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Impact of time delay on the dynamics of SEIR epidemic model using cellular automata

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  • Sharma, Natasha
  • Gupta, Arvind Kumar

Abstract

The delay of an infectious disease is significant when aiming to predict its strength and spreading patterns. In this paper the SEIR ​(susceptible–exposed–infected–recovered) epidemic spread with time delay is analyzed through a two-dimensional cellular automata model. The time delay corresponding to the infectious span, predominantly, includes death during the latency period in due course of infection. The advancement of whole system is described by SEIR transition function complemented with crucial factors like inhomogeneous population distribution, birth and disease independent mortality. Moreover, to reflect more realistic population dynamics some stochastic parameters like population movement and connections at local level are also considered. The existence and stability of disease free equilibrium is investigated. Two prime behavioral patterns of disease dynamics is found depending on delay. The critical value of delay, beyond which there are notable variations in spread patterns, is computed. The influence of important parameters affecting the disease dynamics on basic reproduction number is also examined. The results obtained show that delay plays an affirmative role to control disease progression in an infected host.

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  • Sharma, Natasha & Gupta, Arvind Kumar, 2017. "Impact of time delay on the dynamics of SEIR epidemic model using cellular automata," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 114-125.
    • Handle: RePEc:eee:phsmap:v:471:y:2017:i:c:p:114-125
    DOI: 10.1016/j.physa.2016.12.010
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    1. Acedo, L. & Moraño, J.-A. & Santonja, F.-J. & Villanueva, R.-J., 2016. "A deterministic model for highly contagious diseases: The case of varicella," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 278-286.
    2. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2016. "Asymptotic behavior of a stochastic delayed SEIR epidemic model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 870-882.
    3. Ilnytskyi, Jaroslav & Kozitsky, Yuri & Ilnytskyi, Hryhoriy & Haiduchok, Olena, 2016. "Stationary states and spatial patterning in an SIS epidemiology model with implicit mobility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 36-45.
    4. Ofosuhene O Apenteng & Noor Azina Ismail, 2014. "The Impact of the Wavelet Propagation Distribution on SEIRS Modeling with Delay," PLOS ONE, Public Library of Science, vol. 9(6), pages 1-9, June.
    5. Julien Arino & P. van den Driessche, 2003. "A multi-city epidemic model," Mathematical Population Studies, Taylor & Francis Journals, vol. 10(3), pages 175-193.
    6. Wang, Lianwen & Liu, Zhijun & Zhang, Xingan, 2016. "Global dynamics of an SVEIR epidemic model with distributed delay and nonlinear incidence," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 47-65.
    7. Ruan, Yuhong & Li, Anwei & Huang, Jing, 2015. "Analytic function of local rules of Elementary Cellular Automata," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 404-409.
    8. Jiang, Zhichao & Ma, Wanbiao & Wei, Junjie, 2016. "Global Hopf bifurcation and permanence of a delayed SEIRS epidemic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 122(C), pages 35-54.
    9. Liu, Qun & Jiang, Daqing, 2016. "The threshold of a stochastic delayed SIR epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 140-147.
    10. Liu, Qun & Chen, Qingmei & Jiang, Daqing, 2016. "The threshold of a stochastic delayed SIR epidemic model with temporary immunity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 115-125.
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    3. Hong Zhang & Shigen Shen & Qiying Cao & Xiaojun Wu & Shaofeng Liu, 2020. "Modeling and analyzing malware diffusion in wireless sensor networks based on cellular automaton," International Journal of Distributed Sensor Networks, , vol. 16(11), pages 15501477209, November.
    4. Das, Tanuja & Srivastava, Prashant K., 2023. "Effect of a novel generalized incidence rate function in SIR model: Stability switches and bifurcations," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    5. Gabrick, Enrique C. & Protachevicz, Paulo R. & Batista, Antonio M. & Iarosz, Kelly C. & de Souza, Silvio L.T. & Almeida, Alexandre C.L. & Szezech, José D. & Mugnaine, Michele & Caldas, Iberê L., 2022. "Effect of two vaccine doses in the SEIR epidemic model using a stochastic cellular automaton," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    6. Alzahrani, Faris & Razzaq, Oyoon Abdul & Rehman, Daniyal Ur & Khan, Najeeb Alam & Alshomrani, Ali Saleh & Ullah, Malik Zaka, 2022. "Repercussions of unreported populace on disease dynamics and its optimal control through system of fractional order delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    7. Sharma, Natasha & Verma, Atul Kumar & Gupta, Arvind Kumar, 2021. "Spatial network based model forecasting transmission and control of COVID-19," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    8. Roy, Souvik, 2019. "A study on delay-sensitive cellular automata," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 600-616.
    9. Zhang, Zizhen & Rahman, Ghaus ur & Gómez-Aguilar, J.F. & Torres-Jiménez, J., 2022. "Dynamical aspects of a delayed epidemic model with subdivision of susceptible population and control strategies," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

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