NOTE: Still under construction 🚧🧱👷

Simulation of COVID-19 cases arising from high-risk contacts

Summary

Simulation work

Data sources and acknowledgements

COVID-19 cases and vaccines

Data for Portugal 🇵🇹 on COVID-19 cases (exposed, infected, recovered and deaths) and vaccines (number of individuals completely vaccinated and number of booster doses) was collected through the DSSG data respository (https://github.com/dssg-pt/covid19pt-data).

We would like to aknowledge that this simulation would have been impossible to build without DSSG’s generous contribution in compiling and curating the data reported in PDF format by DGS ( our 🇵🇹 NHS), specially pertaining to exposed individuals identified.

COVID-19 variant prevalence

Data on weekly prevalence of COVID-19 variants in Portugal 🇵🇹 was collected through the ECDC open repository (https://www.ecdc.europa.eu/en/publications-data/data-virus-variants-covid-19-eueea). We used data collected through TESSy.

Simulation description

Epidemiological compartmental model

Compartmental model used. Legend: S – Susceptible individuals; E – Exposed individuals; E0, E1, E2, …, En – Sub-compartments of the exposed compartment. Each number represents the number of days since exposure; I - Infected individuals; V - Subset of susceptible individuals immune to SARS-CoV-2 infection through vaccination.

Transitions

The following equations show the calculations behind each compartment transition

E-S = ∑_(i=0)^n▒〖Ei-S〗

Ei-S = ∑_(w=0)^n▒〖P(Ei-S)w .Ei〗

E-I = ∑_(i=0)^n▒〖Ei-I〗

Ei-I = ∑_(w=0)^n▒〖P(Ei-I)w .Ei〗

Proportion of new cases from exposed = E-I ÷ New cases

S-I = New cases - E-I

S-E = Efinal - Einitial = E0

V = Pprotection . Vaccinated

E-S : Exposed -> Susceptible

Ei-S : Sub-compartment i of compartment E -> Susceptible

E-I : Exposed -> Infected

Ei-I : Sub-compartment i of compartment E -> Infected

S-I : Susceptible -> Infected

S-E : Susceptible -> Exposed

w : COVID-19 variant

Assumptions of the simulation

The transitions between E sub-compartments were defined by a Markov chain Monte Carlo simulation: in each simulation day, an individual in a sub-compartment of the E compartment transitions probabilistically to the following sub-compartment, to compartment S, or to compartment I.

A constant rate was assumed between two events: 1) the efficacy after inoculation and maximum efficacy, and 2) maximum efficacy and waned efficacy. Vaccinated individuals were probabilistically placed in subset V each day. The same procedure was replicated to individuals with booster doses. Individuals in subset V could transition to compartment E, but their infection risk was set at 0. These individuals were included in transition S-E, following the assumption that the proportion of individuals immune due to vaccination in that transition was equal to the proportion of said individuals in compartment S.

Files included and description

functions.R Includes all functions needed to run the simulation

main_simulation.R Builds an example simulation (fully functioning), based on collected data.

datasets Folder with data needed for the simulation, namely the number of individuals to keep in each compartment daily (data_preview.csv), data on daily vaccinated individuals (vaccines_preview.csv) and data on weekly prevalence of each variant (transformed in daily prevalence) (variant_preview.csv). datasets include only a preview of the first 100 rows of each dataset, to show the needed structure for the simulation to run.

How to use the simulation

Data inputs

To properly run, the simulation needs several inputs, namely:

• ds.simulation, a dataframe which includes a minimum of 10 columns

  1. Date
  2. S - susceptible
  3. S(V) - proportion of susceptible (S) individuals protected from infection through vaccination
  4. E - exposed/high risk contacts identified
  5. I - infected
  6. R - recovered
  7. D - deaths
  8. confirmed - total of confirmed COVID-19 cases (= I)
  9. new_confirmed - daily new confirmed cases
  10. and through: variants - must at least have one column named "other"

• transition.table, one dataframe for each variant included. Must at least have one "other"

• model.daily.table, a dataframe to keep daily simulated data. Should have as many columns as the number of compartments and sub-compartments in the model. Automatically generated in the code after defining all variants.

Function inputs

tt.function()

• For each variant included, 5 parameters can be inputed:
  1. max.days.of.vigilance.EI : maximum number of days of vigilance for high risk contacts that become infected (E->I)
  2. mean.time.to.infection.EI : mean number days of vigilance for high risk contacts that become infected (E->I)
  3. max.days.of.vigilance.ES : maximum number of days of vigilance for high risk contacts that return to susceptible (E->S)
  4. mean.time.to.susceptible.ES : mean number days of vigilance for high risk contacts that return to susceptible (E->S)
  5. infection.risk.not.vaccinated : risk of infection for each high risk contact (not vaccinated) to develop the infection

Simulation Outputs

A single dataframe, named simulation.table, which includes 5 columns:

1. Date
2. Sum - summation of the estimated proportion each day
3. Sum of squares - summation of the estimation squared proportion each day
4. Mean - Mean proportion each day
5. SD - Standard deviation for the proportion each day

Special cases

Some parameterizations can lead to "proportions" higher than 1. In such cases, what the model is telling is that we would expect more cases from the exposed individuals alone, than those ultimately observed. In order to correct for this result, a boolean variable was created (keep.proportions). If TRUE, maximum proportion of cases from exposed is 1. If FALSE, "proportions" can be bigger than 1. In the main_simulation.R file (line 132), keep.proportions is set to FALSE.

Works using this simulation

This simulation was built in order to implement the research protocol that won the 1st Edition of the Scholarship Award Amélia Leitão (https://www.anmsp.pt/post/anmsp-premeia-investigacao-na-covid-19-realizada-por-medicos-de-saude-publica).

An article based on the simulation shown in this repository has been submitted to a scientific journal with peer-review.

To allow a more personalized experience of simulation with different parameters, a web app (built using Shiny) is currently in production.