scholarly journals Optimal Control Strategies in an Alcoholism Model

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Xun-Yang Wang ◽  
Hai-Feng Huo ◽  
Qing-Kai Kong ◽  
Wei-Xuan Shi
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Maximum Principle ◽  
Numerical Simulations ◽  
Control Strategies ◽  
Pontryagin’S Maximum Principle ◽  
Social Phenomenon ◽  
Pontryagin's Maximum Principle ◽  
Existence And Stability ◽  
Objective Functional

This paper presents a deterministic SATQ-type mathematical model (including susceptible, alcoholism, treating, and quitting compartments) for the spread of alcoholism with two control strategies to gain insights into this increasingly concerned about health and social phenomenon. Some properties of the solutions to the model including positivity, existence and stability are analyzed. The optimal control strategies are derived by proposing an objective functional and using Pontryagin’s Maximum Principle. Numerical simulations are also conducted in the analytic results.

scholarly journals The COVID-19 Model with Partially Recovered Carriers

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
T. S. Faniran ◽  
E. A. Bakare ◽  
A. O. Falade
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Numerical Simulations ◽  
Pontryagin’S Maximum Principle ◽  
Optimality System ◽  
World Health ◽  
Control Analysis ◽  
Optimal Controls ◽  
Pontryagin's Maximum Principle ◽  
Social Distancing

Novel coronavirus (COVID-19) has been spreading and wreaking havoc globally, despite massive efforts by the government and World Health Organization (WHO). Consideration of partially recovered carriers is hypothesized to play a leading role in the persistence of the disease and its introduction to new areas. A model for transmission of COVID-19 by symptomless partially recovered carriers is proposed and analysed. It is shown that key parameters can be identified such that below a threshold level, built on these parameters, the epidemic tends towards extinction, while above another threshold, it tends towards a nontrivial epidemic state. Moreover, optimal control analysis of the model, using Pontryagin’s maximum principle, is performed. The optimal controls are characterized in terms of the optimality system and solved numerically for several scenarios. Numerical simulations and sensitivity analysis of the basic reproduction number, R c , indicate that the disease is mainly driven by parameters involving the partially recovered carriers rather than symptomatic ones. Moreover, optimal control analysis of the model, using Pontryagin’s maximum principle, is performed. The optimal controls were characterized in terms of the optimality system and solved numerically for several scenarios. Numerical simulations were explored to illustrate our theoretical findings, scenarios were built, and the model predicted that social distancing and treatment of the symptomatic will slow down the epidemic curve and reduce mortality of COVID-19 given that there is an average adherence to social distancing and effective treatment are administered.

scholarly journals A Within-host Tuberculosis Model Using Optimal Control

2021 ◽  
Vol 5 (1) ◽  
pp. 162
Author(s):  
Yudi Ari Adi
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Mycobacterium Tuberculosis ◽  
Maximum Principle ◽  
Numerical Simulations ◽  
Infection Rate ◽  
Hamiltonian Function ◽  
Pontryagin’S Maximum Principle ◽  
Effective Strategies ◽  
Tuberculosis Model

 In this paper, we studied a mathematical model of tuberculosis with vaccination for the treatment of  tuberculosis. We considered an in-host tuberculosis model that described the interaction between Macrophages and Mycobacterium tuberculosis and investigated the effect of vaccination treatments on uninfected macrophages. Optimal control is applied to show the optimal vaccination and effective strategies to control the disease. The optimal control formula is obtained using the Hamiltonian function and Pontryagin's maximum principle. Finally, we perform numerical simulations to support the analytical results. The results suggest that control or vaccination is required if the maximal transmission of infection rate at which macrophages became infected is large. In this paper, we studied a mathematical model of tuberculosis with vaccination for the treatment of  tuberculosis.We considered an in-host tuberculosis model that described the interaction between macrophages Macrophages and Mycobacterium tuberculosis and investigated the effect of vaccination treatments on uninfected macrophages. Optimal controlis applied to show the optimal vaccination and effective strategies to control the disease. The optimal control formula isobtained using the Hamiltonian function and Pontryagin's maximum principle. Finally, we perform numerical simulations to support the analytical results.The results suggest thatcontrol or vaccination is required if the maximal transmission of infection rate at which macrophages became infected is large.

scholarly journals Analysis of seir model with a single control for COVID-19

10.26524/cm89 ◽  
2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Naga soundarya lakshmi V S V ◽  
Sabarmathi A
Keyword(s):  
Mathematical Model ◽  
Maximum Principle ◽  
Numerical Simulations ◽  
Pontryagin’S Maximum Principle ◽  
Pontryagin's Maximum Principle ◽  
Seir Model ◽  
Optimal Values

A SEIR mathematical model with a single control vaccination is formulated. Properties of Pontryagin's maximum principle is verified and found the optimal levels of controls. Optimal values of S, E, I, R were derived by equlibrium analysis. Numerical simulations were carried out to exhibit the Susceptible, Exposed, Infectious and Recovery class with and without vaccination.

scholarly journals Modeling the Effective Control Strategy for the Transmission Dynamics of Global Pandemic COVID-19

2020 ◽  
Author(s):  
M. H. A. Biswas ◽  
M. S. Khatun ◽  
A. K. Paul ◽  
M. R. Khatun ◽  
M. A. Islam ◽  
...  
Keyword(s):  
Maximum Principle ◽  
Control Strategies ◽  
Pontryagin’S Maximum Principle ◽  
Control Measures ◽  
Effective Control ◽  
Human Immune System ◽  
Pontryagin's Maximum Principle ◽  
Social Distancing ◽  
Novel Coronavirus ◽  
Major Factors

AbstractThe novel coronavirus disease (namely COVID-19) has taken attention because of its deadliness across the globe, causing a massive death as well as critical situation around the world. It is an infectious disease which is caused by newly discovered coronavirus. Our study demonstrates with a nonlinear model of this devastating COVID-19 which narrates transmission from human-to-human in the society. Pontryagin’s Maximum principle has also been applied in order to obtain optimal control strategies where the maintenance of social distancing is the major control. The target of this study is to find out the most fruitful control measures of averting coronavirus infection and eventually, curtailed of the COVID-19 transmission among people. The model is investigated analytically by using most familiar necessary conditions of Pontryagin’s maximum principle. Furthermore, numerical simulations have been performed to illustrate the analytical results. The analysis reveals that implementation of educational campaign, social distancing and developing human immune system are the major factors which can be able to plunge the scenario of becoming infected.

scholarly journals Optimal control with a cost of switching control

1976 ◽  
Vol 19 (3) ◽  
pp. 316-332 ◽  
Author(s):  
John M. Blatt
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Existence Theorem ◽  
Switching Control ◽  
Pontryagin’S Maximum Principle ◽  
Pontryagin's Maximum Principle ◽  
Theory Of Optimal Control ◽  
General Existence

AbstractThe Pontryagin theory of optimal control is modified by assuming a positive cost associated with switching control from one discrete value to another. The resulting new theory permits a general existence theorem. Pontryagin's maximum principle is replaced by an “indifference principle”.

scholarly journals OPTIMAL CONTROL USING PONTRYAGIN'S MAXIMUM PRINCIPLE IN A LINEAR QUADRATIC DIFFERENTIAL GAME

2012 ◽  
Vol 09 ◽  
pp. 543-551
Author(s):  
MARZIEH KHAKESTARI ◽  
GAFURJAN IBRAGIMOV ◽  
MOHAMED SULEIMAN
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Differential Game ◽  
Quadratic Differential ◽  
Pontryagin’S Maximum Principle ◽  
Linear Quadratic ◽  
Pontryagin's Maximum Principle ◽  
The Maximum Principle ◽  
Control Functions ◽  
Linear Quadratic Differential Games

This paper deals with a class of two person zero-sum linear quadratic differential games, where the control functions for both players subject to integral constraints. Also the necessary conditions of the Maximum Principle are studied. Main objective in this work is to obtain optimal control by using method of Pontryagin's Maximum Principle. This method for a time-varying linear quadratic differential game is described. Finally, we discuss about an example.

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