A general model for the dynamics of cell volume, global stability, and optimal control

2010 ◽  
Vol 63 (2) ◽  
pp. 339-359 ◽  
Author(s):  
James D. Benson ◽  
Carmen C. Chicone ◽  
John K. Critser
Keyword(s):  
Optimal Control ◽  
Global Stability ◽  
Cell Volume ◽  
General Model

scholarly journals Global Stability and Optimal Control of Dengue with Two Coexisting Virus Serotypes

MATEMATIKA ◽  
2019 ◽  
Vol 35 (4) ◽  
pp. 149-170
Author(s):  
Afeez Abidemi ◽  
Rohanin Ahmad ◽  
Nur Arina Bazilah Aziz
Keyword(s):  
Optimal Control ◽  
Global Stability ◽  
Disease Transmission ◽  
Deterministic Model ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Effective Control ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Boundary Equilibrium

This study presents a two-strain deterministic model which incorporates Dengvaxia vaccine and insecticide (adulticide) control strategies to forecast the dynamics of transmission and control of dengue in Madeira Island if there is a new outbreak with a different virus serotypes after the first outbreak in 2012. We construct suitable Lyapunov functions to investigate the global stability of the disease-free and boundary equilibrium points. Qualitative analysis of the model which incorporates time-varying controls with the specific goal of minimizing dengue disease transmission and the costs related to the control implementation by employing the optimal control theory is carried out. Three strategies, namely the use of Dengvaxia vaccine only, application of adulticide only, and the combination of Dengvaxia vaccine and adulticide are considered for the controls implementation. The necessary conditions are derived for the optimal control of dengue. We examine the impacts of the control strategies on the dynamics of infected humans and mosquito population by simulating the optimality system. The disease-freeequilibrium is found to be globally asymptotically stable whenever the basic reproduction numbers associated with virus serotypes 1 and j (j 2 {2, 3, 4}), respectively, satisfy R01,R0j 1, and the boundary equilibrium is globally asymptotically stable when the related R0i (i = 1, j) is above one. It is shown that the strategy based on the combination of Dengvaxia vaccine and adulticide helps in an effective control of dengue spread in the Island.

scholarly journals Global stability and optimal control for a tuberculosis model with vaccination and treatment

2016 ◽  
Vol 21 (3) ◽  
pp. 1009-1022 ◽  
Author(s):  
Yali Yang ◽  
Sanyi Tang ◽  
Xiaohong Ren ◽  
Huiwen Zhao ◽  
Chenping Guo
Keyword(s):  
Optimal Control ◽  
Global Stability ◽  
Tuberculosis Model

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.

Controlling Asthma Due to Air Pollution

2020 ◽  
pp. 1-22
Author(s):  
Ankush H. Suthar ◽  
Purvi M. Pandya
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Air Pollution ◽  
Control Theory ◽  
Global Stability ◽  
Optimal Control Theory ◽  
Positive Impact ◽  
Equilibrium Points ◽  
Local And Global Stability ◽  
Number Of Individuals

The health of our respiratory systems is directly affected by the atmosphere. Nowadays, eruption of respiratory disease and malfunctioning of lung due to the presence of harmful particles in the air is one of the most sever challenge. In this chapter, association between air pollution-related respiratory diseases, namely dyspnea, cough, and asthma, is analysed by constructing a mathematical model. Local and global stability of the equilibrium points is proved. Optimal control theory is applied in the model to optimize stability of the model. Applied optimal control theory contains four control variables, among which first control helps to reduce number of individuals who are exposed to air pollutants and the remaining three controls help to reduce the spread and exacerbation of asthma. The positive impact of controls on the model and intensity of asthma under the influence of dyspnea and cough is observed graphically by simulating the model.

General Model of Optimal Control of Fully Flexible Vibrating Suspension Systems

2011 ◽  
Vol 383-390 ◽  
pp. 2978-2983
Author(s):  
Jun Chuan Niu ◽  
Ji Qing Zhu ◽  
Fa Wen Ji
Keyword(s):  
Optimal Control ◽  
General Model ◽  
Power Flow ◽  
Control Strategies ◽  
Matrix Approach ◽  
Flexible Beams ◽  
Suspension Systems ◽  
Transfer Matrix Approach ◽  
Structural Mobility ◽  
System Designs

Accounting of the fact that there are so many SMR systems in the isolation practices and investigation that it is not convenient and efficient to deal with them, the paper presents a general model and its mathematical description of fully flexible vibrating suspension systems, in which both machines and bases are considered as finite or infinite flexible beams, by sub-structural mobility technique and transfer matrix approach. Then in accordance with the combination of subsystems and the two proposed optimal control strategies, the formulation of power flow is derived. Some simulations are performed to show the validity and the reliability of the presented model and to obtain some valuable results which can be regarded as a set of general benchmarks of suspension system designs.

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