scholarly journals Global Stability Analysis and Optimal Control of a Harvested Ecoepidemiological Prey Predator Model with Vaccination and Taxation

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Chao Liu ◽  
Qingling Zhang ◽  
Jinna Li
Keyword(s):  
Optimal Control ◽  
Stability Analysis ◽  
Global Stability ◽  
Interaction Mechanism ◽  
Prey Population ◽  
Predator Population ◽  
Optimal Control Strategy ◽  
Global Stability Analysis ◽  
Selective Harvest ◽  
Predator Model

We propose an ecoepidemiological prey predator model, where selective harvest effort on predator population is considered. Vaccination and taxation are introduced as control instruments, which are utilized to control number of susceptible prey population and protect predator population from overexploitation, respectively. Conditions which influence nonnegativity and boundedness of solutions are studied. Global stability analysis around disease-free equilibrium is discussed based on robust Bendixson criterion, which is theoretically beneficial to studying coexistence and interaction mechanism of population within harvested ecoepidemiological system. By using Pontryagin’s maximum principle, an optimal control strategy is derived to maximize the total discounted net economic revenue to society as well as protect prey population from infectious disease. Numerical simulations are carried out to show the consistency with theoretical analysis.

scholarly journals Stability Analysis of a Harvested Prey-Predator Model with Stage Structure and Maturation Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Chao Liu ◽  
Qingling Zhang ◽  
James Huang
Keyword(s):  
Stability Analysis ◽  
Stage Structure ◽  
Model System ◽  
Positive Equilibrium ◽  
Predator Population ◽  
Maturation Delay ◽  
Effort Level ◽  
Selective Harvest ◽  
Proposed Model ◽  
Predator Model

A harvested prey-predator model with density-dependent maturation delay and stage structure for prey is proposed, where selective harvest effort on predator population is considered. Conditions which influence positiveness and boundedness of solutions of model system are analytically investigated. Criteria for existence of all equilibria and uniqueness of positive equilibrium are also studied. In order to discuss effects of maturation delay and harvesting on model dynamics, local stability analysis around all equilibria of the proposed model system is discussed due to variation of maturation delay and harvest effort level. Furthermore, global stability of positive equilibrium is investigated by utilizing an iterative technique. Finally, numerical simulations are carried out to show consistency with theoretical analysis.

scholarly journals Volterra–Lyapunov Stability Analysis of the Solutions of Babesiosis Disease Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1272
Author(s):  
Fengsheng Chien ◽  
Stanford Shateyi
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Global Stability ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Disease Model ◽  
Transmission Dynamics ◽  
Global Stability Analysis ◽  
Lyapunov Stability Analysis ◽  
Disease Free

This paper studies the global stability analysis of a mathematical model on Babesiosis transmission dynamics on bovines and ticks populations as proposed by Dang et al. First, the global stability analysis of disease-free equilibrium (DFE) is presented. Furthermore, using the properties of Volterra–Lyapunov matrices, we show that it is possible to prove the global stability of the endemic equilibrium. The property of symmetry in the structure of Volterra–Lyapunov matrices plays an important role in achieving this goal. Furthermore, numerical simulations are used to verify the result presented.

Sign in / Sign up

Export Citation Format

Share Document