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The Language of Epidemic

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Abstract

Infectious diseases are transmitted from one person to another and spread throughout a network under certain conditions. Considering an example of propagation, we explain how to define an automaton on the network according to the propagation steps and the conditions under which the epidemic is transmitted. We call this automaton forcing automaton. Also, we call the language of this automaton an epidemic language. We describe how forcing automata and epidemic languages allow us to have a more accurate analysis of propagation in reality. Furthermore, we show that by knowing the epidemic language, it is possible to compare the spread of an epidemic in different networks. Finally, we present an algorithm that can predict a network in which the epidemic spreads, by only knowing its epidemic language.

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References

  1. AIM Minimum Rank: Special graphs work group, zero forcing sets and the minimum rank of graphs. Linear Algebra Appl. 428, 1628–1648 (2008)

    Article  MathSciNet  Google Scholar 

  2. Alinaghipour Taklimi, F: Zero forcing sets for graphs, University of Regina, Ph.D. thesis. (2013)

  3. Arino, J., Watmough, J.: Current trends in mathematical epidemiology. Bull. Math. Biol. 81, 4311–4312 (2019)

    Article  MathSciNet  Google Scholar 

  4. Athithan, S., Prasad Shukla, V., Ramachandra Biradar, S.: Dynamic cellular automata based epidemic spread model for population in patches with movement. J. Comput. Environ. Sci. 2014, 8 (2014). (Article ID 518053)

    Google Scholar 

  5. Brauer, F.: Mathematical epidemiology: past, present, and future. Infect Dis Model. 2, 113–127 (2017)

    Google Scholar 

  6. Enrighta, J., Raymond Kaob, R.: Epidemics on dynamic networks. Epidemics. 24, 88–97 (2018)

    Article  Google Scholar 

  7. Golmohamadian, M., Zahedi, M.M., Soltankhah, N.: Some algebraic hyperstructures related to zero forcing sets and forcing digraphs. J. Algebra Appl. 18(10), 19 (2019)

    Article  MathSciNet  Google Scholar 

  8. Hogben, L., Huynh, M., Kingsley, N., Meyer, S., Walker, S., Young, M.: Propagation time for zero forcing on a graph. Discret. Appl. Math. 160, 1994–2005 (2012)

    Article  MathSciNet  Google Scholar 

  9. Li, W.D., Guo, X.H.: Using cellular automata to study the effect of competition for epidemic diseases. Procedia Environ. Sci. 13, 1010–1018 (2012)

    Article  Google Scholar 

  10. Mordeson, J.N., Malik, D.S.: Fuzzy automata and languages, theory and applications. Chapman and Hall/CRC, London/Boca Raton (2002)

    MATH  Google Scholar 

  11. Muellnera, U., Fourniéb, G., Muellnera, P., Ahlstroma, C., Pfeifferb, D.U.: Epidemix—an interactive multi-model application for teaching and visualizing infectious disease transmission. Epidemics 23, 49–54 (2018)

    Article  Google Scholar 

  12. Waltersa, C.E., Mesléb, M.M.I., Halla, I.M.: Modelling the global spread of diseases: a review of current practice and capability. Epidemics 25, 1–8 (2018)

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Tarbiat Modares University, Tehran, Iran

    Masoumeh Golmohamadian

  2. Department of Mathematics, Kerman Graduate University of Advanced Technology, Kerman, Iran

    Mohammad Mehdi Zahedi

Authors
  1. Masoumeh Golmohamadian
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  2. Mohammad Mehdi Zahedi
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Correspondence to Masoumeh Golmohamadian.

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Communicated by Majid Gazor.

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Golmohamadian, M., Zahedi, M.M. The Language of Epidemic. Bull. Iran. Math. Soc. 48, 2105–2123 (2022). https://doi.org/10.1007/s41980-021-00612-9

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  • DOI: https://doi.org/10.1007/s41980-021-00612-9

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