一类具有时滞和空间扩散的SIR传染病模型的行波解
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摘要
研究了一类具有时滞和空间扩散的SIR传染病模型,通过分析相应的特征方程,讨论了系统每个平衡态的局部稳定性,通过运用交叉迭代方法和Schauder不动点定理,把行波解的存在性转化为一对上下解的存在性,通过构造一对上下解,得到了连接无病平衡态和地方病平衡态的行波解的存在性.
A delayed SIR epidemic model with spatial diffusion is investigated in this paper.By analyzing the corresponding characteristic equations, the local stability of each of uniform steady states to this system is discussed. By using a 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 pair of upper-lower solutions, we derive the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state.
A delayed SIR epidemic model with spatial diffusion is investigated in this paper.By analyzing the corresponding characteristic equations, the local stability of each of uniform steady states to this system is discussed. By using a 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 pair of upper-lower solutions, we derive the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state.
引文
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[2]Xu R,Ma Z E.Global stability of a SIR epidemic model with nonlinear incidence rate and time delay[J].Nonlinear Anal RWA,2009,10(5):3175-3189.
[3]Kermack W O,McKendrick A G.Contributions to the mathematical theory of epidemics,part I[J].Proceedings of the Royal Society of London Series A,1927,115:700-721.
[4]Kim K,Lin Z G,Zhang L.Avian-human influenza epidemic model with diffusion[J].Nonlinear Anal RWA,2010,11(1):313-322.
[5]Maidana N,Yang H.Spatial spreading of West Nile Virus described by traveling waves[J].Journal of Theoretical Biology,2009,258(3):403-417.
[6]Xu R,Ma Z E.An HBV model with diffusion and time delay[J].Journal of Theoretical Biology,2009,257(3):499-509.
[7]Huang J H,Zou X F.Travelling wave solutions in delayed reaction diffusion systems with partial monotonicity[J].Acta Math Appl Sin Engl Ser,2006,22(2):243-256.
[8]Wang Q R,Zhou K.Traveling wave solutions in delayed reaction-diffusion systems with mixed monotonicity[J].Appl Math,2010,233(2):2549-2562.