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 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 KONTROL OPTIMAL PADA PEYEBARAN TUBERKULOSIS DENGAN EXOGENOUS REINFECTION

2019 ◽  
Vol 16 (1) ◽  
pp. 42-50
Author(s):  
J Nainggolan ◽  
F J Iswar ◽  
Abraham Abraham
Keyword(s):  
Numerical Simulation ◽  
Optimal Control ◽  
Mycobacterium Tuberculosis ◽  
Maximum Principle ◽  
Pontryagin Maximum Principle ◽  
Pontryagin’S Maximum Principle ◽  
Pontryagin's Maximum Principle ◽  
Simulation Results ◽  
The Pontryagin Maximum Principle ◽  
Exogenous Reinfection

Tuberculosis is a disease caused by Mycobacterium tuberculosis. Tuberculosis can be controlled through treatment, chemoprophylaxis and vaccination. Optimal control of treatment in the exposed compartment can be done in an effort to reduce the number of exposed compartments individual into the active compartment of tuberculosis. Optimal control can be completed by the Pontryagin Maximum Principle Method. Based on numerical simulation results, optimal control of treatment in the exposed compartment can reduce the number of infected compartments individual with active TB.Keywords : Exogenous Reinfection, Optimal Control, Pontryagin's Maximum Principle, Spread Of Tuberculosis.

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 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.

Optimal Control of a Tuberculosis Model with Chemoprophylaxis Treatment

2013 ◽  
Vol 647 ◽  
pp. 595-599
Author(s):  
Ya Li Yang ◽  
Jian Feng Cheng ◽  
Fang Chen ◽  
Ya Yi Xu
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Control Strategy ◽  
Latent Infection ◽  
Optimal Level ◽  
Pontryagin’S Maximum Principle ◽  
Optimality System ◽  
Pontryagin's Maximum Principle ◽  
Tuberculosis Model

Seeking to reduce the latent and infectious tuberculosis groups, we use the control strategy which incorporates chemoprophylaxis treatment for latent infection. The optimal control is characterized in terms of the optimality system, and we characterize the optimal level of the control strategy by using Pontryagin's Maximum Principle. Furthermore, we give the solved numerically for several scenarios.

A hamiltonian approach to optimal stochastic resource allocation

1977 ◽  
Vol 9 (01) ◽  
pp. 55-68 ◽  
Author(s):  
P. Nash ◽  
J. C. Gittins
Keyword(s):  
Optimal Control ◽  
Resource Allocation ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Schedule ◽  
Pontryagin’S Maximum Principle ◽  
Hamiltonian Approach ◽  
Stochastic Resource Allocation ◽  
Service Times

The problem of scheduling items for service with random service times is formulated as an optimal control problem. Pontryagin's maximum principle is used to determine the optimal schedule in certain cases.

scholarly journals Stability and optimal control in a mathematical model of online game addiction

Filomat ◽  
2019 ◽  
Vol 33 (17) ◽  
pp. 5691-5711 ◽  
Author(s):  
Tingting Li ◽  
Youming Guo
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Maximum Principle ◽  
Control Strategy ◽  
Reproduction Number ◽  
Direct Transfer ◽  
Online Game ◽  
Optimal Control Strategy ◽  
Game Addiction ◽  
The Basic Reproduction Number

In this paper, we construct an online game addiction model(including susceptible, infective, professional and quitting compartments). We also consider that the direct transfer from the susceptible individuals to the professional individuals. Some properties of the model are derived by the basic reproduction number R0 and stability of all kinds of equilibria is obtained. Then we use Pontriagin?s maximum principle to solve the optimal control strategy. Finally, Numerical simulations are also conducted in the analytic results.

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