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Mathematical analysis of topological and random m-order spread models

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Abstract

This paper focuses on the analysis of two particular models, from deterministic and random perspective respectively, for spreading processes. With a proper encoding of propagation patterns, the spread rate of each pattern is discussed for both models by virtue of the substitution dynamical systems and branching process. In view of this, we are empowered to draw a comparison between two spreading processes according to their spreading models, based on which explanations are proposed on a higher frequency of a pattern in one model than the other. These results are then supported by the numerical evidence later in the article.

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Notes

  1. We will call \({\mathcal {A}}\) the \(type set \) in Sect. 2.

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Acknowledgements

The authors sincerely thank the anonymous reviewers for the valuable comments which helped improve and clarify the manuscript.

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Authors and Affiliations

  1. Department of Mathematical Sciences, National Chengchi University, Taipei, 11605, Taiwan, ROC

    Jung-Chao Ban & Jyy-I Hong

  2. Mathematics Division, National Center for Theoretical Science, National Taiwan University, Taipei, 10617, Taiwan, ROC

    Jung-Chao Ban

  3. Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, 90014, Oulu, Finland

    Yu-Liang Wu

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  1. Jung-Chao Ban
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Correspondence to Jyy-I Hong.

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This work was supported by the Ministry of Science and Technology, ROC [Grant numbers MOST 109-2115-M-004-002-MY2, MOST 109-2115-M-004 -001 -MY2].

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Ban, JC., Hong, JI. & Wu, YL. Mathematical analysis of topological and random m-order spread models. J. Math. Biol. 86, 40 (2023). https://doi.org/10.1007/s00285-023-01874-z

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