On avian influenza epidemic models with time delay.

Area of Science:

• Epidemiology
• Mathematical Biology
• Virology

Background:

• Avian influenza A virus (H7N9) emerged in China in 2013-2014, causing significant human cases and mortality.
• Previous outbreaks, like H5N1 in 1997, highlight the threat of avian influenza crossing species barriers.

Purpose of the Study:

• To develop a mathematical model for bird-to-human transmission of avian influenza A virus.
• To incorporate incubation periods and survival probabilities into the transmission dynamics.
• To analyze the model's behavior and identify key factors influencing prevalence.

Main Methods:

• Construction of a mathematical model simulating avian influenza A virus transmission.
• Inclusion of distinct time delays for avian and human populations.
• Analysis of the model's dynamical behavior, including stability of equilibria.

Main Results:

• Identification of a critical threshold value for avian influenza prevalence.
• Investigation into the local and global asymptotic stability of the model's equilibrium points.
• Quantification of the impact of incubation periods and survival probabilities on transmission dynamics.

Conclusions:

• The developed model provides insights into H7N9 transmission dynamics.
• The identified threshold is essential for predicting and managing avian influenza outbreaks.
• Understanding latent periods and survival rates is critical for effective disease control strategies.