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 Complex Dynamics of an Impulsive Chemostat Model

2019 ◽  
Vol 29 (08) ◽  
pp. 1950101 ◽  
Author(s):  
Jin Yang ◽  
Yuanshun Tan ◽  
Robert A. Cheke
Keyword(s):  
Periodic Solution ◽  
Global Stability ◽  
Substrate Concentration ◽  
Complex Dynamics ◽  
Control Strategies ◽  
Phase Portraits ◽  
Global Dynamics ◽  
Chemostat Model ◽  
Existence And Stability ◽  
Theoretical Results

We propose a novel impulsive chemostat model with the substrate concentration as the basis for the implementation of control strategies, and then investigate the model’s global dynamics. The exact domains of the impulsive and phase sets are discussed in the light of phase portraits of the model, and then we define the Poincaré map and study its complex properties. Furthermore, the existence and stability of the microorganism eradication periodic solution are addressed, and the analysis of a transcritical bifurcation reveals that an order-1 periodic solution is generated. We also provide the conditions for the global stability of an order-1 periodic solution and show the existence of order-[Formula: see text] [Formula: see text] periodic solutions. Moreover, the PRCC results and bifurcation analyses not only substantiate our results, but also indicate that the proposed system exists with complex dynamics. Finally, biological implications related to the theoretical results are discussed.

scholarly journals Periodicity in a ratio-dependent predator-prey system with stage structure for predator

2005 ◽  
Vol 2005 (2) ◽  
pp. 153-169 ◽  
Author(s):  
Fengde Chen
Keyword(s):  
Periodic Solution ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Stage Structure ◽  
Positive Periodic Solution ◽  
Positive Periodic Solutions ◽  
Priori Estimate ◽  
Predator Prey ◽  
Prey System ◽  
Ratio Dependent

With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of a delayed ratio-dependent predator-prey system with stage structure for predator. The approach involves some new technique of priori estimate. For the system without delay, by constructing a suitable Lyapunov function, some sufficient conditions which guarantee the existence of a unique global attractive positive periodic solution are obtained. Those results have further applications in population dynamics.

scholarly journals The Study of a Class of Pest Control Pollution Model with Stage-Structure and Time Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Jianwen Jia ◽  
Bo Wu
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Time Delay ◽  
Comparison Theorem ◽  
Pest Control ◽  
Impulsive Differential Equation ◽  
Stage Structure ◽  
Globally Attractive

We construct a pest control pollution model with stage-structure for pests and with epidemic in the predator by spraying pesticides and releasing susceptible predators together. We assume that only the pests and infective predators are affected by pesticide. We show that there exists a globally attractive pest-extinction periodic solution and we get the condition of global attractiveness of the pest-extinction periodic solution by applying comparison theorem of impulsive differential equation. Further, the condition for the permanence of the system is also given.

scholarly journals Existence and Global Attractivity of Positive Periodic Solutions for a Two-Species Competitive System with Stage Structure and Impulse

2011 ◽  
Vol 2011 ◽  
pp. 1-28 ◽  
Author(s):  
Changjin Xu ◽  
Daxue Chen
Keyword(s):  
Periodic Solution ◽  
Lyapunov Functional ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Stage Structure ◽  
Positive Periodic Solution ◽  
Positive Periodic Solutions ◽  
Competitive System

A class of nonautonomous two-species competitive system with stage structure and impulse is considered. By using the continuation theorem of coincidence degree theory, we derive a set of easily verifiable sufficient conditions that guarantee the existence of at least a positive periodic solution, and, by constructing a suitable Lyapunov functional, the uniqueness and global attractivity of the positive periodic solution are presented. Finally, an illustrative example is given to demonstrate the correctness of the obtained results.

scholarly journals Analysis of an Impulsive One-Predator and Two-Prey System with Stage-Structure and Generalized Functional Response

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Xiangmin Ma ◽  
Yuanfu Shao ◽  
Zhen Wang ◽  
Xianjia Fang ◽  
Zhenguo Luo
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Global Attractivity ◽  
Control Strategies ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Reasonable Assumption ◽  
Functional Responses ◽  
Prey System ◽  
Dynamical Properties

An impulsive one-predator and two-prey system with stage-structure and generalized functional response is proposed and analyzed. By reasonable assumption and theoretical analysis, we obtain conditions for the existence and global attractivity of the predator-extinction periodic solution. Sufficient conditions for the permanence of this system are established via impulsive differential comparison theorem. Furthermore, abundant results of numerical simulations are given by choosing two different and concrete functional responses, which indicate that impulsive effects, stage-structure, and functional responses are vital to the dynamical properties of this system. Finally, the biological meanings of the main results and some control strategies are given.

scholarly journals A new approach to persistence and periodicity of logistic systems with jumps

2021 ◽  
Vol 6 (11) ◽  
pp. 12245-12259
Author(s):  
Kegang Zhao ◽  
Keyword(s):  
Periodic Solution ◽  
Control Theory ◽  
Differential System ◽  
Positive Periodic Solution ◽  
New Approach ◽  
Discontinuous Control ◽  
Globally Attractive

<abstract><p>This paper considers a class of logistic type differential system with jumps. Based on discontinuous control theory, a new approach is developed to guarantee the persistence and existence of a unique globally attractive positive periodic solution. The development results of this paper emphasize the effects of jumps on system, which are different from the existing ones in the literature. Two examples and their simulations are given to illustrate the effectiveness of the proposed results.</p></abstract>

Dynamics of Infectious Diseases: Local Versus Global Awareness

2021 ◽  
Vol 31 (07) ◽  
pp. 2150102
Author(s):  
Pankaj Kumar Tiwari ◽  
Rajanish Kumar Rai ◽  
Arvind Kumar Misra ◽  
Joydev Chattopadhyay
Keyword(s):  
Social Media ◽  
Growth Rate ◽  
Periodic Solution ◽  
Hopf Bifurcation ◽  
Disease Modeling ◽  
Public Awareness ◽  
Positive Periodic Solution ◽  
Global Awareness ◽  
Precautionary Measures ◽  
Globally Attractive

Public awareness programs may deeply influence the epidemic pattern of a contagious disease by altering people’s perception of risk and individuals behavior during the course of the epidemic outbreak. Regardless of the veracity, social media advertisements are expected to execute an increasingly prominent role in the field of infectious disease modeling. In this paper, we propose a model which portrays the interplay between dissemination of awareness at local and global levels, and prevalence of disease. Our sensitivity results determine the correlations between some epidemiologically important parameters and disease prevalence. The growth rate of broadcasting information through social media is found to destabilize the system through limit cycle oscillations whereas the baseline number of social media advertisements stabilize the system by terminating persistent oscillations. The system first undergoes supercritical Hopf-bifurcation and then subcritical Hopf-bifurcation on gradual increase in dissemination rate of awareness at local/global level. Moreover, the disease is eradicated if the dissemination rates of awareness and baseline number of social media advertisements are too large. We also study the effect of seasonal variation of the growth rate of social media advertisements. Our nonautonomous system generates globally attractive positive periodic solution if the growth rate of social media advertisements lies between certain ranges. However, the global attractivity is affected on enhancement in growth rate of social media advertisements and three-periodic solution is observed. Our findings show that baseline number of social media advertisements and dissemination of awareness at individual as well as community levels play a tremendous role in eliminating the burden of disease. Furthermore, a comparison of the effects of local and global awareness reveals that the latter is more effective in curtailing the disease. We believe these findings may be beneficial to understand the contagion characteristics of real epidemics and help to adopt suitable precautionary measures in the form of nonpharmaceutical interventions.

scholarly journals Global dynamics of an immunosuppressive infection model with stage structure

2020 ◽  
Vol 17 (3) ◽  
pp. 2082-2102
Author(s):  
Hongying Shu ◽  
◽  
Wanxiao Xu ◽  
Zenghui Hao ◽  
Keyword(s):  
Stage Structure ◽  
Infection Model ◽  
Global Dynamics
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