The SIRC model and influenza A

Casagrandi, Renato; Bolzoni, Luca; Levin, Simon A.; Andreasen, Viggo

doi:10.1016/j.mbs.2005.12.029

Cited by 156 publications

(128 citation statements)

References 76 publications

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“…Also, by substituting Eq. (20) in the initial conditions (2) we can obtain 4⌈α⌉ equations as follows…”

Section: ) In Order To Use Chebyshev Collocation Method We First Amentioning

confidence: 99%

“…Because model (1) monitors the dynamics of human populations, all the parameters are assumed to be nonnegative. Furthermore, it can be shown that all state variables of the model are nonnegative for all time t ≥ 0 ( [2], [3], [21]). …”

Section: Introductionmentioning

confidence: 99%

“…where the parameter β is the contact rate for the influenza disease also called the rate of transmission for susceptible to infected, γ −1 is the cross-immune period, θ −1 is the infectious period, δ −1 is the total immune period and σ is the fraction of the exposed cross-immune individuals who are recruited in an unit time into the infective subpopulation ( [2], [6]). …”

Section: Introductionmentioning

confidence: 99%

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Numerical Simulation for the Fractional SIRC Model and Influenza A

Khader¹,

Sweilam²,

Mahdy³

et al. 2014

Appl. Math. Inf. Sci.

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Abstract:In this paper, A Chebyshev spectral method is presented to study the deals with the fractional SIRC model associated with the evolution of influenza A disease in human population. The properties of the Chebyshev polynomials are used to derive an approximate formula of the Caputo fractional derivative. This formula reduces the SIRC model to the solution of a system of algebraic equations which is solved using Newton iteration method. The convergence analysis and an upper bound of the error of the derived formula are given. We compared our numerical solutions with those numerical solutions using fourth-order Runge-Kutta method. The obtained results of the SIRC model show the simplicity and the efficiency of the proposed method. Also, illustration for propagation of influenza A virus and the relation between the four cases of it along the time at the fractional derivative are given.

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“…Also, by substituting Eq. (20) in the initial conditions (2) we can obtain 4⌈α⌉ equations as follows…”

Section: ) In Order To Use Chebyshev Collocation Method We First Amentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical Simulation for the Fractional SIRC Model and Influenza A

Khader¹,

Sweilam²,

Mahdy³

et al. 2014

Appl. Math. Inf. Sci.

View full text Add to dashboard Cite

show abstract

“…η −1 is the cross-immune period, while θ −1 is the infectious period and δ −1 is the total immune period. σ represents the fraction of the exposed cross-immune individuals who are recruited in a unit time into the infective subpopulation [24,26] …”

Section: Construction Of the Modelmentioning

confidence: 99%

“…The authors in Ref. [24] introduced a new compartment into the SIR model, which is called cross-immune compartment to be called SIRC model. The added compartment cross-immune CðtÞ describes an intermediate state between the fully susceptible SðtÞ and the fully protected RðtÞ one.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Salmonella Infection

Rihan¹

2017

Current Topics in Salmonella and Salmonellosis

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In this chapter, we propose a mathematical epidemic model, with integer and fractional order to describe the dynamics of Salmonella infection in animal herds. We investigate the qualitative behaviors of such model and find the conditions that guarantee the asymptotic stability of disease-free and endemic steady states. To assess the severity of the outbreak, as well as the strength of the medical and/or behavioral interventions necessary for control, we estimate basic reproduction number R 0 . This threshold parameter specifies the average number of secondary infections caused by one infected individual during his/her entire infectious period at the start of an outbreak. We also provide an unconditionally stable implicit scheme for the fractional-order epidemic model. The theoretical and computational results give insight into the modelers and infectious disease specialists.

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Empirical study of dynamics of amoebiasis transmission in mobile ad hoc networks (MANETs)

Mishra

Saha

Makhija

et al. 2019

Int J Communication

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SummaryWe present a study of the novel mathematical model, CISER, in this work. The proposed model is a more general variant of the SIR epidemic model for representing information spread. The work provides an analysis of the mathematical model, in particular, the inclusion of carrier and exposed states in providing a more generalized representation toward SIR. The model also provides an accurate description of the disease amoebiasis and relates the disease characteristics to message propagation. We derive various properties of importance and depict the model representation of various states of spread (message propagation) through numerical results. Based on this model, we then provide an epidemic controlled flooding mechanism for information spread in a mobile ad hoc network (MANET). This is accomplished through a reactive IPv4‐based routing protocol built on top of the MAC 802.11b layer. We further present our simulated results and perform a comparative analysis against other epidemic routing protocols such as SIR and SEIR. We discover our model performing better in terms of most performance metrics.

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The SIRC model and influenza A

Cited by 156 publications

References 76 publications

Numerical Simulation for the Fractional SIRC Model and Influenza A

Numerical Simulation for the Fractional SIRC Model and Influenza A

Dynamics of Salmonella Infection

Empirical study of dynamics of amoebiasis transmission in mobile ad hoc networks (MANETs)

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