Fractional SIR epidemiological models

  1. Amirhossein Taghvaei
  2. Tryphon T. Georgiou
  3. Larry Norton
  4. Allen Tannenbaum

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Abstract

The purpose of this work is to make a case for epidemiological models with fractional exponent in the contribution of sub-populations to the incidence rate. More specifically, we question the standard assumption in the literature on epidemiological models, where the incidence rate dictating propagation of infections is taken to be proportional to the product between the infected and susceptible sub-populations; a model that relies on strong mixing between the two groups and widespread contact between members of the groups. We contend, that contact between infected and susceptible individuals, especially during the early phases of an epidemic, takes place over a (possibly diffused) boundary between the respective sub-populations. As a result, the rate of transmission depends on the product of fractional powers instead. The intuition relies on the fact that infection grows in geographically concentrated cells, in contrast to the standard product model that relies on complete mixing of the susceptible to infected sub-populations. We validate the hypothesis of fractional exponents (1) by numerical simulation for disease propagation in graphs imposing a local structure to allowed disease transmissions and (2) by fitting the model to the JHU CSSE COVID-19 Data for the period Jan-22-20 to April-30-20, for the countries of Italy, Germany, France, and Spain.

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  1. Version published to 10.1038/s41598-020-77849-7
  2. ScreenIT

    SciScore for 10.1101/2020.04.28.20083865: (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: Thank you for sharing your code and data.

    Results from LimitationRecognizer: We detected the following sentences addressing limitations in the study:
    Several limitations of our experiment are noted. Firstly, the value of I(t) is only an estimated value since recording of all infected individuals is not guaranteed. Secondly, the value of ΔI(t) is estimated as being the difference I(t) − I(t − 1); we cannot take into account individuals who may have recovered. However, it is deemed that the uncertainty in the actual value of R(t) that quantifies the recovered sub-population is not significant; this can be argued based on the basis that the COVID-19 recovery period is of the order of weeks. It is anticipated that, in a similar manner as in the Norton-Simon hypothesis on cancer treatment [7], the rate of regression under effective intervention is proportional to the expected rate of growth of a population of that size, and that the most efficient intervention would be dose dense, either continuous if possible or as frequently applied as possible. This is important since should relaxation of social distancing be allowed to proceed too long before re-institution of same, this would be predicted to be disadvantageous. The authors believe that it is imperative that a deeper and more extensive study is carried out, whereupon the values of I(t), ΔI(t), R(t) are estimated from more extensive datasets. The effect of mediation efforts, such as social distancing, should be recorded as well and taken into account by differentiating data for the periods before and after such mediation protocols take effect. It is the authors’ hope that qu...

    Results from TrialIdentifier: No clinical trial numbers were referenced.

    Results from Barzooka: We did not find any issues relating to the usage of bar graphs.

    Results from JetFighter: We did not find any issues relating to colormaps.

    Results from rtransparent:
    • Thank you for including a conflict of interest statement. Authors are encouraged to include this statement when submitting to a journal.
    • Thank you for including a funding statement. Authors are encouraged to include this statement when submitting to a journal.
    • No protocol registration statement was detected.

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  3. Version published to 10.1101/2020.04.28.20083865v2 on medRxiv
  4. Version published to 10.1101/2020.04.28.20083865v1 on medRxiv