Epidemic dynamics model with delay and impulsive vaccination control base on variable population
Identifieur interne : 002322 ( Main/Merge ); précédent : 002321; suivant : 002323Epidemic dynamics model with delay and impulsive vaccination control base on variable population
Auteurs : Zhihui Yang [République populaire de Chine] ; Hanmei Jia [République populaire de Chine]Source :
- Mathematical Methods in the Applied Sciences [ 0170-4214 ] ; 2011-10.
English descriptors
- Teeft :
- Anhui, Anhui province, Anhui university, Appl, Capita birth rate, Comparison theorem, Computer modelling, Copyright, Epidemic model, Fourth equations, Global, Global attractivity, Global stability, Hethcote, Immune responses, Impulsive, Impulsive vaccination, Infectious diseases, Infectious population, Initial conditions, Initial value, Initial values, John wiley sons, Latent delay, Latent period, Long period, Mathematical biology, Mathematical biosciences, Measles, Meth, Modelling, Natural science foundation, Other hand, Periodic solution, Periodic solutions, Positive solution, Pulse vaccination, Pulse vaccination policy, Pulse vaccination strategy, Second case, Second equation, Seir, Seir epidemic model, Seir model, Small pulse vaccination rate, Susceptible individuals, Total population size, Uncountable intervals, Vaccination, Vaccination campaign, Vaccination effort, Vaccination rate, Vaccination strategy, Vaccine, Variable population, Vertical transmission.
Abstract
Pulse vaccination is an effective strategy for the elimination of infectious diseases. In this paper, we considered an SEIR epidemic model with delay and impulsive vaccination direct at a variable population and analyzed its dynamic behaviors. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection‐free periodic solution of the impulsive epidemic system, further, prove that the infection‐free periodic solution is globally attractive if the vaccination rate is larger than θ* or the length of latent period of disease is larger than τ* or the length of period of impulsive vaccination is smaller than T*. We also prove that a short latent period of the disease (with τ) or a long period of pulsing (with T) or a small pulse vaccination rate (with θ) is sufficient to bring about the disease is uniformly persistent. Copyright © 2011 John Wiley & Sons, Ltd.
Url:
DOI: 10.1002/mma.1481
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<term>Computer modelling</term>
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<term>Global attractivity</term>
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<term>Mathematical biology</term>
<term>Mathematical biosciences</term>
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<term>Modelling</term>
<term>Natural science foundation</term>
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<term>Uncountable intervals</term>
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<term>Vaccination campaign</term>
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<front><div type="abstract">Pulse vaccination is an effective strategy for the elimination of infectious diseases. In this paper, we considered an SEIR epidemic model with delay and impulsive vaccination direct at a variable population and analyzed its dynamic behaviors. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection‐free periodic solution of the impulsive epidemic system, further, prove that the infection‐free periodic solution is globally attractive if the vaccination rate is larger than θ* or the length of latent period of disease is larger than τ* or the length of period of impulsive vaccination is smaller than T*. We also prove that a short latent period of the disease (with τ) or a long period of pulsing (with T) or a small pulse vaccination rate (with θ) is sufficient to bring about the disease is uniformly persistent. Copyright © 2011 John Wiley & Sons, Ltd.</div>
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