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A DELAYED SIR EPIDEMIC MODEL WITH NONLINEAR INCIDENCE RATE AND PULSE VACCINATION
Yanke Du,Rui Xu 한국전산응용수학회 2010 Journal of applied mathematics & informatics Vol.28 No.5
An SIR epidemic model with pulse vaccination and time delay describing infection period is investigated. The global attractiveness of the infection-free periodic solution is discussed,and sufficient condition is obtained for the permanence of the system. Our results indicate that a large vaccination rate or a short period of pulsing leads to the eradication of the disease.
A DELAYED SIR EPIDEMIC MODEL WITH NONLINEAR INCIDENCE RATE AND PULSE VACCINATION
Du, Yanke,Xu, Rui The Korean Society for Computational and Applied M 2010 Journal of applied mathematics & informatics Vol.28 No.5
An SIR epidemic model with pulse vaccination and time delay describing infection period is investigated. The global attractiveness of the infection-free periodic solution is discussed, and sufficient condition is obtained for the permanence of the system. Our results indicate that a large vaccination rate or a short period of pulsing leads to the eradication of the disease.
TRAVELING WAVES OF AN SIRS EPIDEMIC MODEL WITH SPATIAL DIFFUSION AND TIME DELAY
Du, Yanke,Xu, Rui The Korean Society for Computational and Applied M 2012 Journal of applied mathematics & informatics Vol.30 No.3
This paper is concerned with an SIRS epidemic model with spatial diffusion and time delay representing the length of the immunity period. By using a new cross iteration scheme and Schauder's fixed point theorem, we reduce the existence of traveling wave solutions to the existence of a pair of upper-lower solutions. By constructing a newfashioned pair of upper-lower solutions, we derive the existence of a traveling wave solution connecting the uninfected steady state and the infected steady state.
TRAVELING WAVES OF AN SIRS EPIDEMIC MODEL WITH SPATIAL DIFFUSION AND TIME DELAY
Yanke Du,Rui Xu 한국전산응용수학회 2012 Journal of applied mathematics & informatics Vol.30 No.3
This paper is concerned with an SIRS epidemic model with spatial diffusion and time delay representing the length of the immunity period. By using a new cross iteration scheme and Schauder's fixed point theorem, we reduce the existence of traveling wave solutions to the existence of a pair of upper-lower solutions. By constructing a newfashioned pair of upper-lower solutions, we derive the existence of a traveling wave solution connecting the uninfected steady state and the infected steady state.