Spatiotemporal Dynamics of a Diffusive Immunosuppressive Infection Model with Nonlocal Competition and Crowley–Martin Functional Response

In this paper, we introduce the Crowley–Martin functional response and nonlocal competition into a reaction–diffusion immunosuppressive infection model. First, we analyze the existence and stability of the positive constant steady states of the systems with nonlocal competition and local competition...

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Bibliographic Details
Published in:Axioms 2023-11, Vol.12 (12), p.1085
Main Authors: Xue, Yuan, Xu, Jinli, Ding, Yuting
Format: Article
Language:English
Subjects:
Canonical forms
Competition
Crowley–Martin functional response
delay
Hepatitis
HIV
Hopf bifurcation
Human immunodeficiency virus
Immune system
Immunosuppression
immunosuppressive infection model
Infection
Infections
Mathematical models
nonlocal competition
Pathogens
Stability analysis
Viruses
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Summary:In this paper, we introduce the Crowley–Martin functional response and nonlocal competition into a reaction–diffusion immunosuppressive infection model. First, we analyze the existence and stability of the positive constant steady states of the systems with nonlocal competition and local competition, respectively. Second, we deduce the conditions for the occurrence of Turing, Hopf, and Turing–Hopf bifurcations of the system with nonlocal competition, as well as the conditions for the occurrence of Hopf bifurcations of the system with local competition. Furthermore, we employ the multiple time scales method to derive the normal forms of the Hopf bifurcations reduced on the center manifold for both systems. Finally, we conduct numerical simulations for both systems under the same parameter settings, compare the impact of nonlocal competition, and find that the nonlocal term can induce spatially inhomogeneous stable periodic solutions. We also provide corresponding biological explanations for the simulation results.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms12121085