On avian influenza epidemic models with time delay.
After the outbreak of the first avian influenza A virus (H5N1) in Hong Kong in 1997, another avian influenza A virus (H7N9) crossed the species barrier in mainland China in 2013 and 2014 and caused more than 400 human cases with a death rate of nearly 40%. In this paper, we take account of the incubation periods of avian influenza A virus and construct a bird-to-human transmission model with different time delays in the avian and human populations combining the survival probability of the infective avian and human populations at the latent time. By analyzing the dynamical behavior of the model, we obtain a threshold value for the prevalence of avian influenza and investigate local and global asymptotical stability of equilibria of the system.
School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China.|Department of Basic Education, Wenhua College, Wuhan, 430074, Hubei, China.
Sanhong
S
Liu
Department of Mathematics, University of Miami, Coral Gables, FL, 33124-4250, USA. ruan@math.miami.edu.
Shigui
S
Ruan
School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China.
Xinan
X
Zhang
D000818:Animals; D001717:Birds; D003198:Computer Simulation; D004196:Disease Outbreaks / Q000706:statistics & numerical data*; D006801:Humans; D015994:Incidence; D055256:Infectious Disease Incubation Period; D053124:Influenza A Virus, H5N1 Subtype; D064766:Influenza A Virus, H7N9 Subtype; D005585:Influenza in Birds / Q000453:epidemiology*; D007251:Influenza, Human / Q000453:epidemiology*; D015233:Models, Statistical; D011159:Population Surveillance / Q000379:methods*; D018570:Risk Assessment / Q000379:methods; D012307:Risk Factors; D013997:Time Factors
Avian influenza; Basic reproduction number; Incubation period; Local and global asymptotical stability; Time delay