Nonlinear dynamics of avian influenza epidemic models

Abstract

Avian influenza is a zoonotic disease caused by the transmission of the avian influenza A virus, such as H5N1 and H7N9, from birds to humans. The avian influenza A H5N1 virus has caused more than 500 human infections worldwide with nearly a 60% death rate since it was first reported in Hong Kong in 1997. The four outbreaks of the avian influenza A H7N9 in China from March 2013 to June 2016 have resulted in 580 human cases including 202 deaths with a death rate of nearly 35%. In this paper, we construct two avian influenza bird-to-human transmission models with different growth laws of the avian population, one with logistic growth and the other with Allee effect, and analyze their dynamical behavior. We obtain a threshold value for the prevalence of avian influenza and investigate the local or global asymptotical stability of each equilibrium of these systems by using linear analysis technique or combining Liapunov function method and LaSalle's invariance principle, respectively. Moreover, we give necessary and sufficient conditions for the occurrence of periodic solutions in the avian influenza system with Allee effect of the avian population. Numerical simulations are also presented to illustrate the theoretical results.

Dynamics Analysis of Avian Influenza A(H7N9) Epidemic Model

“…Chen and Wen [10] based on the bilinear disease incidence studied 2 Discrete Dynamics in Nature and Society a model with mutant avian influenza A(H7N9) virus in 2015. In 2017, Liu et al [11] proposed two avian influenza models with different growth rates of the avian population, one with logistic growth and the other with Allee effect.…”

Avian Influenza A (H7N9) Model Based on Poultry Transport Network in China

“…Many authors investigated the epidemic model which describes the transmission of avian influenza among birds and humans [ 8 – 15 ]. Liu et al [ 16 ] constructed two avian influenza bird-to-human transmission models with different growth laws of the avian population, one with logistic growth and the other with Allee effect, and analyzed their dynamical behavior. Lin et al [ 17 ] developed three different SIRS models to fit the observed human cases between March 2013 and July 2015 in China and found that environmental transmission via viral shedding of infected chickens had contributed to the spread of H7N9 human cases in China.…”

Global Dynamics of an Avian Influenza A(H7N9) Epidemic Model with Latent Period and Nonlinear Recovery Rate

“…(i) Taking into account the factors such as poultry market mobility, environment capacity, and the existing populations, the susceptible poultry is subject to the logistic growth [ 6 ] where r p and K p are the intrinsic growth rate and maximal carrying capacity of the poultry.…”

“…Liu and Fang [ 5 ] formulated a two-host model to investigate the impact of screening and culling of infected poultry. Liu et al [ 6 ] considered different growth laws of the avian population, to present that the necessary and sufficient condition for periodic solution existing is the Allee effect in avian population. However, most of these models ignore the latent period between infection and symptom onset in human populations, which does exist on the basis of the reported infection cases.…”