Multistability, chaos, and transient dynamics in an avian influenza mathematical model

Abstract Influenza, commonly known as the flu, is a highly contagious respiratory infection that causes symptoms, such as cough, aches, and malaise in infected individuals. One important form of influenza A infection is avian influenza, caused by the H5N1 virus, which has been a concern since the late twentieth century due to its high mortality rate. Monitoring and controlling avian influenza is of great importance for public health issues due to its ability to infect other mammals and its potential risk for spillover to humans. Mathematical models capable of describing the dynamics of avian influenza have been proposed to explore the spread of the disease and adapt control measures to contain it. In this work, we analyze the dynamical behavior of an avian influenza model consisting of two coupled SI (susceptible-infected) models, one describing the bird population and the other the human population. Using the bird mortality rate as the control parameter and hysteresis-type bifurcation diagrams, we identify bistability over a wide parameter range. As this parameter increases, we observe a significant range of hyperchaos. Furthermore, we uncover and quantify transient chaos and boundary crises for a given set of parameter values. These findings contribute to a more detailed understanding of the non-linear dynamics that may arise in mathematical models of avian influenza transmission.