What is this?
This is an interactive simulation tool to study different mitigation strategies for the Covid-19 pandemic. The user is free to choose start- and end-times of multiple phases, during which
- social distancing,
- repetitive testing (of people without symptoms, who subsequently isolate themselves, if tested positive) and
- vaccination
can be combined at specified intensities.
How Can Repetitive Testing Reduce R?
Repetitive Testing can lead to a dramatic reduction of the reproduction number (R), if infected people without symptoms can be detected and isolated. Otherwise these individuals would continue to spread the virus. It is crucial that testing has to be continued; otherwise the reproduction number will go up again to its previous value. If executed consequently, repetitive testing has the same effect as extreme social distancing, e.g. testing 90% of the mobile population once every two weeks roughly corresponds to reducing the number of physical contacts by half (in both cases the reproduction number would be reduced by half). The great benefit of repetitive is that it allows to relax social distancing measures.
Note that mitigation by testing also works, if the employed tests have a significant false negative rate (like antigen tests); this just means that a larger fraction of the population has to get tested per day, such that the same number of infected persons get detected.
It is important to understand that detecting and isolating infected people without symptoms has a much stronger effect on the reproduction number than detecting and isolating symptomatic people. This is due to the following two reasons:
- Undetected infected people who are asymptomatic keep up their contacts and thus contribute to the virus spread, while undetected symptomatic people typically reduce their social interactions due to illness.
- Undetected infected people who are asymptomatic have in average a longer infectious period ahead of them than undetected symptomatic people.
At the same time one may also test symptomatic people, but most important is to test enough people without symptoms.
In general it can be said that the achieved reduction of R is very sensitive on the test-to-notice time and the fraction of the population who participates.
How Can the Effect of Invested Test Resources be Increased?
- Pool Testing: A very efficient use of virus RNA tests is pool testing (~20 persons in each pool). Members of positive pool tests are then tested individually. Note that pool testing is in particular efficient, if the prevalence is low. The high sensitivity of virus RNA tests even allows for the use of saliva, which dramatically increases the willingness to participate.
- Two-Stage Testing: Another attractive way to keep costs and logistics of testing low is two stage testing [2], that is, participants are tested via virus antigen tests, and those who are positive are tested again with virus RNA tests for confirmation (since the virus antigen test false positive rate is higher than that of virus RNA tests).
- Testing High Contact Sub-Populations: Also, the effect of invested testing resources can dramatically be increased, if one focuses on sub-populations with an above average prevalence [1]. It is intuitive and has been shown that this correlates with people who have many contacts.
Model
The model is based on a reaction mechanism, which is depicted in the graph below; each compartment represents the number of people who are in the corresponding state. The dynamics of the system depends on the rates at which people are "transfered" from one compartment to another.
It is crucial that the model distinguishes between individuals detected by symptoms (light blue), and those detected by virus testing (inserted graph). The detection rates of exposed, asymptomatic and mild symptomatic persons due to testing are proportional to ke, ka, ks, respectively. These individuals are then accounted for in the inserted graph with the white compartments, which is very similar as the main one.
More details on the Model can be found in the paper and the supplemental information of [1, 2, 3].
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The corresponding system of ordinary differential equations (ODEs) reads
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which leads to the expression
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for the effective reproduction number, where f is the fraction of the population participating in repetitive testing and the k-values are polynomials of the test frequency, the false negative rate and the test-to-notice time.
Note that the effect of vaccination is treated in a far more simplistic way than the effect of testing and social distancing. It is based on the assumption that after vaccination a persion is immune immediately (with the probability "Vaccination Eff.", which can be specified) and can not spread the virus anymore.
More details on the model (without vaccination) can be found in the following articles and their supplementary information:
[3] Gorji, M. Arnoldini, D. F. Jenny, W.-D. Hardt, and P. Jenny. Dynamic Modeling to Identify Mitigation Strategies for the Covid-19 Pandemic. Jan. 2021 (accepted).
Thanks for visiting and stay safe!
Smart Investment of Virus RNA Testing Resources to Enhance Covid-19 Mitigation
Base Case
Plot showing the evolution of the pandemic for a base case without mitigation with a basic reproduction number (R) of 2.4.
Your Simulation
Plot showing the evolution of the pandemic, if your mitigation strategy is applied; it can consist of multiple phases and each can be any combination of social distancing, repetitive mass testing and vaccination.
Input Data
Phase 1
Required Tests
Plot showing the reproduction number as a function of the test frequency (one over the test interval in days); dependent on fraction of the mobile population who participates (%), the test-to-notice time (days), the test sensitivity (%), the fraction of contacts with external people (%), the ratio of external to internal prevalave and the reproduction number without testing.