The Stability Analysis and Transmission Dynamics of the SIR Model with Nonlinear Recovery and Incidence Rates

Khan, Ihsan Ullah; Qasim, Muhammad; Koufi, Amine El; Ullah, Hafiz

doi:10.1155/2022/6962160

Cited by 4 publications

(3 citation statements)

References 27 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%

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%

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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“…A theoretical performance shown in this paper is the existence solution of the dynamical model, the reproduction number, and the stability analysis. The analysis described in this research was carried out from [15], [16], [17] and [18].…”

Section: Introductionmentioning

confidence: 99%

Traffic Congestion Analysis Using Sir Epidemic Model

Rafsanjani,

Herdiana,

Tjahjana

et al. 2023

BAREKENG: J. Math. & App.

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In this work, we propose a mathematical model to represent traffic congestion in the street under some consideration. A congestion problem in a city highway becomes a critical issue since congestion at one point affected congestion propagation on the other points. We focus on the propagation of traffic propagation by adopting the concept of disease spread using the SIR model. We consider that the disease in traffic problems is congestion. Meanwhile, vehicles that enter the highway are susceptible to congestion. In contrast, vehicles free from traffic jams represent individuals free from disease. The SIR model can explain the spread of congestion by looking at the congestion variable as an infected variable. We discuss and analyze the existence and stability of the equilibrium points. The local stability equilibrium point is verified using the Routh-Hurwitz criteria. At the same time, the global stability is analyzed using Lyapunov function. The numerical simulation is provided in the last section to validate the discussion results.

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The Stability Analysis and Transmission Dynamics of the SIR Model with Nonlinear Recovery and Incidence Rates

Cited by 4 publications

References 27 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

Traffic Congestion Analysis Using Sir Epidemic Model

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