In Boise, gyms are open! I visited [Axiom Fitness](https://www.axiomfitness.com/parkcenter) the other morning. The facility was great, but I was pretty uncomfortable with the maskless environment. Below, I estimate my risk of catching COVID from a single gym session, and find that **my risk of catching COVID from a single gym session is ~0.03%**. With ~10 gym sessions remaining in my time in Idaho, my total risk of catching COVID specifically from the gym is `1 - (1 - risk_per_session)^10` = `0.003037839182`, or about **0.3%**. This is well within my personal risk tolerance, so I decided to buy a single-month pass!

This page is interactive: try estimating risk for your own gym sessions!



## Assumptions & Constants

- The people I interact with at the gym are independent per session - this likely **over-estimates risk**
- Infected individuals are exactly as likely to be out and about as uninfected individuals. It's unclear to me how this assumption affects our risk calculation:
  - it overestimates because sick people will stay home
  - underestimates because people undergoing risky behaviors are more likely to be infected
- `active_infection_days` = <input type="number" id="active-infection-days" value=30 disabled onchange="calculate()" max=99 min=0 />
  - An infected individual is infectious for <span class="active-infection-days"></span> days, after which they've either recovered or passed away.
- `risky_behavior_multiplier` = <input type="number" id="risky-behavior-multiplier" step=0.1 value=1.5 onchange="calculate()" min=0 max=99 />
  - I assumed that gym-goers are more likely to be infected because they're more likely to conduct risky activities.
- `infected_transmission_risk_min` = <input type="number" disabled id="infected-transmission-risk-min" value=0.001 min=0 max=1000 />
  - [microcovid.org](https://www.microcovid.org/paper/5-activity-risk) calculates transmission risk of a one-hour, indoor, unmasked interaction with someone who has COVID from three feet away to be 6%.
- `gym_6ft_interaction_rate` = <input type="number" id="gym-6ft-interaction-rate" value=0.15 onchange="calculate()" min=0 max=1000 step=0.01 />
  - % of time inside a gym where I am within 6 ft of another person
  - obtained empirically from a gym session, multiplied by 1.5 to conservatively account for missing observations
- `gym_session_duration` = <input type="number" id="gym-session-duration" value=60 onchange="calculate()" min=0 max=999 />
  - How long a gym session lasts, in minutes.

## Variables

- `county_cases_reported` = <input type="number" id="county-cases-reported" value=1686 onchange="calculate()" min=0 max=999999 />
  - cases in the county during the last `active_infection_days` days
  - [In the last 4 weeks of full reporting (9/13 - 10/4), Ada county reported 1686 cases](https://public.tableau.com/profile/central.district.health#!/vizhome/CDHCOVID-19/CDHCOVID-19Information)
- `county_postivity_rate` = <input type="number" id="county-positivity-rate" value=0.07 onchange="calculate()" min=0 max=1000 step=0.01 />
  - test positivity rate over the last `active_infection_days`
- `county_population` = <input type="number" id="county-population" value=502970 onchange="calculate()" min=0 max=99999999 />
  - number of people in the county
  - [Ada county demographics](https://adacounty.id.gov/developmentservices/wp-content/uploads/sites/37/Population-Demographics.pdf)
- `county_true_active_infections` = `county_cases_reported * (16 * (county_positivity_rate ^ 0.5) + 2.5)` = <input type="number" id="county-true-active-infections" disabled value=11352 min=0 max=999999 />
  - [This paper](https://covid19-projections.com/estimating-true-infections/) provides the above formula.
- `gym_goer_infection_probability` = `county_true_active_infections * risky_behavior_multiplier / county_population` = <input type="number" id="gym-goer-infection-probability" disabled value=0.0338 min=0 max=999999 />

## Formula

Finally, we can calculate our risk per session, which is the amount of time spent within 6ft of another person in a single session multiplied by the probability that they are infectious.

`risk_per_session` = `gym_goer_infection_probability * gym_6ft_interaction_rate * gym_session_duration * infected_transmission_risk_min` = <br /> <strong id="risk-per-session">0.0003042</strong> = <strong id="risk-per-session-pct">0.0003042%</strong>.

<script>
function calculate() {
  var activeInfectionDays = document.getElementById("active-infection-days").value;
  var riskyBehaviorMultiplier = document.getElementById("risky-behavior-multiplier").value;
  var infectedTransmissionRiskMin = document.getElementById("infected-transmission-risk-min").value;
  var gym6ftInteractionRate = document.getElementById("gym-6ft-interaction-rate").value;
  var gymSessionDuration = document.getElementById("gym-session-duration").value;
  var countyCasesReported = document.getElementById("county-cases-reported").value;
  var countyPositivityRate = document.getElementById("county-positivity-rate").value;
  var countyPopulation = document.getElementById("county-population").value;

  var countyTrueActiveInfections = Math.round(countyCasesReported * (16 * Math.sqrt(countyPositivityRate) + 2.5));
  var gymGoerInfectionProbability = countyTrueActiveInfections * riskyBehaviorMultiplier / countyPopulation;

  var riskPerSession = gymGoerInfectionProbability * gym6ftInteractionRate * gymSessionDuration * infectedTransmissionRiskMin;

  document.getElementById("county-true-active-infections").value = countyTrueActiveInfections;
  document.getElementById("gym-goer-infection-probability").value = gymGoerInfectionProbability.toFixed(4);
  document.getElementById("risk-per-session").innerText = riskPerSession.toFixed(6);
  document.getElementById("risk-per-session-pct").innerText = (riskPerSession * 100).toFixed(4) + "%";

}

calculate();
</script>

<p>In Boise, gyms are open! I visited <a href="https://www.axiomfitness.com/parkcenter" target="_blank" rel="nofollow noopener noreferrer" onclick="window.gtag(&#x22;event&#x22;, &#x22;link-click&#x22;, {&#x22;event_label&#x22;:&#x22;markdown&#x22;,&#x22;value&#x22;:&#x22;https://www.axiomfitness.com/parkcenter&#x22;})">Axiom Fitness</a> the other morning. The facility was great, but I was pretty uncomfortable with the maskless environment. Below, I estimate my risk of catching COVID from a single gym session, and find that <strong>my risk of catching COVID from a single gym session is ~0.03%</strong>. With ~10 gym sessions remaining in my time in Idaho, my total risk of catching COVID specifically from the gym is <code>1 - (1 - risk_per_session)^10</code> = <code>0.003037839182</code>, or about <strong>0.3%</strong>. This is well within my personal risk tolerance, so I decided to buy a single-month pass!</p>
<p>This page is interactive: try estimating risk for your own gym sessions!</p>

<h2 id="assumptions--constants">Assumptions &#x26; Constants</h2>
<ul>
<li>The people I interact with at the gym are independent per session - this likely <strong>over-estimates risk</strong></li>
<li>Infected individuals are exactly as likely to be out and about as uninfected individuals. It’s unclear to me how this assumption affects our risk calculation:
<ul>
<li>it overestimates because sick people will stay home</li>
<li>underestimates because people undergoing risky behaviors are more likely to be infected</li>
</ul>
</li>
<li><code>active_infection_days</code> = <input type="number" id="active-infection-days" value=30 disabled onchange="calculate()" max=99 min=0 />
<ul>
<li>An infected individual is infectious for <span class="active-infection-days"></span> days, after which they’ve either recovered or passed away.</li>
</ul>
</li>
<li><code>risky_behavior_multiplier</code> = <input type="number" id="risky-behavior-multiplier" step=0.1 value=1.5 onchange="calculate()" min=0 max=99 />
<ul>
<li>I assumed that gym-goers are more likely to be infected because they’re more likely to conduct risky activities.</li>
</ul>
</li>
<li><code>infected_transmission_risk_min</code> = <input type="number" disabled id="infected-transmission-risk-min" value=0.001 min=0 max=1000 />
<ul>
<li><a href="https://www.microcovid.org/paper/5-activity-risk" target="_blank" rel="nofollow noopener noreferrer" onclick="window.gtag(&#x22;event&#x22;, &#x22;link-click&#x22;, {&#x22;event_label&#x22;:&#x22;markdown&#x22;,&#x22;value&#x22;:&#x22;https://www.microcovid.org/paper/5-activity-risk&#x22;})">microcovid.org</a> calculates transmission risk of a one-hour, indoor, unmasked interaction with someone who has COVID from three feet away to be 6%.</li>
</ul>
</li>
<li><code>gym_6ft_interaction_rate</code> = <input type="number" id="gym-6ft-interaction-rate" value=0.15 onchange="calculate()" min=0 max=1000 step=0.01 />
<ul>
<li>% of time inside a gym where I am within 6 ft of another person</li>
<li>obtained empirically from a gym session, multiplied by 1.5 to conservatively account for missing observations</li>
</ul>
</li>
<li><code>gym_session_duration</code> = <input type="number" id="gym-session-duration" value=60 onchange="calculate()" min=0 max=999 />
<ul>
<li>How long a gym session lasts, in minutes.</li>
</ul>
</li>
</ul>
<h2 id="variables">Variables</h2>
<ul>
<li><code>county_cases_reported</code> = <input type="number" id="county-cases-reported" value=1686 onchange="calculate()" min=0 max=999999 />
<ul>
<li>cases in the county during the last <code>active_infection_days</code> days</li>
<li><a href="https://public.tableau.com/profile/central.district.health#!/vizhome/CDHCOVID-19/CDHCOVID-19Information" target="_blank" rel="nofollow noopener noreferrer" onclick="window.gtag(&#x22;event&#x22;, &#x22;link-click&#x22;, {&#x22;event_label&#x22;:&#x22;markdown&#x22;,&#x22;value&#x22;:&#x22;https://public.tableau.com/profile/central.district.health#!/vizhome/CDHCOVID-19/CDHCOVID-19Information&#x22;})">In the last 4 weeks of full reporting (9/13 - 10/4), Ada county reported 1686 cases</a></li>
</ul>
</li>
<li><code>county_postivity_rate</code> = <input type="number" id="county-positivity-rate" value=0.07 onchange="calculate()" min=0 max=1000 step=0.01 />
<ul>
<li>test positivity rate over the last <code>active_infection_days</code></li>
</ul>
</li>
<li><code>county_population</code> = <input type="number" id="county-population" value=502970 onchange="calculate()" min=0 max=99999999 />
<ul>
<li>number of people in the county</li>
<li><a href="https://adacounty.id.gov/developmentservices/wp-content/uploads/sites/37/Population-Demographics.pdf" target="_blank" rel="nofollow noopener noreferrer" onclick="window.gtag(&#x22;event&#x22;, &#x22;link-click&#x22;, {&#x22;event_label&#x22;:&#x22;markdown&#x22;,&#x22;value&#x22;:&#x22;https://adacounty.id.gov/developmentservices/wp-content/uploads/sites/37/Population-Demographics.pdf&#x22;})">Ada county demographics</a></li>
</ul>
</li>
<li><code>county_true_active_infections</code> = <code>county_cases_reported * (16 * (county_positivity_rate ^ 0.5) + 2.5)</code> = <input type="number" id="county-true-active-infections" disabled value=11352 min=0 max=999999 />
<ul>
<li><a href="https://covid19-projections.com/estimating-true-infections/" target="_blank" rel="nofollow noopener noreferrer" onclick="window.gtag(&#x22;event&#x22;, &#x22;link-click&#x22;, {&#x22;event_label&#x22;:&#x22;markdown&#x22;,&#x22;value&#x22;:&#x22;https://covid19-projections.com/estimating-true-infections/&#x22;})">This paper</a> provides the above formula.</li>
</ul>
</li>
<li><code>gym_goer_infection_probability</code> = <code>county_true_active_infections * risky_behavior_multiplier / county_population</code> = <input type="number" id="gym-goer-infection-probability" disabled value=0.0338 min=0 max=999999 /></li>
</ul>
<h2 id="formula">Formula</h2>
<p>Finally, we can calculate our risk per session, which is the amount of time spent within 6ft of another person in a single session multiplied by the probability that they are infectious.</p>
<p><code>risk_per_session</code> = <code>gym_goer_infection_probability * gym_6ft_interaction_rate * gym_session_duration * infected_transmission_risk_min</code> = <br /> <strong id="risk-per-session">0.0003042</strong> = <strong id="risk-per-session-pct">0.0003042%</strong>.</p>
<script>
function calculate() {
  var activeInfectionDays = document.getElementById("active-infection-days").value;
  var riskyBehaviorMultiplier = document.getElementById("risky-behavior-multiplier").value;
  var infectedTransmissionRiskMin = document.getElementById("infected-transmission-risk-min").value;
  var gym6ftInteractionRate = document.getElementById("gym-6ft-interaction-rate").value;
  var gymSessionDuration = document.getElementById("gym-session-duration").value;
  var countyCasesReported = document.getElementById("county-cases-reported").value;
  var countyPositivityRate = document.getElementById("county-positivity-rate").value;
  var countyPopulation = document.getElementById("county-population").value;

  var countyTrueActiveInfections = Math.round(countyCasesReported * (16 * Math.sqrt(countyPositivityRate) + 2.5));
  var gymGoerInfectionProbability = countyTrueActiveInfections * riskyBehaviorMultiplier / countyPopulation;

  var riskPerSession = gymGoerInfectionProbability * gym6ftInteractionRate * gymSessionDuration * infectedTransmissionRiskMin;

  document.getElementById("county-true-active-infections").value = countyTrueActiveInfections;
  document.getElementById("gym-goer-infection-probability").value = gymGoerInfectionProbability.toFixed(4);
  document.getElementById("risk-per-session").innerText = riskPerSession.toFixed(6);
  document.getElementById("risk-per-session-pct").innerText = (riskPerSession * 100).toFixed(4) + "%";

}

calculate();
</script>

Jeff Chen

Estimating Gym COVID Risk

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