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Numerical Algebra, Control & Optimization

2015 , Volume 5 , Issue 4

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Dynamic simulation of a SEIQR-V epidemic model based on cellular automata
Xinxin Tan , Shujuan Li , Sisi Liu , Zhiwei Zhao , Lisa Huang and  Jiatai Gang
2015, 5(4): 327-337 doi: 10.3934/naco.2015.5.327 +[Abstract](46) +[PDF](1330.7KB)
A SEIQR-V epidemic model, including the exposure period, is established based on cellular automata. Considerations are made for individual mobility and heterogeneity while introducing measures of vaccinating susceptible populations and quarantining infectious populations. Referencing the random walk cellular automata and extended Moore neighborhood theories, influenza A(H1N1) is used as example to create a dynamic simulation using Matlab software. The simulated results match real data released by the World Health Organization, indicating the model is valid and effective. On this basis, the effects of vaccination proportion and quarantine intensity on epidemic propagation are analogue simulated, obtaining their trends of influence and optimal control strategies are suggested.
Optimal control of microbial fed-batch culture involving multiple feeds
Jinggui Gao , Xiaoyan Zhao and  Jinggang Zhai
2015, 5(4): 339-349 doi: 10.3934/naco.2015.5.339 +[Abstract](45) +[PDF](402.1KB)
In this paper, we consider optimal control problem in the fed-batch fermentation of glycerol by Klebsiella pneumoniae with open loop glycerol input and pH logic control, while the feeding volume of glycerol is regarded as the control variable. To maximize the concentration of 1,3-PD at the terminal time, an optimal control model is established, and a computational approach is constructed to solve the control model. Finally, the numerical simulations show that the terminal concentration of producing 1,3-PD has been increased obviously by employing the optimal feeding strategy.
Solving the seepage problems with free surface by mathematical programming method
Jinzhi Wang and  Yuduo Zhang
2015, 5(4): 351-357 doi: 10.3934/naco.2015.5.351 +[Abstract](33) +[PDF](286.0KB)
The nonsmooth equations model for seepage problems is proposed based on the basic principles of the seepage dynamic system and the finite element discrete method. The mathematical programming method is therefore applied. The free surface of seepage is plotted through interpolation with pressure intensity on the nodes. The numerical results show the new method is simple and rapid in convergence rate.
Modeling and identification of hybrid dynamic system in microbial continuous fermentation
Yanan Mao , Caixia Gao , Ruidong Yan and  Aruna Bai
2015, 5(4): 359-368 doi: 10.3934/naco.2015.5.359 +[Abstract](32) +[PDF](340.6KB)
In this paper, a hybrid dynamic model using fuzzy expert system is investigated in the process of glycerol bioconversion to 1,3-PD by Klebsiella pneumoniae(K.pneumoniae). In continuous culture, we assume that 1,3-PD passes the cell membrane of K.pneumoniae by passive diffusion coupling with active transport. To determine the parameters of the proposed system, a parameter identification model is established according to the biological robustness. An optimization algorithm is developed in order to solve the identification model. Numerical simulations indicate that proposed hybrid model adding fuzzy system is more appropriate and the optimization algorithm is effective.
Nonlinear state-dependent impulsive system in fed-batch culture and its optimal control
Bangyu Shen , Xiaojing Wang and  Chongyang Liu
2015, 5(4): 369-380 doi: 10.3934/naco.2015.5.369 +[Abstract](116) +[PDF](404.7KB)
In fed-batch culture, feeding substrates is to provide sufficient nutrition and reduce inhibitions simultaneously for cells growth. Hence, when and how much to feed substrates are important during the process. In this paper, a nonlinear impulsive controlls system, in which the volume of feeding is taken as the control function, is proposed to formulate the fed-batch fermentation process.In the system, both impulsive moments and jumps size of state are state-dependent. Some important properties of the system are investigated. To maximize the concentration of target product at the terminal time, an optimal control model involving the nonlinear state-dependent impulsive controlled system is presented.The optimal control problem is subject to the continuous state inequality constraint and the control constraint. The existence of optimal control is also obtained. In order to derive the optimality conditions, the optimal control model is transcribed into an equivalent one by treating the constraints. Finally, the optimality conditions of the optimal control model are obtained via calculus of variations.
A stochastic model for microbial fermentation process under Gaussian white noise environment
Yan Wang , Lei Wang , Yanxiang Zhao , Aimin Song and  Yanping Ma
2015, 5(4): 381-392 doi: 10.3934/naco.2015.5.381 +[Abstract](79) +[PDF](355.3KB)
In this paper, we propose a stochastic model for the microbial fermentation process under the framework of white noise analysis, where Gaussian white noises are used to model the environmental noises and the specific growth rate is driven by Gaussian white noises. In order to keep the regularity of the terminal time, the adjustment factors are added in the volatility coefficients of the stochastic model. Then we prove some fundamental properties of the stochastic model: the regularity of the terminal time, the existence and uniqueness of a solution and the continuous dependence of the solution on the initial values.
Modeling and identification of dynamical system with Genetic Regulation in batch fermentation of glycerol
Xu Zhang and  Xiang Li
2015, 5(4): 393-403 doi: 10.3934/naco.2015.5.393 +[Abstract](41) +[PDF](338.4KB)
The background of this paper is the production of 1,3-PD by batch fermentation of glycerol, supposed that glycerol and 1,3-PD pass the cell membrane by passive diffusion with active transportation. We present a nonlinear enzyme-catalytic dynamical system with genetic regulation and our purpose is to identify these parameters in the dynamical system. Since the intracellular substance concentrations are immeasurable, we refer to the robustness definition of parameter disturbance in biological system, then we establish a parameter identification model. We prove the existence of the solution to the optimization model. At last, we get the parameters of dynamical systems by particle swarm algorithm. Numerical results show that the optimization algorithm is valid and the genetic regulations can help to understand the intracellular reaction process.




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