具有时滞的禽流感模型数值模拟分析  

Numerical Simulation Analysis of Avian Influenza Model with Time Delay

作　　者：王经民[1] 石行 WANG Jing-min, SHI Hang(College of science, Northwest A＆F University, YangLing 712100, Chin)

机构地区：[1]西北农林科技大学理学院

出　　处：《数学的实践与认识》2018年第17期291-300,共10页Mathematics in Practice and Theory

摘　　要：近年来禽流感大肆流行不仅对人类健康造成了极大地威胁,同时也严重影响了我国家禽市场行业的发展.在本文中,我们考虑了禽流感病毒在人类和禽类种群中具有不同的潜伏期并且在潜伏期内染病者的生存概率不同,从而构建了一个时滞微分方程.通过分析该时滞系统的动力学性态,证明了系统平衡点的局部和全局渐近稳定性并获得了禽流感流行的阈值,最后通过数值模拟来说明如果减少染病禽类与易感禽类和易感人类的接触率,染病人数会随之减少;当接触率低于阈值时,禽流感会逐渐消失,反之会成为一种地方病在人群中流行.如果延长禽流感病毒在禽类和人类种群中的潜伏期,染病的人数则会随之减少;当潜伏期时滞高于阈值时,禽流感会逐渐消失,反之会成为一种地方病在人群中流行.In recent years, avian flu has become popular, not only posed a great threat to human health, but also seriously affected the development of China＇s poultry market. In this paper, we consider that incubation periods of avian influenza virus in human and avian population are different and the survival probability of infectives during incubation period is different too, thus we construct a time delay differential equation.By analyzing the dynamical behavior of the Time-delay system, the local and global asymptotic stability of the system equilibrium point is proved and the threshold of the avian influenza epidemic is obtained. Finally, the numerical simulation shows that if the contact rate of infected birds and susceptible birds and susceptible human beings is reduced, the number of infected pa- tients will decrease. When the contact rate is below the threshold, the bird flu will gradually disappear, whereas the disease will become endemic in the population. If the incubation period of avian influenza virus in avian and human population is prolonged, the number of infected persons will decrease. When the incubation period is above the threshold, the avian flu will gradually disappear, whereas the disease will become endemic in the population.

关 键 词：禽流感 时滞 接触率 稳定性 

分 类 号：O241.8[理学—计算数学]