Epidemic model with vaccinated age that exhibits backward bifurcation (original) (raw)
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Vaccination strategies and backward bifurcation in an age-since-infection structured model
Mathematical Biosciences, 2002
We consider models for a disease with acute and chronic infective stages, and variable infectivity and recovery rates, within the context of a vaccination campaign. Models for SIRS and SIS disease cycles exhibit backward bifurcations under certain conditions, which complicate the criteria for success of the vaccination campaign by making it possible to have stable endemic states when R 0 < 1. We also show the extent to which the forms of the infectivity and recovery functions affect the possibility of backward bifurcations. SIR and SI models examined do not exhibit this behavior. Ó structure 0025-5564/02/$ -see front matter Ó 2002 Elsevier Science Inc. All rights reserved. PII: S 0 0 2 5 -5 5 6 4 ( 0 1 ) 0 0 0 9 9 -2
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Abstract. A compartmental epidemic model, introduced by Gumel and Moghadas [1], is considered. The model incorporates a nonlinear incidence rate and an imperfect preventive vaccine given to susceptible individuals. A bifurcation analysis is performed by applying the bifurcation method introduced in [2], which is based on the use of the center manifold theory. Conditions ensuring the occurrence of backward bifurcation are derived. The obtained results are numerically validated and then discussed from both the mathematical and the ...
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Vaccination that gives partial protection for both newborns and susceptibles is included in a transmission model for a disease that confers no immunity. A general form of the vaccine waning function is assumed, and the interplay of this together with the vaccine efficacy and vaccination rates is discussed. The integro-differential system describing the model is studied for a constant vaccine waning rate, in which case it reduces to an ODE system, and for a constant waning period, in which case it reduces to a system of delay differential equations. For some parameter values, the model is shown to exhibit a backward bifurcation, leading to the existence of subthreshold endemic equilibria. Numerical examples are presented that demonstrate the consequence of this bifurcation in terms of epidemic control. The model can alternatively be interpreted as one consisting of two social groups, with education playing the role of vaccination.
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This paper presents a two stage SIS epidemic model in animal population with bovine tuberculosis (BTB) in African buffalo as a guiding example. The proposed model is rigorously analyzed. The analysis reveals that the model exhibits the phenomenon of backward bifurcation, where a stable disease-free equilibrium (DFE) coexists with a stable endemic equilibrium (EE) when the associated reproduction number (R v) is less than unity. It is shown under two special cases of the presented model, that this phenomenon of backward bifurcation does not arise depending on vaccination coverage and efficacy of vaccine. Numerical simulations of the model show that, the use of an imperfect vaccine can lead to effective control of the disease if the vaccination coverage and the efficacy of vaccine are high enough.
Abstract and Applied Analysis, 2015
In this paper, we formulate a susceptible-vaccinated-infected-recovered (SVIR) model by incorporating the vaccination of newborns, vaccine-age and mortality induced by the disease into the SIR epidemic model. It is assumed that the period of immunity induced by vaccines varies depending on the vaccine-age. Using the direct Lyapunov method with Volterra-type Lyapunov function, we show the global asymptotic stability of the infection-free and endemic steady states. Keyword: Age-dependent epidemic model; Vaccine-age; Waning vaccine-induced immunity; Volterra-type Lyapunov function; Global stability
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In this paper, an SEIV epidemic model with vaccination and nonlinear incidence rate is formulated. The analysis of the model is presented in terms of the basic reproduction number R 0. It is shown that the model has multiple equilibria and using the center manifold theory, the model exhibits the phenomenon of backward bifurcation where a stable diseasefree equilibrium coexists with a stable endemic equilibrium for a certain defined range of R 0. We also dis
Abstract and Applied Analysis, 2015
We formulate a susceptible-vaccinated-infected-recovered (SVIR) model by incorporating the vaccination of newborns, vaccineage, and mortality induced by the disease into the SIR epidemic model. It is assumed that the period of immunity induced by vaccines varies depending on the vaccine-age. Using the direct Lyapunov method with Volterra-type Lyapunov function, we show the global asymptotic stability of the infection-free and endemic steady states.