# American Institute of Mathematical Sciences

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

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

 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

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.
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 and 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. [2] Jiatai Gang, Pengyan Shi and Sanshan Gang, A epidemic Model with Inhomogeneity And Mobility based on Cellular Automata, Advanced Material Research, 709 (2013), 871-874. [3] C. Guan, W. Yuan and Y. Peng, A cellular automaton model with extended neighborhood for epidemic propagation, Computational Sciences and Optimization, (2011), 623-627. [4] Guangliang Li, Tao Wang and Chunling Zhang, Research on the Spread of infectious Diseases With Incubation Period, Digital Technology and Application, (2013), 203-204. [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), 5-8. [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), 209-223. [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), 1065-1068. [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), 908-914. [9] , World Health Organization, Global Alert and Response (GAR): Influenza A(H1N1), 2009,Report of World Health Organization, 2009. Available from: http://www.who.int/csr/don/archive/year/2009/en/. [10] WenXiao Tu, YuanSheng Chen and Lu Li, Major epidemiological characteristics of pandemic (H1N1) 2009, Disease Surveillance, 24 (2009), 906-909. [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), 392-398.

show all references

##### References:
 [1] Xiaodong Duan, Cunrui Wang and Xiangdong Liu, Cellular Automata Theory Research and Simulation Application, Science press, 2012. [2] Jiatai Gang, Pengyan Shi and Sanshan Gang, A epidemic Model with Inhomogeneity And Mobility based on Cellular Automata, Advanced Material Research, 709 (2013), 871-874. [3] C. Guan, W. Yuan and Y. Peng, A cellular automaton model with extended neighborhood for epidemic propagation, Computational Sciences and Optimization, (2011), 623-627. [4] Guangliang Li, Tao Wang and Chunling Zhang, Research on the Spread of infectious Diseases With Incubation Period, Digital Technology and Application, (2013), 203-204. [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), 5-8. [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), 209-223. [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), 1065-1068. [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), 908-914. [9] , World Health Organization, Global Alert and Response (GAR): Influenza A(H1N1), 2009,Report of World Health Organization, 2009. Available from: http://www.who.int/csr/don/archive/year/2009/en/. [10] WenXiao Tu, YuanSheng Chen and Lu Li, Major epidemiological characteristics of pandemic (H1N1) 2009, Disease Surveillance, 24 (2009), 906-909. [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), 392-398.
 [1] Rodolfo Acuňa-Soto, Luis Castaňeda-Davila, Gerardo Chowell. A perspective on the 2009 A/H1N1 influenza pandemic in Mexico. Mathematical Biosciences & Engineering, 2011, 8 (1) : 223-238. doi: 10.3934/mbe.2011.8.223 [2] Raimund Bürger, Gerardo Chowell, Pep Mulet, Luis M. Villada. Modelling the spatial-temporal progression of the 2009 A/H1N1 influenza pandemic in Chile. Mathematical Biosciences & Engineering, 2016, 13 (1) : 43-65. doi: 10.3934/mbe.2016.13.43 [3] Olivia Prosper, Omar Saucedo, Doria Thompson, Griselle Torres-Garcia, Xiaohong Wang, Carlos Castillo-Chavez. Modeling control strategies for concurrent epidemics of seasonal and pandemic H1N1 influenza. Mathematical Biosciences & Engineering, 2011, 8 (1) : 141-170. doi: 10.3934/mbe.2011.8.141 [4] Arni S.R. Srinivasa Rao. Modeling the rapid spread of avian influenza (H5N1) in India. Mathematical Biosciences & Engineering, 2008, 5 (3) : 523-537. doi: 10.3934/mbe.2008.5.523 [5] T.K. Subrahmonian Moothathu. Homogeneity of surjective cellular automata. Discrete and Continuous Dynamical Systems, 2005, 13 (1) : 195-202. doi: 10.3934/dcds.2005.13.195 [6] Achilles Beros, Monique Chyba, Oleksandr Markovichenko. Controlled cellular automata. Networks and Heterogeneous Media, 2019, 14 (1) : 1-22. doi: 10.3934/nhm.2019001 [7] Marcus Pivato. Invariant measures for bipermutative cellular automata. Discrete and Continuous Dynamical Systems, 2005, 12 (4) : 723-736. doi: 10.3934/dcds.2005.12.723 [8] M. De Boeck, P. Vandendriessche. On the dual code of points and generators on the Hermitian variety $\mathcal{H}(2n+1,q^{2})$. Advances in Mathematics of Communications, 2014, 8 (3) : 281-296. doi: 10.3934/amc.2014.8.281 [9] Linfang Liu, Xianlong Fu, Yuncheng You. Pullback attractor in $H^{1}$ for nonautonomous stochastic reaction-diffusion equations on $\mathbb{R}^n$. Discrete and Continuous Dynamical Systems - B, 2017, 22 (10) : 3629-3651. doi: 10.3934/dcdsb.2017143 [10] Frédéric Vanhove. A geometric proof of the upper bound on the size of partial spreads in $H(4n+1,$q2$)$. Advances in Mathematics of Communications, 2011, 5 (2) : 157-160. doi: 10.3934/amc.2011.5.157 [11] Stephen C. Preston, Ralph Saxton. An $H^1$ model for inextensible strings. Discrete and Continuous Dynamical Systems, 2013, 33 (5) : 2065-2083. doi: 10.3934/dcds.2013.33.2065 [12] Marco Arieli Herrera-Valdez, Maytee Cruz-Aponte, Carlos Castillo-Chavez. Multiple outbreaks for the same pandemic: Local transportation and social distancing explain the different "waves" of A-H1N1pdm cases observed in México during 2009. Mathematical Biosciences & Engineering, 2011, 8 (1) : 21-48. doi: 10.3934/mbe.2011.8.21 [13] Achilles Beros, Monique Chyba, Kari Noe. Co-evolving cellular automata for morphogenesis. Discrete and Continuous Dynamical Systems - B, 2019, 24 (5) : 2053-2071. doi: 10.3934/dcdsb.2019084 [14] Qiang Tu. A class of prescribed shifted Gauss curvature equations for horo-convex hypersurfaces in $\mathbb{H}^{n+1}$. Discrete and Continuous Dynamical Systems, 2021, 41 (11) : 5397-5407. doi: 10.3934/dcds.2021081 [15] Eunha Shim. Prioritization of delayed vaccination for pandemic influenza. Mathematical Biosciences & Engineering, 2011, 8 (1) : 95-112. doi: 10.3934/mbe.2011.8.95 [16] Hiroshi Ito, Michael Malisoff, Frédéric Mazenc. Strict Lyapunov functions and feedback controls for SIR models with quarantine and vaccination. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022029 [17] Bernard Host, Alejandro Maass, Servet Martínez. Uniform Bernoulli measure in dynamics of permutative cellular automata with algebraic local rules. Discrete and Continuous Dynamical Systems, 2003, 9 (6) : 1423-1446. doi: 10.3934/dcds.2003.9.1423 [18] Marcelo Sobottka. Right-permutative cellular automata on topological Markov chains. Discrete and Continuous Dynamical Systems, 2008, 20 (4) : 1095-1109. doi: 10.3934/dcds.2008.20.1095 [19] Majid Jaberi-Douraki, Seyed M. Moghadas. Optimal control of vaccination dynamics during an influenza epidemic. Mathematical Biosciences & Engineering, 2014, 11 (5) : 1045-1063. doi: 10.3934/mbe.2014.11.1045 [20] Roberta Ghezzi, Frédéric Jean. A new class of $(H^k,1)$-rectifiable subsets of metric spaces. Communications on Pure and Applied Analysis, 2013, 12 (2) : 881-898. doi: 10.3934/cpaa.2013.12.881

Impact Factor: