Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy methods
Aim. Evidence-backed execution summary for Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy methods from Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy.
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This experiment, in seven questions
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Shopping and prep list
What do I need before I start?
human
Subject model for the experiment.
- Use
- confirm full cohort details in the source paper
Methods
reagent used in the protocol.
- Use
- In the model, we omit the probability rate of becoming susceptible again, after having already recovered from the infection, because this appears to be negligible based on early evidence. Given the scarcity of available data, it is impossible to have conclusive evidence about immunity at this stage. Immunity might...
Main
The model does not consider reduced availability of medical care due to the healthcare system reaching or even surpassing its capacity. These analyses can only be done indirectly. For example, when the number of seriously affected individuals is high (above a threshold), the mortality coefficient will be increased...
- Use
- The model does not consider reduced availability of medical care due to the healthcare system reaching or even surpassing its capacity. These analyses can only be done indirectly. For example, when the number of seriously affected individuals is high (above a threshold), the mortality coefficient will be increased...
Analysis of the mathematical model
The overall system can be recast in a feedback structure, where the IDART subsystem can be seen as a positive linear system subject to a feedback signal u as follows.
- Use
- The overall system can be recast in a feedback structure, where the IDART subsystem can be seen as a positive linear system subject to a feedback signal u as follows.
Proof of proposition 1
The transfer function from u to y S in the system ( )-( ) is G ( s ) = N ( s )/ D ( s ). Because the system is positive, the H ∞ norm of G ( s ) is equal to the static gain G (0) = N (0)/ D (0).
- Use
- The transfer function from u to y S in the system ( )-( ) is G ( s ) = N ( s )/ D ( s ). Because the system is positive, the H ∞ norm of G ( s ) is equal to the static gain G (0) = N (0)/ D (0).
Methods
The SIDARTHE dynamical system consists of eight ordinary differential equations, describing the evolution of the population in each stage over time: 1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepacka...
- Use
- The SIDARTHE dynamical system consists of eight ordinary differential equations, describing the evolution of the population in each stage over time: 1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepacka...
Methods
Finally, the SIDARTHE model is a mean-field type of model, where the average effect of phenomena involving the whole population is captured. Social mixing patterns are incorporated into our contagion parameters in an averaged fashion over the whole population, irrespective of age. However, our model is fully flexibl...
- Use
- Finally, the SIDARTHE model is a mean-field type of model, where the average effect of phenomena involving the whole population is captured. Social mixing patterns are incorporated into our contagion parameters in an averaged fashion over the whole population, irrespective of age. However, our model is fully flexibl...
Analysis of the mathematical model
The SIDARTHE model ( )-( ) is a bilinear system with eight differential equations. The system is positive: all the state variables take non-negative values for t ≥ 0 if initialized at time 0 with non-negative values. Note that H ( t ) and E ( t ) are cumulative variables that depend only on...
- Use
- The SIDARTHE model ( )-( ) is a bilinear system with eight differential equations. The system is positive: all the state variables take non-negative values for t ≥ 0 if initialized at time 0 with non-negative values. Note that H ( t ) and E ( t ) are cumulative variables that depend only on...
Analysis of the mathematical model
The system is compartmental and demonstrates the mass conservation property: as can be immediately checked, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69p...
- Use
- The system is compartmental and demonstrates the mass conservation property: as can be immediately checked, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69p...
Analysis of the mathematical model
To understand the system behavior, we partition it into three subsystems: the first includes just variable S (corresponding to susceptible individuals), the second includes I, D, A, R and T (the infected individuals), which are non-zero only during the transient, and the third includes variables H and E (represen...
- Use
- To understand the system behavior, we partition it into three subsystems: the first includes just variable S (corresponding to susceptible individuals), the second includes I, D, A, R and T (the infected individuals), which are non-zero only during the transient, and the third includes variables H and E (represen...
Before you run
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First confirmation
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Open the source paper before finalizing run-specific details.
Procurement checkpoint
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Open quote workflowStep-by-step procedure
What do I do, in order?
Main
Figure shows, if the lockdown is weakened, a sudden and strong increase of the spread of disease, a prolonged emergency and more deaths (0.12% of the population in the first 350 days). Figure shows the benefits of stricter lockdown measures: after 350 days, 0.41% of the population would contract the virus (0.30% diagnosed) and 0.04% of the population would die. Fig. 3 The effect of lockdown. a - d, Epidemic evolution predicted by the model for the COVID-19 outbreak in Italy when, after day 50, the social distancing countermeasures are weakened, leading to a larger R 0 = 0.98 ( a, b ), or strengthened, leading to a smaller R 0 = 0.50 ( c, d ). a, c, The difference between the actual (real cases) and perceived (diagnosed cases) evolution of the epidemics. The plots in b and d distinguish between the different categories of infected patients: non-diag...
Main
A policy of population-wide testing and contact tracing would help to rapidly end the epidemic, as suggested by Peto. Figure shows the effect of such measures: the peak would be reached sooner and, after 350 days, 0.43% of the population would contract the virus (0.33% diagnosed), with an estimated 0.05% dying. Figure shows the effect of combining a milder lockdown with widespread testing and contact tracing: after 350 days, 0.52% of the population would contract the virus (0.41% diagnosed) and 0.05% would die. Fig. 4 The effect of testing. a - d, Epidemic evolution predicted by the model for the COVID-19 outbreak in Italy when, after day 50, massive testing and contact tracing is enforced ( a, b ), leading to R 0 = 0.59, as well as in parallel with weakening social-distancing measures ( c, d ), leading to R 0 = 0.77. The plots in a and c show the d...
Fit of the model for the COVID-19 outbreak in Italy
Extended Data Fig. shows that, in the absence of further countermeasures after day 22 (just closing schools and hygiene recommendations), we have α = 0.422, γ = 0.285 and β = δ = 0.0057, hence R 0 = 1.66 and the model predicts an evolution that leads to 73% of the population having contracted the virus (and ~64% having been diagnosed) and ~5.2% of the population having died because of the contagion over a 300-day horizon (Extended Data Fig. ). The peak of the number of concurrently infected individuals occurs at around 76 days and amounts to ~44% of the population; however, the peak of concurrently diagnosed infected individuals occurs later, around 82 days, and amounts to 39% of the population. Extended Data Fig. shows how the different subpopulations of infected individuals evolve over time, and it...
Measurement outputs
What raw and processed outputs should exist?
The overall system can be recast in a feedback structure, where the IDART subsystem can be seen as a positive linear system subject to a feedback signal u as follows.
- Raw artifact
- Per-sample or per-animal endpoint measurements collected during the experiment
- Processed artifact
- Structured table with cleaned measurements ready for comparison
- Reported as
- Summary statistics and between-group or across-timepoint comparisons
Although we do consider a delay in the emergence of symptoms, through asymptomatic (or pauci-symptomatic) patients, categorized as undetected (infected) and detected (diagnosed)...
- Raw artifact
- Per-sample or per-animal endpoint measurements collected during the experiment
- Processed artifact
- Structured table with cleaned measurements ready for comparison
- Reported as
- Summary statistics and between-group or across-timepoint comparisons
The SIDARTHE model ( )-( ) is a bilinear system with eight differential equations. The system is positive: all the state variables take non-negative values for t &#...
- Raw artifact
- Per-sample or per-animal endpoint measurements collected during the experiment
- Processed artifact
- Structured table with cleaned measurements ready for comparison
- Reported as
- Summary statistics and between-group or across-timepoint comparisons
The system is compartmental and demonstrates the mass conservation property: as can be immediately checked, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysy...
- Raw artifact
- Per-sample or per-animal endpoint measurements collected during the experiment
- Processed artifact
- Structured table with cleaned measurements ready for comparison
- Reported as
- Summary statistics and between-group or across-timepoint comparisons
Analysis plan
How should the outputs become interpretable results?
Acquisition
Collect raw experimental outputs with enough metadata to preserve sample identity, condition, and timing.
inferred from protocolPreprocessing / cleaning
Predictive mathematical models for epidemics - are fundamental to understand the course of the epidemic and to plan effective control strategies.
from paperScoring or quantification
Quantify the primary readouts for this experiment: The overall system can be recast in a feedback structure, where the IDART subsystem can be seen as a positive linear system subject to a feedback signal u as follows.; Although we do consider a delay in the emergence of symptoms, through asymptomatic (or pauci-symptomatic) patients, categorized as undetected (infected) and detected (diagnosed)...; The SIDARTHE model ( )-( ) is a bilinear system with eight differential equations. The system is positive: all the state variables take non-negative values for t &#...; The system is compartmental and demonstrates the mass conservation property: as can be immediately checked, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysy....
from paperStatistical comparison
Predictive mathematical models for epidemics - are fundamental to understand the course of the epidemic and to plan effective control strategies. One commonly used model i...; Distinguishing between diagnosed and non-diagnosed cases highlights a distortion in disease statistics. The discrepancy between the actual CFR (total number of deaths due to the...; Finally, the SIDARTHE model is a mean-field type of model, where the average effect of phenomena involving the whole population is captured. Social mixing patterns are incorpora...; Data about the number of deaths (corresponding to E ( t ) in our model) appear particularly high with respect to the CFR reported in the literature; this can be largely explaine...
from paperReporting output
Report representative outputs alongside summary comparisons for The overall system can be recast in a feedback structure, where the IDART subsystem can be seen as a positive linear system subject to a feedback signal u as follows., Although we do consider a delay in the emergence of symptoms, through asymptomatic (or pauci-symptomatic) patients, categorized as undetected (infected) and detected (diagnosed)..., The SIDARTHE model ( )-( ) is a bilinear system with eight differential equations. The system is positive: all the state variables take non-negative values for t &#..., The system is compartmental and demonstrates the mass conservation property: as can be immediately checked, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysy....
inferred from protocolStructured statistical methods
Predictive mathematical models for epidemics - are fundamental to understand the course of the epidemic and to plan effective control strategies. One commonly used model i...; Distinguishing between diagnosed and non-diagnosed cases highlights a distortion in disease statistics. The discrepancy between the actual CFR (total number of deaths due to the...; Finally, the SIDARTHE model is a mean-field type of model, where the average effect of phenomena involving the whole population is captured. Social mixing patterns are incorpora...; Data about the number of deaths (corresponding to E ( t ) in our model) appear particularly high with respect to the CFR reported in the literature; this can be largely explaine...
source structuredSource and audit
What supports the facts on this page?
Evidence quotes (3)
Figure shows, if the lockdown is weakened, a sudden and strong increase of the spread of disease, a prolonged emergency and more deaths (0.12% of the population in the first 350 days). Figure shows the benefits of stricter lockdown measures: after 350 days, 0.41% of the population would contract the virus (0.30% diagnosed) and 0.04% of the population would die. Fig. 3 The effect of lockdown. a - d, Epidemic evolution predicted by the model for the COVID-19 outbreak in Italy when, after day 50, the social distancing countermeasures are weakened, leading to a larger R 0 = 0.98 ( a, b ), or strengthened, leading to a smaller R 0 = 0.50 ( c, d ). a, c, The difference between the actual (real cases) and perceived (diagnosed cases) evolution of the epidemics. The plots in b and d distinguish between the different categories of infected patients: non-diagnosed asymptomatic (ND AS), diagnosed asymptomatic (D AS), non-diagnosed symptomatic (ND S), diagnosed symptomatic (D S) and diagnosed with life-threatening symptoms (D IC). Note that a, c and b, d have different scales.
A policy of population-wide testing and contact tracing would help to rapidly end the epidemic, as suggested by Peto. Figure shows the effect of such measures: the peak would be reached sooner and, after 350 days, 0.43% of the population would contract the virus (0.33% diagnosed), with an estimated 0.05% dying. Figure shows the effect of combining a milder lockdown with widespread testing and contact tracing: after 350 days, 0.52% of the population would contract the virus (0.41% diagnosed) and 0.05% would die. Fig. 4 The effect of testing. a - d, Epidemic evolution predicted by the model for the COVID-19 outbreak in Italy when, after day 50, massive testing and contact tracing is enforced ( a, b ), leading to R 0 = 0.59, as well as in parallel with weakening social-distancing measures ( c, d ), leading to R 0 = 0.77. The plots in a and c show the difference between the actual (real cases) and the perceived (diagnosed cases) evolution of the epidemics. The plots in b and d distinguish between the different categories of infected patients: non-diagnosed asymptomatic (ND AS), diagnosed asymptomatic (D AS), non-diagnosed symptomatic (ND S), diagn...
Extended Data Fig. shows that, in the absence of further countermeasures after day 22 (just closing schools and hygiene recommendations), we have α = 0.422, γ = 0.285 and β = δ = 0.0057, hence R 0 = 1.66 and the model predicts an evolution that leads to 73% of the population having contracted the virus (and ~64% having been diagnosed) and ~5.2% of the population having died because of the contagion over a 300-day horizon (Extended Data Fig. ). The peak of the number of concurrently infected individuals occurs at around 76 days and amounts to ~44% of the population; however, the peak of concurrently diagnosed infected individuals occurs later, around 82 days, and amounts to 39% of the population. Extended Data Fig. shows how the different subpopulations of infected individuals evolve over time, and it is interesting to notice that each subpopulation reaches its peak at a different time. In particular, the fraction of infected who need intensive care reaches its peak, almost 16.5% of the population, after 107 days.
Machine-readable layer
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