Positive periodic solution for a nonautonomous periodic model of population with time delays and impulses

2010 ◽  
Vol 25 (1) ◽  
pp. 18-24
Author(s):  
Gang Zhou ◽  
Bao Shi ◽  
Ming-jiu Gai ◽  
De-cun Zhang
Keyword(s):  
Periodic Solution ◽  
Time Delays ◽  
Positive Periodic Solution ◽  
Periodic Model

scholarly journals Global dynamics of a stage-structured hantavirus infection model with seasonality

2021 ◽  
Vol 26 (1) ◽  
pp. 21-40
Author(s):  
Junli Liu ◽  
Tailei Zhang
Keyword(s):  
Periodic Solution ◽  
Control Strategies ◽  
Stage Structure ◽  
Positive Periodic Solution ◽  
Clethrionomys Glareolus ◽  
Hantavirus Infection ◽  
Infection Model ◽  
Global Dynamics ◽  
Periodic Model ◽  
Globally Attractive

In this paper, we study a time-periodic model, which incorporates seasonality and host stage-structure. This model describes the propagation of Puumala hantavirus within the bank vole population of Clethrionomys glareolus. The basic reproduction number R0 is obtained. By appealing to the theory of monotone dynamical systems and chain transitive sets, we establish a threshold-type result on the global dynamics in terms of R0, that is, the virus-free periodic solution is globally attractive, and the virus dies out if R0 ≤ 1, while there exists a unique positive periodic solution, which is globally attractive, and the virus persists if R0 > 1. Numerical simulations are given to confirm our theoretical results and to show that cleaning environment and controlling the grow of mice population are essential control strategies to reduce hantavirus infection.

scholarly journals Dynamics of a Nonautonomous Leslie-Gower Type Food Chain Model with Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Hongying Lu ◽  
Weiguo Wang
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Food Chain ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Chain Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Food Chain Model

A nonautonomous Leslie-Gower type food chain model with time delays is investigated. It is proved the general nonautonomous system is permanent and globally asymptotically stable under some appropriate conditions. Furthermore, if the system is periodic one, some sufficient conditions are established, which guarantee the existence, uniqueness, and global asymptotic stability of a positive periodic solution of the system. The conditions for the permanence, global stability of system, and the existence, uniqueness of positive periodic solution depend on delays; so, time delays are profitless.

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