scholarly journals Optimal Control Strategy for SEIR with Latent Period and a Saturated Incidence Rate

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Abta Abdelhadi ◽  
Laarabi Hassan
Keyword(s):  
Optimal Control ◽  
Latent Period ◽  
Incidence Rate ◽  
Nonlinear Model ◽  
Control Strategy ◽  
Optimal Control Strategy ◽  
Vaccination Strategies ◽  
Saturated Incidence Rate ◽  
Saturated Incidence

We propose an SEIR epidemic model with latent period and a modified saturated incidence rate. This work investigates the fundamental role of the vaccination strategies to reduce the number of susceptible, exposed, and infected individuals and increase the number of recovered individuals. The existence of the optimal control of the nonlinear model is also proved. The optimality system is derived and then solved numerically using a competitive Gauss-Seidel-like implicit difference method.

scholarly journals Optimal Control Strategy for a Discrete Time Smoking Model with Specific Saturated Incidence Rate

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Abderrahim Labzai ◽  
Omar Balatif ◽  
Mostafa Rachik
Keyword(s):  
Optimal Control ◽  
Incidence Rate ◽  
Discrete Time ◽  
Control Strategy ◽  
Optimal Controls ◽  
Optimization Strategy ◽  
Optimal Control Strategy ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Heavy Smokers

The aim of this paper is to study and investigate the optimal control strategy of a discrete mathematical model of smoking with specific saturated incidence rate. The population that we are going to study is divided into five compartments: potential smokers, light smokers, heavy smokers, temporary quitters of smoking, and permanent quitters of smoking. Our objective is to find the best strategy to reduce the number of light smokers, heavy smokers, and temporary quitters of smoking. We use three control strategies which are awareness programs through media and education, treatment, and psychological support with follow-up. Pontryagins maximum principle in discrete time is used to characterize the optimal controls. The numerical simulation is carried out using MATLAB. Consequently, the obtained results confirm the performance of the optimization strategy.

Role of pine wilt disease based on optimal control strategy at multiple scales: A case study of Korea

2021 ◽  
Vol 46 (4) ◽  
Author(s):  
Muhammad Ozair ◽  
Takasar Hussain ◽  
Kashif Ali Abro ◽  
Sajid Jameel ◽  
Aziz Ullah Awan
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Multiple Scales ◽  
Pine Wilt Disease ◽  
Wilt Disease ◽  
Optimal Control Strategy ◽  
Pine Wilt

scholarly journals Optimal costless extraction rate changes from a non-renewable resource

2014 ◽  
Vol 25 (6) ◽  
pp. 681-705 ◽  
Author(s):  
G. W. EVATT ◽  
P. V. JOHNSON ◽  
P. W. DUCK ◽  
S. D. HOWELL
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Renewable Resources ◽  
Investment Decision ◽  
Operating Cost ◽  
Renewable Resource ◽  
Analytic Solutions ◽  
Optimal Control Strategy ◽  
Critical Resource

This paper considers the role of costless decisions relating to the extraction of a non-renewable resource in the presence of uncertainty. We begin by deriving a size scale of the extractable resource, above which the solution to the valuation and optimal control strategy can be described by analytic solutions; we produce solutions for a general form of operating cost function. Below this critical resource size level the valuation and optimal control strategy must be solved by numerical means; we present a robust numerical algorithm that can solve such a class of problem. We also allow for the embedding of an irreversible investment decision (abandonment) into the optimisation. Finally, we conduct experimentation for each of these two approaches (analytical and numerical), and show how they are consistent with one another when used appropriately. The extensions of this paper's techniques to renewable resources are explored.

Closed-Loop Optimal Control Strategy for Cancer Chemotherapy

2007 ◽  
Author(s):  
Barathram Ramkumar ◽  
D. Subbaram Naidu
Keyword(s):  
Optimal Control ◽  
Cancer Cells ◽  
Cancer Chemotherapy ◽  
Nonlinear Model ◽  
Control Strategy ◽  
Closed Loop ◽  
Drug Level ◽  
Open Loop ◽  
The Body ◽  
Optimal Control Strategy

Cancer chemotherapy is the treatment of cancer using drugs that kill the cancer cells, when the drugs are administered either orally or through veins. The drugs are delivered according to a schedule so that a particular dosage of drug level is maintained in the body. The disadvantage of these drugs is that they not only kill the cancer cells but also kill the normal healthy cells. The role of optimal control in chemotherapy is to maintain an optimum amount of drug level in the body so that only cancer cells are killed and hence the effect of drug on the healthy cells is minimized. Three different mathematical models for cancer growth are considered: log-kill hypothesis, Norton-simon model, and Emax model. Two different cost functions are considered for constrained and unconstrained optimal control, respectively. An open loop optimal control strategy has been reported in the literature. In this paper, a closed-loop optimal control strategy is addressed using all the three models and for both the cases of constrained and unconstrained drug delivery. For the unconstrained case the original nonlinear model has been linearized and the closed loop design is obtained by using matrix Riccati solutions. On the other hand, for the constrained case the original nonlinear model has been used to obtain closed loop optimal control using bang-bang strategy. Final simulation results show the advantages of closed loop implementation in terms of simpler and elegant controller design and incorporating the effect of current state variations.

scholarly journals Stability analysis in a delayed SIR epidemic model with a saturated incidence rate

2010 ◽  
Vol 15 (3) ◽  
pp. 299-306 ◽  
Author(s):  
A. Kaddar
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Asymptotically Stable ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
The Basic Reproduction Number

We formulate a delayed SIR epidemic model by introducing a latent period into susceptible, and infectious individuals in incidence rate. This new reformulation provides a reasonable role of incubation period on the dynamics of SIR epidemic model. We show that if the basic reproduction number, denoted, R0, is less than unity, the diseasefree equilibrium is locally asymptotically stable. Moreover, we prove that if R0 > 1, the endemic equilibrium is locally asymptotically stable. In the end some numerical simulations are given to compare our model with existing model.

scholarly journals Optimal control of an epidemic model with a saturated incidence rate

2012 ◽  
Vol 17 (4) ◽  
pp. 448-459 ◽  
Author(s):  
Hassan Laarabi ◽  
El Houssine Labriji ◽  
Mostafa Rachik ◽  
Abdelilah Kaddar
Keyword(s):  
Optimal Control ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Control Framework ◽  
Adjoint Variables ◽  
Saturated Incidence Rate ◽  
Saturated Incidence

In this study we consider a mathematical model of an SIR epidemic model with a saturated incidence rate. We used the optimal vaccination strategies to minimize the susceptible and infected individuals and to maximize the number of recovered individuals. We work in the nonlinear optimal control framework. The existence result was discussed. A characterization of the optimal control via adjoint variables was established. We obtained an optimality system that we sought to solve numerically by a competitive Gauss–Seidel like implicit difference method.

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