The Continuous and Discrete Stability Characterization of Hepatitis B Deterministic Model

Li, Shuo; Hussain, Amjid; Khan, Ihsan Ullah; Koufi, Amine El; Mehmood, Arif

doi:10.1155/2022/1893665

Cited by 6 publications

(3 citation statements)

References 32 publications

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“…In this section we constructed the purposed NSFD scheme which is more reliable scheme for numerically analyzed the mathematical model of infectious disease. Mickens [20][21][22][23][24] gave the idea of NSFD scheme, which approximately estimate the solution of ordinary and partial differential equations.…”

Section: Nsfd Schemementioning

confidence: 99%

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Mathematical Model of Typhoid Disease Using Standard and Non-standard Finite Difference Schemes

Irfan,

Ghour,

et al. 2023

Preprint

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In the current paper, typhoid disease is mathematically simulated, and its positivity and boundedness are also discussed. The fundamental reproduction number \({R}_{0}\), which is significant in epidemiology, is sorted out. The Lyapunov function for global stability and the Routh-Hurwitz criterion for local stability of the intended NSFD scheme are studied for disease-free and endemic equilibrium points, respectively. The standard finite difference (SFD) scheme and non-standard finite difference (NSFD) scheme are used to approximate the solution of the PSEIT epidemic model.

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Section: Nsfd Schemementioning

confidence: 99%

“…The Routh Hurwitz criterion [24] can be used to determine the roots of the above-mentioned equation. The eigenvalues are less than one if 𝑅 0 < 1.…”

Section: Stability Analysis Of Dfe Points For Nsfd Schemementioning

confidence: 99%

Mathematical Model of Typhoid Disease Using Standard and Non-standard Finite Difference Schemes

Irfan,

Ghour,

et al. 2023

Preprint

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“…By employing mathematical modeling, we may concentrate on how an infectious disease transmits all over a population. In order to explain epidemic infectious diseases, the researchers are employing both integer orders [11][12][13][14][15] as well as fractional orders [16][17][18] mathematical models. Tese models can be used to improve all of their sources and more efectively implement control measures.…”

Section: Introductionmentioning

confidence: 99%

Epidemiological Characteristics of Generalized COVID-19 Deterministic Disease Model

Li,

Hussain,

Khan

et al. 2023

Discrete Dynamics in Nature and Society

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Coronavirus disease 2019 (COVID-19) is an infection that can result in lung issues such as pneumonia and, in extreme situations, the most severe acute respiratory syndrome. COVID-19 is widely investigated by researchers through mathematical models from different aspects. Inspired from the literature, in the present paper, the generalized deterministic COVID-19 model is considered and examined. The basic reproduction number is obtained which is a key factor in defining the nonlinear dynamics of biological and physical obstacles in the study of mathematical models of COVID-19 disease. To better comprehend the dynamical behavior of the continuous model, two unconditionally stable schemes, i.e., mixed Euler and nonstandard finite difference (NSFD) schemes are developed for the continuous model. For the discrete NSFD scheme, the boundedness and positivity of solutions are discussed in detail. The local stability of disease-free and endemic equilibria is demonstrated by constructing Jacobian matrices for NSFD scheme; nevertheless, the global stability of aforementioned equilibria is verified by using Lyapunov functions. Numerical simulations are also presented that demonstrate how both the schemes are effective and suitable for solving the continuous model. Consequently, the outcomes obtained through these schemes are completely according to the solutions of the continuous model.

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Exploring local and global stability of COVID-19 through numerical schemes

Xiao,

Xu,

Morani

et al. 2024

Sci Rep

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Respiratory sensitivity and pneumonia are possible outcomes of the coronavirus (COVID-19). Surface characteristics like temperature and sunshine affect how long the virus survives. This research article analyzes COVID-19 mathematical model behavior based on symptomatic and non-symptomatic individuals. In the reproductive model, the best result indicates the intensity of the epidemic. Our model remained stable at a certain point under controlled conditions after we evaluated a specific element. This approach is in place of traditional approaches such as Euler’s and Runge–Kutta’s. An unusual numerical approach known as the non-standard finite difference (NSFD) scheme is used in this article. This numerical approach gives us positivity. A dependable numerical analysis allowed us to evaluate different approaches and verify our theoretical results. Unlike the widely used Euler and RK4 approaches, we investigated the benefits of implementing NSFD schemes. By numerically simulating COVID-19 in a variety of scenarios, we demonstrated how our theoretical concepts work. The simulation findings support the usefulness of both approaches.

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The Continuous and Discrete Stability Characterization of Hepatitis B Deterministic Model

Cited by 6 publications

References 32 publications

Mathematical Model of Typhoid Disease Using Standard and Non-standard Finite Difference Schemes

Mathematical Model of Typhoid Disease Using Standard and Non-standard Finite Difference Schemes

Epidemiological Characteristics of Generalized COVID-19 Deterministic Disease Model

Exploring local and global stability of COVID-19 through numerical schemes

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