Optimal Control Model of Malaria Disease with Standard Incidence Rate

Nana-Kyere, Sacrifice; Doe, Richmond

doi:10.9734/jamcs/2017/35011

Cited by 7 publications

(9 citation statements)

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“…Here, we empty the formulas (11)-(12) for * = ( * , * ) the characteristic of the optimal control. The optimal control and the state are found by solving the optimality system, which consists of the state system (3), the adjoint (9), initial condition at = 0, boundary conditions (10), and the characterization of the optimal control (11)- (12). To solve the optimality system, we use the initial and transversality conditions together with the characterization of the optimal control ( * , * ) given by (11)- (12).…”

Section: Theorem 32mentioning

confidence: 99%

“…Optimal control models have produced another dimension in the modeling of infectious diseases, as it has come with insightful models that focus on variant control strategies for quality decision making on control intervention strategies with minimal cost [10,11,12]. Even though an imperative contributions have been made by researchers in explaining the bacteria interaction with human and their biology, the complexities in the life cycle of the bacteria, highly environmental factors that to a larger extent affects the transmission dynamics of the disease, coupled with the evolutionary challenge posed by the bacteria in drug resistance has thrown a challenge to researchers and modelers to come up with a combination of different methodologies, rather than the single type of deterministic models which have been applied in the attempt to eliminate the epidemic.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic Optimal Control Model of Haemorrhagic Conjunctivitis Disease

Nana-Kyere

Banon²,

Marmah

et al. 2019

JAMCS

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In this research article, a model for the transmission dynamics of haemorrhagic conjunctivitis disease is presented. The tool of dynamical system is employed in investigating the potency of the spreading of the epidemic. The analysis revealed the likelihood of the epidemic to spread when the basic reproduction number exceeds one. The model is reformulated as optimal control problem to assess the effectiveness of the proposed control strategy. Maximum Principle was employed to derive the necessary conditions for the existence of optimal control. Numerical solution of the optimality was derived and computed to investigate the optimum control strategy that would be efficacious to be implemented in reducing the number of exposed and infected individuals. Stochastic version of the model is deduced by introducing stochastic perturbations in the deterministic one. Numerical simulations are provided to illustrate the differences in the dynamics of the models and to understand the epidemic phenomenon.

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Section: Theorem 32mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stochastic Optimal Control Model of Haemorrhagic Conjunctivitis Disease

Nana-Kyere

Banon²,

Marmah

et al. 2019

JAMCS

Self Cite

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show abstract

“…Thus, here we must have 0 Q  and R > 0. In addition, the pair [A, B] is assumed stabilizable [18] and [A, Q 1/2 ] is observable (see [19]). The choice of specific values for the weight functions Q and R demands knowledge of the system to be controlled.…”

Section: T a T P T P T A T P T B T R B T P T Q T P T Smentioning

confidence: 99%

A Model of Oral and Parenteral Drug Administration with Control

Nzerem¹,

H.C²

2018

(GLM)

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Drug administration is largely a frontier in pharmacokinetics and pharmacodynamics. Kinetics and dynamics are of science in general, and therefore issues on drug administration may be of interdisciplinary interest. This paper treated pharmacokinetics from the standpoints of a subject-specific drug administration and control. A compartment-based mathematical model of drug administration was presented. Besides the endearing impacts of drug administration, the optimal control of drug regimen is a sine qua non to the therapeutic benefits derivable from a drug at the physiologic site(s). This argument motivated the control method applied hereto. The variable of interest for control is the time-dependent drug concentration in the bloodstream. It was considered essential since the concentration of a drug in the body within a finite time horizon is partly a measure of therapeutic response. To this end, the optimal controller discussed here must be, and indeed is, the one that could furnish the concentration that is both therapy-effectual and time-minimizing. It is only when these two conditions are met that a drug regimen may be seen to have achieved the desired goal.

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“…They investigated the impact of underreporting and behavior changes on the transmission rate in Mexico. Optimal control models have produced another dimension in the modeling of infectious diseases, as it has come with insightful models that focus on variant control strategies for quality decision making on control intervention strategies with minimal cost [10][11][12]. Even though an imperative contributions have been made by researchers in explaining the bacteria interaction with human and their biology, the complexities in the life cycle of the bacteria, highly environmental factors that to a larger extent affects the transmission dynamics of the disease, coupled with the evolutionary challenge posed by the bacteria in drug resistance has thrown a challenge to researchers and modelers to come up with a combination of different methodologies, rather than the single type of deterministic models which have been applied in the attempt to eliminate the epidemic.…”

Section: /7mentioning

confidence: 99%

“…( , ) w w w = the characteristic of the optimal control. The optimal control and the state are found by solving the optimality system, which consists of the state system (3), the adjoint (9), initial condition at t=0, boundary conditions (10), and the characterization of the optimal control (11)- (12). To solve the optimality system, we use the initial and transversality conditions together with the characterization of the optimal control * * 1 2…”

Section: /7mentioning

confidence: 99%

Optimal Control Model of Haemorhagic Conjunctivitis Disease

Nana-Kyere¹,

Titus²,

Boateng³

et al. 2018

Adv Comput Sci

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In this research article, a model for the transmission dynamics of haemorghagic conjunctivitis disease is presented. The tool of dynamical system is employed in investigating the potency of the spreading of the epidemic. The analysis revealed the likelihood of the epidemic to spread when the the basic reproduction number exceeds one. The model is reformulated as optimal control problem to assess the effectiveness of the proposed control strategy. Maximum Principle was employed to derive the necessary conditions for the existence of optimal control. Numerical solution of the optimality was derived and computed to investigate the optimum control strategy that would be efficacious to be implemented in reducing the number of exposed and infected individuals.

show abstract

Optimal Control Model of Malaria Disease with Standard Incidence Rate

Cited by 7 publications

References 0 publications

Stochastic Optimal Control Model of Haemorrhagic Conjunctivitis Disease

Stochastic Optimal Control Model of Haemorrhagic Conjunctivitis Disease

A Model of Oral and Parenteral Drug Administration with Control

Optimal Control Model of Haemorhagic Conjunctivitis Disease

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