mathematics and Computers in Simulation

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A boundedness and monotonicity preserving method for a generalized population model

Cited by 3 publications

References 22 publications

Dynamical analysis of a generalized hepatitis B epidemic model and its dynamically consistent discrete model

Dynamical analysis of a generalized hepatitis B epidemic model and its dynamically consistent discrete model

Dynamically consistent nonstandard finite difference schemes for a virus-patch dynamic model

Dynamical analysis of a generalized hepatitis B epidemic model and its dynamically consistent discrete model

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