Ultrametric model for covid-19 dynamics: an attempt to explain slow approaching herd immunity in Sweden

  1. Andrei Khrennikov

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Abstract

We present a mathematical model of infection dynamics that might explain slower approaching the herd immunity during the covid-19 epidemy in Sweden than it was predicted by a variety of other models; see graphs Fig. 2. The new model takes into account the hierarchic structure of social clusters in the human society. We apply the well developed theory of random walk on the energy landscapes represented mathematically with ultrametric spaces. This theory was created for applications to spin glasses and protein dynamics. To move from one social cluster (valley) to another, the virus (its carrier) should cross a social barrier between them. The magnitude of a barrier depends on the number of social hierarchy’s levels composing this barrier. As the most appropriate for the recent situation in Sweden, we consider linearly increasing (with respect to hierarchy’s levels) barriers. This structure of barriers matches with a rather soft regulations imposed in Sweden in March 2020. In this model, the infection spreads rather easily inside a social cluster (say working collective), but jumps to other clusters are constrained by social barriers. This model’s feature matches with the real situation during the covid-19 epidemy, with its cluster spreading structure. Clusters need not be determined solely geographically, they are based on a number of hierarchically ordered social coordinates. The model differs crucially from the standard mathematical models of spread of disease, such as the SIR-model. In particular, our model describes such a specialty of spread of covid-19 virus as the presence of “super-spreaders” who by performing a kind of random walk on a hierarchic landscape of social clusters spreads infection. In future, this model will be completed by adding the SIR-type counterpart. But, the latter is not a specialty of covid-19 spreading.

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    SciScore for 10.1101/2020.07.04.20146209: (What is this?)

    Please note, not all rigor criteria are appropriate for all manuscripts.

    Table 1: Rigor

    Institutional Review Board Statementnot detected.
    Randomizationnot detected.
    Blindingnot detected.
    Power Analysisnot detected.
    Sex as a biological variablenot detected.

    Table 2: Resources

    No key resources detected.

    Results from OddPub: We did not detect open data. We also did not detect open code. Researchers are encouraged to share open data when possible (see Nature blog).

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    • Thank you for including a conflict of interest statement. Authors are encouraged to include this statement when submitting to a journal.
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  2. Version published to 10.1101/2020.07.04.20146209v1 on medRxiv