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 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 Harvesting on Facultative Mutualist Prey Species in Presence of a Predator

2017 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
Saroj Kumar Chattopadhyay
Keyword(s):  
Maximum Principle ◽  
Numerical Simulations ◽  
Prey Species ◽  
Pontryagin’S Maximum Principle ◽  
Pontryagin's Maximum Principle ◽  
Interior Equilibrium ◽  
Optimal Harvest ◽  
The Stability ◽  
Optimal Harvest Policy

<p><em>This paper proposes a model with two preys of facultative mutualist type and one predator. Linear predation functions are considered and preys are only considered to be harvested. The stability of the model is analyzed theoretically and numerically in this paper. The optimal harvest policy is studied and the solution is derived in the interior equilibrium case using Pontryagin’s maximum principle. Finally, some numerical simulations are discussed.</em></p>

A New Discrete Anologue of Pontryagin’s Maximum Principle

2018 ◽  
Vol 483 (1) ◽  
pp. 15-18
Author(s):  
M. Mardanov ◽  
◽  
T. Melikov ◽  
Keyword(s):  
Maximum Principle ◽  
Pontryagin’S Maximum Principle ◽  
Pontryagin's Maximum Principle
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