Global attractivity and permanence of a SVEIR epidemic model with pulse vaccination and time delay

Wei, Huiming; Jiang, Yu; Song, Xinyu; Su, Guanghui; Qiu, Suizheng

doi:10.1016/j.cam.2008.10.046

Cited by 27 publications

(18 citation statements)

References 20 publications

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“…For simplicity, it is assumed that the size of population remains constant over time, that is, it is assumed that birth ( μ ) and mortality ( v ) rates are equal. Thus, the SIR model is given by

dS / dt = μN - ∋ S - βIS / N

dI / dt = βIS / N - γI - vI

dR / dt = γI - vR,

where S ( t ) + I ( t ) + R ( t ) = N .…”

Section: Susceptible–infected–recovered Models and Models Based On Inmentioning

confidence: 99%

CUDA parallel programming for simulation of epidemiological models based on individuals

Filho

Paula

Coelho

et al. 2015

Math. Meth. Appl. Sci.

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Mathematical models are of great value in epidemiology to help understand the dynamics of the various infectious diseases, as well as in the conception of effective control strategies. The classical approach is to use differential equations to describe, in a quantitative manner, the spread of diseases within a particular population. An alternative approach is to represent each individual in the population as a string or vector of characteristic data and simulate the contagion and recovery processes by computational means. This type of model, referred in the literature as MBI (models based on individuals), has the advantage of being flexible as the characteristics of each individual can be quite complex, involving, for instance, age, sex, pre‐existing health conditions, environmental factors, social habits, etc. However, when it comes to simulations involving large populations, MBI may require a large computational effort in terms of memory storage and processing time. In order to cope with the problem of heavy computational effort, this paper proposes a parallel implementation of MBI using a graphics processor unit compatible with CUDA. It was found that, even in the case of a simple susceptible–infected–recovered model, the computational gains in terms of processing time are significant. Copyright © 2015 John Wiley & Sons, Ltd.

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dS / dt = μN - ∋ S - βIS / N

dI / dt = βIS / N - γI - vI

dR / dt = γI - vR,

where S ( t ) + I ( t ) + R ( t ) = N .…”

Section: Susceptible–infected–recovered Models and Models Based On Inmentioning

confidence: 99%

CUDA parallel programming for simulation of epidemiological models based on individuals

Filho

Paula

Coelho

et al. 2015

Math. Meth. Appl. Sci.

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“…The qualitative study of epidemiological models such as the "SIS", "SIR", "SEIR" and "SVEIR" models has been a field of intense and varied research [6,7,8,9,10,11,12,13,14,15,16,17]. An excellent review of the literature, but not very recent, was made by Hethcote [18].…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Fractional-order “SVEIR” Epidemic Mo del with a General Nonlinear Saturated Incidence Rate in a Continuous Reactor

Hajji¹,

Sayari²

2019

ARJOM

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In this paper, I propose a fractional-order mathematical five-dimensional dynamical system modeling a SVEIR model of infectious disease transmission in a chemostat. A profound qualitative analysis is given. The analysis of the local and global stability of equilibrium points is carried out. It is proved that if R > 1, then the disease-persistence (endemic) equilibrium is globally asymptotically stable. However, if R ≤ 1, then the disease-free equilibrium is globally asymptotically stable in R 5. Finally, some numerical tests are done using the ”PECE” method in order to validate the obtained results.

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“…For example, in [20], the authors used compound matrix techniques to show the global stability of the endemic equilibrium under some constraints on the parameters of the system. Huiming Wei et al [29] proposed an SVEIR model with time delay, and analyzed the dynamic behavior under pulse vaccination. Using comparison theorem, they showed that the infection-free periodic solution is globally attractive.…”

Section: Introductionmentioning

confidence: 99%

Global Stability of a SVEIR Epidemic Model: Application to Poliomyelitis Transmission Dynamics

Nkamba¹,

Ntaganda²,

Abboubakar³

et al. 2017

OJMSi

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The lack of treatment for poliomyelitis doing that only means of preventing is immunization with live oral polio vaccine (OPV) or/and inactivated polio vaccine (IPV). Poliomyelitis is a very contagious viral infection caused by poliovirus. Children are principally attacked. In this paper, we assess the impact of vaccination in the control of spread of poliomyelitis via a deterministic SVEIR (Susceptible-VaccinatedLatent-Infectious-Removed) model of infectious disease transmission, where vaccinated individuals are also susceptible, although to a lesser degree. Using LyapunovLasalle methods, we prove the global asymptotic stability of the unique endemic equilibrium whenever vac 1 >  . Numerical simulations, using poliomyelitis data from Cameroon, are conducted to approve analytic results and to show the importance of vaccinate coverage in the control of disease spread.

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Global attractivity and permanence of a SVEIR epidemic model with pulse vaccination and time delay

Cited by 27 publications

References 20 publications

CUDA parallel programming for simulation of epidemiological models based on individuals

CUDA parallel programming for simulation of epidemiological models based on individuals

Analysis of a Fractional-order “SVEIR” Epidemic Mo del with a General Nonlinear Saturated Incidence Rate in a Continuous Reactor

Global Stability of a SVEIR Epidemic Model: Application to Poliomyelitis Transmission Dynamics

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