Stability analysis and optimal vaccination of an SIR epidemic model

Zaman, Gul; Kang, Yong Han; Jung, Il Hyo

doi:10.1016/j.biosystems.2008.05.004

Cited by 344 publications

(206 citation statements)

References 12 publications

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“…The values of some parameters have been studied in some literatures while others don't. Here, we consider the idea presented in [11,12]. When a person first becomes a smoker it is not likely that she/he quits for several years since tobacco contains nicotine, which is shown to be an addictive drug.…”

Section: Numerical Simulationsmentioning

confidence: 99%

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Smoking as Epidemic: Modeling and Simulation Study

Matintu¹

2017

AJAM

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Abstract:In this paper we propose smoking epidemic model which analyzes the spread of smoking in a population. The model consists of five compartments corresponding to five population classes, namely, potential-moderate-heavy-temporarily recoveredpermanently recovered class. The basic reproduction number R 0 has been derived, and then the dynamical behaviors of both smoking free equilibrium and smoking persistent equilibrium are analyzed by the theory of differential equation, and Numerical simulation has been carried out and the results have confirmed the verification of analytical results. Sensitivity analysis of R 0 identifies β 1 , the transmission coefficient from potential smokers to moderate smokers and β 2 , the transmission coefficient from potential smokers to heavy smokers, as the most useful parameters to target for the reduction of R 0 .

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Section: Numerical Simulationsmentioning

confidence: 99%

“…One of an interesting area in epidemiology to study is smoking subject. There are a lot of studies that has been done on the epidemics of smoking [3][4][5][6][7][8][9][10][11][12]. In order to understand the dynamics of this disease, like many infectious diseases, mathematical models can be used.…”

Section: Introductionmentioning

confidence: 99%

Smoking as Epidemic: Modeling and Simulation Study

Matintu¹

2017

AJAM

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“…Proof: To prove the existence of an optimal control we use techniques presented in [7,24]. Since both the control variables and the state variables are non-negative values.…”

Section: Theorem 61: There Exists An Optimal Control Umentioning

confidence: 99%

“…Optimal control is one of the useful mathematical tools through which we are able to design the control strategy for controlling various kind of infectious diseases. To develop a control strategy, we use the optimal control theory [24,25]. Our purpose here is to reduce HBV infection from the population by maximizing the number of susceptible S(t) and recovered individuals R(t) and minimizing the number of infected with acute hepatitis B individuals I 1 (t), infected with chronic hepatitis B individuals I 2 (t) by using the time-dependent control variables isolation u 1 (t) of infected and non-infected individuals, treatment u 2 (t) and hepatitis B vaccination u 3 (t).…”

Section: Optimal Control Applicationmentioning

confidence: 99%

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The transmission dynamic and optimal control of acute and chronic hepatitis B

Khan

Zaman

Chohan

2016

Journal of Biological Dynamics

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In this article, we present the transmission dynamic of the acute and chronic hepatitis B epidemic problem and develop an optimal control strategy to control the spread of hepatitis B in a community. In order to do this, first we present the model formulation and find the basic reproduction number R 0 . We show that if R 0 ≤ 1, then the disease-free equilibrium is both locally as well as globally asymptotically stable. Then, we prove that the model is locally and globally asymptotically stable, if R 0 > 1. To control the spread of this infection, we develop a control strategy by applying three control variables such as isolation of infected and non-infected individuals, treatment and vaccination to minimize the number of acute infected, chronically infected with hepatitis B individuals and maximize the number of susceptible and recovered individuals. Finally, we present numerical simulation to illustrate the feasibility of the control strategy. ARTICLE HISTORY

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Optimal control strategy for fed‐batch enzymatic hydrolysis of lignocellulosic biomass based on epidemic modeling

Tai

Keshwani

Voltan

et al. 2015

Biotech & Bioengineering

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A mathematical optimal control strategy for feeding operation was developed for fed-batch enzymatic hydrolysis of dilute acid pretreated lignocellulosic biomass based on a modified epidemic model. Cellulose conversion was maximized and glucose concentration achieved highest possible value over a fixed hydrolysis time. Boundaries of feeding rate and lignin content were set for feasible controls. Using the optimal control feeding strategy, glucose concentration and accumulated cellulose conversion reached up to 77.31 g/L and 72.08% in 100 h, which are 108.76% and 37.50% higher than in batch hydrolysis with same amount of enzyme consumption. Solids content in feeding source has a significant interference on system mass transfer. Optimal control is a useful tool for guiding operations in fed-batch and continuous processes as it enables process optimization through clear objective functions and feasible controls.

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Stability analysis and optimal vaccination of an SIR epidemic model

Cited by 344 publications

References 12 publications

Smoking as Epidemic: Modeling and Simulation Study

Smoking as Epidemic: Modeling and Simulation Study

The transmission dynamic and optimal control of acute and chronic hepatitis B

Optimal control strategy for fed‐batch enzymatic hydrolysis of lignocellulosic biomass based on epidemic modeling

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