# Spread of Infectious Disease Modeling and Analysis of Different Factors on Spread of Infectious Disease Based on Cellular Automata

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## Abstract

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## 1. Introduction

- A more realistic epidemic spread model based on cellular automata was established and achieved good results in simulation experiments.
- The effects of population density, sex ratio, and age structure on the spread of infectious diseases were discussed, and the simulation results were analyzed to observe the effects of the above three factors on the spread process of infectious diseases.
- The suggestions given in this paper based on the three influencing factors provided strong support for researchers to study the spread process of infectious diseases in different environments.

## 2. Methodology

#### 2.1. SLIRDS Model

#### 2.2. Influence Analysis of Different Factors on Infectious Disease Spread

#### 2.2.1. Population Density, Sex Ratio, and Age Structure

#### 2.2.2. Individual Heterogeneity

#### 2.2.3. Model Evolution Rules

## 3. Simulation Results and Analysis

#### 3.1. Influence of Population Density on Infectious Disease Spread

#### 3.2. Influence of Sex Ratio on Infectious Disease Spread

#### 3.2.1. Influence of Infectious Disease Spread under Different Coefficients

#### 3.2.2. Influence of Infectious Disease Spread under Different Sex Ratios

#### 3.3. Influence of Age Structure on Infectious Disease Spread

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Giles, P. The Mathematical Theory of Infectious Diseases and Its Applications. J. Oper. Res. Soc.
**1977**, 28, 479–480. [Google Scholar] [CrossRef] - Hethcote, H.W. The Mathematics of Infectious Diseases. Siam Rev.
**2000**, 42, 599–653. [Google Scholar] [CrossRef] - Funk, S. Modelling the influence of human behaviour on the spread of infectious diseases: A review. J. R. Soc. Interface
**2010**, 7, 1247–1256. [Google Scholar] [CrossRef] [PubMed] - Hans, H.; Anderson, R.M.; Viggo, A. Modeling infectious disease dynamics in the complex landscape of global health. Science
**2015**, 347, aaa4339. [Google Scholar] - Siettos, C.I.; Russo, L. Mathematical modeling of infectious disease dynamics. Virulence
**2013**, 4, 295–306. [Google Scholar] [CrossRef] - Qin, W.; Tang, S.; Xiang, C. Effects of limited medical resource on a Filippov infectious disease model induced by selection pressure. Appl. Math. Comput.
**2016**, 283, 339–354. [Google Scholar] [CrossRef] - Bernoulli, D. Essai D’ Une Nouvelle Analyse de la Mortalite Cause Par La Petite Werole et Desavantages de I’ Inoculation Pour al Prevenir, in Memories de Mathematiques et de Physique; Academie Royale des Sciences: Paris, France, 1760; pp. 1–45. [Google Scholar]
- Hamer, W.H. Epidemic disease in England. Lancet
**1906**, 1, 733–739. [Google Scholar] - Kermack, W.O.; Mckendrick, A.G. Contributions to the mathematical theory of epidemics. Proc. R. Soc. A
**1927**, 115, 700–721. [Google Scholar] [CrossRef] - Sun, G.X.; Bin, S. Router-Level Internet Topology Evolution Model based on Multi-Subnet Composited Complex Network Model. J. Int. Technol.
**2017**, 18, 1275–1283. [Google Scholar] - Aron, J.L.; Schwartz, I.B. Seasonality and period-doubling bifurcations in an epidemic model. J. Theor. Biol.
**1984**, 18, 665–679. [Google Scholar] [CrossRef] - Safi, M.A.; Gumel, A.B. Mathematical analysis of a disease transmission model with quarantine, isolation and an imperfect vaccine. Comput. Math. Appl.
**2011**, 61, 3044–3070. [Google Scholar] [CrossRef] - Small, M.; Chi, K.T. Small world and scale free model of transmission of SARS. Int. J. Bifurc. Chaos
**2005**, 15, 1745–1755. [Google Scholar] [CrossRef] - Boklund, A.; Toft, N.; Alban, L. Comparing the epidemiological and economic effects of control strategies against classical swine fever in Denmark. Prev. Vet. Med.
**2009**, 90, 180–193. [Google Scholar] [CrossRef] [PubMed] - Meng, L.; Bai, C.; Ke, W. Asymptotic stability of a two-group stochastic SEIR model with infinite delays. Commun. Nonlinear Sci. Numer. Simul.
**2014**, 19, 3444–3453. [Google Scholar] - Misra, S.; Das, A.K.; Chowdhury, D.R. Cellular Automata—Theory and Applications. IETE J. Res.
**2015**, 36, 251–259. [Google Scholar] [CrossRef] - Johansen, A. A Simple Model of Recurrent Epidemics. J. Theor. Biol.
**1996**, 178, 45–51. [Google Scholar] [CrossRef] - Apenteng, O.O.; Azina, I.N.; Khudyakov, Y.E. The Impact of the Wavelet Propagation Distribution on SEIRS Modeling with Delay. PLoS ONE
**2014**, 9, e98288. [Google Scholar] [CrossRef] - Ahn, J.; Sathiamoorthy, M.; Krishnamachari, B. Optimizing Content Dissemination in Vehicular Networks with Radio Heterogeneity. IEEE Trans. Mob. Comput.
**2014**, 13, 1312–1325. [Google Scholar] - Cissé, B.; Yacoubi, S.E.; Gourbière, S. A cellular automaton model for the transmission of Chagas disease in heterogeneous landscape and host community. Appl. Math. Model.
**2016**, 40, 782–794. [Google Scholar] [CrossRef] - Pan, Z.; Yang, F.; Shen, Q. A Model Research on AIDS Diffusion Based on Cellular Automaton. J. Biomed. Eng.
**2011**, 28, 479–487. [Google Scholar] - López, L.; Burguerner, G.; Giovanini, L. Addressing population heterogeneity and distribution in epidemics models using a cellular automata approach. BMC Res. Notes
**2014**, 7, 1–11. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Gao, B.G.; Zhang, T.; Xuan, H.Y. A Heterogeneous Cellular Automata Model for SARS Transmission. J. Syst. Manag.
**2006**, 15, 205–209. [Google Scholar] - The National Legal Report of Infectious Diseases from the Year 2009 to 2010. Available online: http://www. moh.gov.cn/publicfiles/business/htmlfiles/mohbgt/pwsbgb/index.htm (accessed on 10 May 2017).

**Figure 2.**The state transition diagram of the Susceptible-Latent-Infected-Recovered-Dead-Susceptible (SLIRDS) model.

**Figure 3.**Comparison of actual data and simulation data for pandemic influenza A (H1N1) in Beijing in Mainland China (June–July 2009).

**Figure 4.**Infectious disease spread state distribution with different population density. (

**a**) Death rate curve; (

**b**) Susceptibility rate curve; (

**c**) Infection rate curve; (

**d**) Immunization rate curve.

**Figure 5.**Infectious disease spread state distribution with different coefficients. (

**a**) Death rate curve; (

**b**) Susceptibility rate curve; (

**c**) Infection rate curve; (

**d**) Immunization rate curve.

**Figure 6.**Infectious disease spread state distribution with different sex ratios. (

**a**) Death rate curve; (

**b**) Susceptibility rate curve; (

**c**) Infection rate curve; (

**d**) Immunization rate curve.

**Figure 7.**Infectious disease spread state distribution with different age structure. (

**a**) Death rate curve; (

**b**) Susceptibility rate curve; (

**c**) Infection rate curve; (

**d**) Immunization rate curve.

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**MDPI and ACS Style**

Bin, S.; Sun, G.; Chen, C.-C.
Spread of Infectious Disease Modeling and Analysis of Different Factors on Spread of Infectious Disease Based on Cellular Automata. *Int. J. Environ. Res. Public Health* **2019**, *16*, 4683.
https://doi.org/10.3390/ijerph16234683

**AMA Style**

Bin S, Sun G, Chen C-C.
Spread of Infectious Disease Modeling and Analysis of Different Factors on Spread of Infectious Disease Based on Cellular Automata. *International Journal of Environmental Research and Public Health*. 2019; 16(23):4683.
https://doi.org/10.3390/ijerph16234683

**Chicago/Turabian Style**

Bin, Sheng, Gengxin Sun, and Chih-Cheng Chen.
2019. "Spread of Infectious Disease Modeling and Analysis of Different Factors on Spread of Infectious Disease Based on Cellular Automata" *International Journal of Environmental Research and Public Health* 16, no. 23: 4683.
https://doi.org/10.3390/ijerph16234683