Asymptotic analysis of a nonlinear stochastic eco-epidemiological system with feedback control

This paper proposes a new stochastic eco-epidemiological model with nonlinear incidence rate and feedback controls. First, we prove that the stochastic system has a unique global positive solution. Second, by constructing a series of appropriate stochastic Lyapunov functions, the asymptotic behavior...

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Bibliographic Details
Published in:Applied Mathematics-A Journal of Chinese Universities 2022-09, Vol.37 (3), p.317-339
Main Authors: Zhang, Sheng-qiang, Meng, Xin-zhu
Format: Article
Language:English
Subjects:
Applications of Mathematics
Asymptotic properties
Control systems
Epidemiology
Feedback control
Liapunov functions
Markov processes
Mathematical models
Mathematics
Mathematics and Statistics
Perturbation
Stochastic systems
Survivability
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Summary:This paper proposes a new stochastic eco-epidemiological model with nonlinear incidence rate and feedback controls. First, we prove that the stochastic system has a unique global positive solution. Second, by constructing a series of appropriate stochastic Lyapunov functions, the asymptotic behaviors around the equilibria of deterministic model are obtained, and we demonstrate that the stochastic system exists a stationary Markov process. Third, the conditions for persistence in the mean and extinction of the stochastic system are established. Finally, we carry out some numerical simulations with respect to different stochastic parameters to verify our analytical results. The obtained results indicate that the stochastic perturbations and feedback controls have crucial effects on the survivability of system.
ISSN:1005-1031
1993-0445
DOI:10.1007/s11766-022-3631-6