https://doi.org/10.1140/epjp/s13360-024-05889-3
Regular Article
Stability and Hopf bifurcation for a multi-delay PSIS eco-epidemic model with saturation incidence and Beddington–DeAngelis functional response
1
College of Mathematics and Systems Science, Xinjiang University, 830017, Urumqi, People’s Republic of China
2
Department of Mathematics and Statistics, Xinjiang Medical University, 830017, Urumqi, People’s Republic of China
3
Xinjiang Key Laboratory of Applied Mathematics, 830017, Urumqi, People’s Republic of China
Received:
1
November
2024
Accepted:
28
November
2024
Published online:
12
December
2024
In order to characterize the complicated infection process of infectious diseases in population systems, in this paper, a multiple delay eco-epidemic model with saturation incidence and Beddington–DeAngelis functional response is proposed. Firstly, we establish the positivity, uniform boundedness, and persistence of the model solutions. Next, the existence of three equilibria and its global dynamic behavior are discussed. And then we select the time delay as the bifurcation parameter to identify the criterion for the existence of Hopf bifurcation. By utilizing the central manifold theorem and the normal form theory, an explicit formula for determining the bifurcation periodic solution and evaluating the directionality of the bifurcation as well as the stability of the periodic solution is derived. Finally, some numerical simulations are conducted to validate the theories results.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024
