Dynamic simulation of a SEIQR-V epidemic model based on cellular automata

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2015, 5(4): 327-337. doi: 10.3934/naco.2015.5.327

Dynamic simulation of a SEIQR-V epidemic model based on cellular automata

Xinxin Tan ^1, , Shujuan Li ^1, , Sisi Liu ^1, , Zhiwei Zhao ^2, , Lisa Huang ^3, and Jiatai Gang ^1,

1.	College of Information Engineering, Dalian University, Dalian 116622, China, China, China, China
2.	College of Environmental and Chemical Engineering, Dalian University, Dalian, 116622, China
3.	Portacom NZ Limited, Auckland 1061, New Zealand

Received November 2014 Revised October 2015 Published October 2015

Abstract
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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.

Keywords: Cellular automata, vaccination proportion, dynamic simulation, quarantine intensity, influenza A(H1N1)..

Mathematics Subject Classification: Primary: 92B02; Secondary: 37F0.

Citation: Xinxin Tan, Shujuan Li, Sisi Liu, Zhiwei Zhao, Lisa Huang, Jiatai Gang. Dynamic simulation of a SEIQR-V epidemic model based on cellular automata. Numerical Algebra, Control & Optimization, 2015, 5 (4) : 327-337. doi: 10.3934/naco.2015.5.327

References:

[1]	Xiaodong Duan, Cunrui Wang and Xiangdong Liu, Cellular Automata Theory Research and Simulation Application,, Science press, (2012). Google Scholar
[2]	Jiatai Gang, Pengyan Shi and Sanshan Gang, A epidemic Model with Inhomogeneity And Mobility based on Cellular Automata,, Advanced Material Research, 709 (2013), 871. Google Scholar
[3]	C. Guan, W. Yuan and Y. Peng, A cellular automaton model with extended neighborhood for epidemic propagation,, Computational Sciences and Optimization, (2011), 623. Google Scholar
[4]	Guangliang Li, Tao Wang and Chunling Zhang, Research on the Spread of infectious Diseases With Incubation Period,, Digital Technology and Application, (2013), 203. Google Scholar
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[6]	G. Ch. Sirakoulis, I Karafyllidis and A Thanailakis, A cellular automaton model for the effects of population movement and vaccination on epidemic propagation,, Ecological Modelling, 133 (2000), 209. Google Scholar
[7]	Xinxin Tan, Shujuan Li, Qinwu Dai and Jiatai Gang, An Epidemic Model with Isolated Intervention Based on Cellular Automata,, Advanced Materials Research, 926 (2014), 1065. Google Scholar
[8]	Xinxin Tan, Qinwu Dai and Pengyan Shi, CA-based epidemic propagation model with inhomogeneity and mobility,, Journal of Dalian University of Technology, 53 (2013), 908. Google Scholar
[9]	, World Health Organization, Global Alert and Response (GAR): Influenza A(H1N1), 2009,Report of World Health Organization,, 2009. Available from: , (). Google Scholar
[10]	WenXiao Tu, YuanSheng Chen and Lu Li, Major epidemiological characteristics of pandemic (H1N1) 2009,, Disease Surveillance, 24 (2009), 906. Google Scholar
[11]	Sanlin Yuan, Litao Han and Zhien Ma, A Kind of Epidemic Model Having Infectious Force in both Latent Periodand Infected Period,, Journal of Biomathematics, 16 (2001), 392. Google Scholar

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References:

[1]	Xiaodong Duan, Cunrui Wang and Xiangdong Liu, Cellular Automata Theory Research and Simulation Application,, Science press, (2012). Google Scholar
[2]	Jiatai Gang, Pengyan Shi and Sanshan Gang, A epidemic Model with Inhomogeneity And Mobility based on Cellular Automata,, Advanced Material Research, 709 (2013), 871. Google Scholar
[3]	C. Guan, W. Yuan and Y. Peng, A cellular automaton model with extended neighborhood for epidemic propagation,, Computational Sciences and Optimization, (2011), 623. Google Scholar
[4]	Guangliang Li, Tao Wang and Chunling Zhang, Research on the Spread of infectious Diseases With Incubation Period,, Digital Technology and Application, (2013), 203. Google Scholar
[5]	Jian Liu, Dong Chen, Dehai Liu and Weijun Xu, A study on government control measures of h7h9 avian influenza in different stages of development,, New Chinese Medicine, 45 (2014), 5. Google Scholar
[6]	G. Ch. Sirakoulis, I Karafyllidis and A Thanailakis, A cellular automaton model for the effects of population movement and vaccination on epidemic propagation,, Ecological Modelling, 133 (2000), 209. Google Scholar
[7]	Xinxin Tan, Shujuan Li, Qinwu Dai and Jiatai Gang, An Epidemic Model with Isolated Intervention Based on Cellular Automata,, Advanced Materials Research, 926 (2014), 1065. Google Scholar
[8]	Xinxin Tan, Qinwu Dai and Pengyan Shi, CA-based epidemic propagation model with inhomogeneity and mobility,, Journal of Dalian University of Technology, 53 (2013), 908. Google Scholar
[9]	, World Health Organization, Global Alert and Response (GAR): Influenza A(H1N1), 2009,Report of World Health Organization,, 2009. Available from: , (). Google Scholar
[10]	WenXiao Tu, YuanSheng Chen and Lu Li, Major epidemiological characteristics of pandemic (H1N1) 2009,, Disease Surveillance, 24 (2009), 906. Google Scholar
[11]	Sanlin Yuan, Litao Han and Zhien Ma, A Kind of Epidemic Model Having Infectious Force in both Latent Periodand Infected Period,, Journal of Biomathematics, 16 (2001), 392. Google Scholar

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