一类离散SISV传染病模型的理论与仿真分析  

Theory and simulation analysis of a discrete-time SISV epidemic model

作　　者：董福安[1] 危敏剑[1,2] 于斌[1] 

机构地区：[1]空军工程大学理学院 [2]94923部队

出　　处：《西北师范大学学报（自然科学版）》2011年第1期12-16,共5页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11071256);陕西省自然科学基金资助项目(SJ08-ZT13)

摘　　要：引入相应的概率来描述个体的死亡、染病者的恢复、被接种者免疫的失去以及疾病的传染,建立了具有非线性发生率的离散SISV传染病模型.对于总种群动力学性态是补偿的情形,确定了决定其动力学性态的阈值,在阈值之下模型的无病平衡点是局部渐近稳定的,且仿真显示在一些参数取值下模型发生了后向分支,在阈值之上模型是一致持续的;对于总种群动力学性态是过度补偿的情形,仿真显示当总种群动力学性态出现倍周期和混沌现象时,易感类、染病类和被接种类也出现倍周期和混沌现象.The probability is introduced to formulate the death of individuals,the recovery of the infected individuals,the loss immunity of the vaccinal individuals and incidence of epidemic disease.Discrete-time SISV epidemic model with nonlinear incidence rate is established.In case of the total population dynamic is compensator,the threshold determining its dynamical behavior is found.Below the threshold the disease-free equilibrium is locally asymptotically stable and simulation shows the model occurs backward bifurcation at certain parameter values.Above the threshold the model is uniformly persistent.In the case that the total population dynamics is overcompensatory,simulation show while the total population dynamics undergoes period-doubling bifurcation route to chaos,the susceptive population dynamics,infective population dynamics and vaccinal population dynamics also undergo period-doubling bifurcation route to chaos.

关 键 词：离散传染病模型 动力学性态 平衡点 稳定性 

分 类 号：O175.7[理学—数学] N945.12[理学—基础数学]