Two patterns of recruitment in an epidemic model with difference in immunity of individuals

Ji, Xuehui; Pei, Yongzhen; Li, Changguo

doi:10.1016/j.nonrwa.2009.06.001

Cited by 6 publications

(7 citation statements)

References 22 publications

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“…Pulse vaccination is an effective method to use in controlling the transmission of diseases which has gained prominence. Epidemiological models with pulse vaccination have been set up and investigated in many literatures [1][2][3][4][5][6][7][8]. This kind of vaccination strategy is usually called pulse vaccination strategy (PVS).…”

Section: Introductionmentioning

confidence: 99%

Dynamic Behaviors of an SEIR Epidemic Model in a Periodic Environment with Impulse Vaccination

Yan

Xiang

2014

Discrete Dynamics in Nature and Society

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We consider a nonautonomous SEIR endemic model with saturation incidence concerning pulse vaccination. By applying Floquet theory and the comparison theorem of impulsive differential equations, a threshold parameter which determines the extinction or persistence of the disease is presented. Finally, numerical simulations are given to illustrate the main theoretical results and it shows that pulse vaccination plays a key role in the disease control.

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Section: Introductionmentioning

confidence: 99%

Dynamic Behaviors of an SEIR Epidemic Model in a Periodic Environment with Impulse Vaccination

Yan

Xiang

2014

Discrete Dynamics in Nature and Society

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“…Nie et al [19] and Ji et al [39] respectively considered a delay SIR epidemic model with nonlinear incidence rate and density-dependent birth and death rates. Motivated by the main idea described in [6,39], in this paper, we consider a delay SIR model with difference in immunity and successive vaccination and an abstract incidence rate. The main difference between our study and those described in [6,39] is the difference in immunity and successive vaccination and an abstract incidence rate.…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by the main idea described in [6,39], in this paper, we consider a delay SIR model with difference in immunity and successive vaccination and an abstract incidence rate. The main difference between our study and those described in [6,39] is the difference in immunity and successive vaccination and an abstract incidence rate. An abstract incidence rate of type ( ) is employed to model the spread of the disease which is propagated through the infective individuals, under a few biologically feasible assumptions upon ( ).…”

Section: Introductionmentioning

confidence: 99%

Successive Vaccination and Difference in Immunity of a Delay SIR Model with a General Incidence Rate

Pei

et al. 2014

Abstract and Applied Analysis

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A delay SIR epidemic model with difference in immunity and successive vaccination is proposed to understand their effects on the disease spread. From theorems, it is obtained that the basic reproduction number governs the dynamic behavior of the system. The existence and stability of the possible equilibria are examined in terms of a certain threshold condition about the basic reproduction number. By use of new computational techniques for delay differential equations, we prove that the system is permanent. Our results indicate that the recovery rate and the vaccination rate are two factors for the dynamic behavior of the system. Numerical simulations are carried out to investigate the influence of the key parameters on the spread of the disease, to support the analytical conclusion, and to illustrate possible behavioral scenarios of the model.

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“…Epidemiology is the study of the spread of diseases in space and time, aiming at tracing factors that give rise totheir occurrence. Various epidemic models have been formulated and analyzed in [1][2][3][4]. In particular, some authors have studied population dynamics models wit agestructured [3]; some authors have studied the effects of treatment on the spread of Diseases [1].…”

Section: Introductionmentioning

confidence: 99%

A SIRS Epidemic Model Incorporating Treatment and Age-Structured of Recovered Period

Wang

Pei

Li³

et al. 2011

2011 International Conference on Control, Automation and Systems Engineering (CASE)

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A SIR model incorporating treatment and agestructured of recovered period is investigated. It is assumed that infective ones recover from the disease with temporary immunity. Here the rate at which recovered individual move to susceptible class again, depends upon vaccine age and hence it is assumed to be a variable. By using the existence of root and characteristic values analysis, we show that 0 ℜ determines whether the disease will become endemic or die out. From a biological point of view, our results indicate that (1) the disease can be eradicated if the treatment rate is controlled under relatively low threshold provided 0 0 I I ≤ ≤ ; (2) When 0 I I > , the equilibrium 1 E is unstable whenever it exists.

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Two patterns of recruitment in an epidemic model with difference in immunity of individuals

Cited by 6 publications

References 22 publications

Dynamic Behaviors of an SEIR Epidemic Model in a Periodic Environment with Impulse Vaccination

Dynamic Behaviors of an SEIR Epidemic Model in a Periodic Environment with Impulse Vaccination

Successive Vaccination and Difference in Immunity of a Delay SIR Model with a General Incidence Rate

A SIRS Epidemic Model Incorporating Treatment and Age-Structured of Recovered Period

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