A simplified model for the analysis of COVID-19 evolution during the lockdown period in Italy
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Abstract
A simplified model applied to COVID-19 cases detected and officially published by the italian government [1], seems to fit quite well the time evolution of the disease in Italy during the period feb-24th - may-19th 2020.
The hypothesis behind the model is based on the fact that in the lockdown period the infection cannot be transmitted due to social isolation and, more generally, due to the strong protection measures in place during the observation period. In this case a compartment model is used and the interactions between the different compartments are simplified. The sample of cases detected is intended as a set of individuals susceptible to infection which, after being exposed and undergoing the infection, were isolated (’treated’) in such a way they can no longer spread the infection.
The values obtained are to be considered indicative.
The same model has been applied both to the data relating to Italy and to some regions of Italy (Lombardia, Piemonte, Lazio, Campania, Calabria, Sicilia, Sardegna), generally finding a good response and indicatively interesting values (see chap. 5).
The only tuning parameter is the ‘incubation period’ τ that, together with the calculated growth rate κ of the exponential curve used to approximate the early stage data.
Conclusions
A simplified compartmental model that uses only the incubation period and the exponential growth rate as parameters is applied to the COVID-19 data for Italy in the lockdown period finding a good fitting.
Revision History
This section summarize the history of revisions.
Revision # 1
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Errata corrige in section 1 (Introduction): the equations that summarize the relationship between the parameters were wrong. This revised version contains the correct equations at page 2.
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The synchronization criteria is updated. No need to use a threshold different to the one used to determine the growth coefficient. The results are now updated with the synchronization point near to the 20% of the maximum value of the cases detected per day:
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Modifications in section 4 (Model results for Italy). It is appropriate to use an exponential function instead of a logistic function to find the growth rate in the initial phase. Section 4 and the results are now updated.
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Some non-substantial corrections in the descriptive part.
Revision # 2
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Errata corrige in the system differential equation 6: in the the derivative of S were reported a wrong additional term N. Now the equation 6 is correct.
Revision # 3
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New approach to detect the exponential rate and new concept for the transfer coefficients.
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Exponential rate:
The old criteria was oriented to the growth of the cases: y Δ t = y 0 * e k Δ t thus: y 0 + Δ y = y 0 * e k Δ t . The exponential growth rate was then: k = log (1 + Δ y / y 0 )/Δ t .
The new criteria is oriented to the growth of the differences Δ y = e k Δ t − 1 obtaining: k = log (1 + Δ y )/Δ t .
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Transfer coefficients:
The new approach is based on the following assumptions:
α SE = ke kδ [ day −1 ]: this coefficent is supposed to be the variation of the exponential growth per unit of time ( δ = 1 day ).
α EI = 1/ τ [ day −1 ] where t is the incubation period (this assumption is not changed).
α IT = kδ/T [ day −1 ] this coefficent is supposed to be proportional to the ratio kδ / τ .
The constant δ =1 [ day ] represent the unit variation in time.
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Basic reproduction number:
With the above assumptions, the basic reproduction number become:
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Revision summary:
The old approach, although adapting well to the data, presented several inconsistencies in the parameters, and in particular on the relationship between and k .
In this revision the new approach still shows a good fit to the data and shows congruent relationships between the parameters.
Article activity feed
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SciScore for 10.1101/2020.06.02.20119883: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
Institutional Review Board Statement not detected. Randomization not detected. Blinding not detected. Power Analysis not detected. Sex as a biological variable not 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).
Results from LimitationRecognizer: An explicit section about the limitations of the techniques employed in this study was not found. We encourage authors to address study limitations.Results from TrialIdentifier: No clinical trial numbers were referenced.
Results from Barzooka: We did not find any issues relating to the usage of bar …
SciScore for 10.1101/2020.06.02.20119883: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
Institutional Review Board Statement not detected. Randomization not detected. Blinding not detected. Power Analysis not detected. Sex as a biological variable not 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).
Results from LimitationRecognizer: An explicit section about the limitations of the techniques employed in this study was not found. We encourage authors to address study limitations.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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