Original: 2022 Jan 6th

Last Updated: 2022 Jan 7th (with latest official data)

**NOTE: THIS POST DOES NOT CONSTITUTE MEDICAL ADVICE. I HAVE NO MEDICAL QUALIFICATIONS WHATSOEVER. CONSULT WITH YOUR DOCTOR.**

The unvaccinated are being shunned in New Zealand, including being legally barred from certain kinds of venues. This is because people are afraid they will catch COVID-19 from them.

So how likely is it that you would catch symptomatic COVID-19 from an unvaccinated person in New Zealand if you were to interact with them? Let's find out.

People quote statistics and run calculations all the time. But oftentimes it is very hard to check their work. How did they come up with the numbers they are showing? In this post I try very hard to show all the calculations and fully explain the methods, as well as to provide references. In a few places I've had to guess. You should be able to fully check my work. I've also allowed values to be edited in case I made a mistake or the data has changed. If you view the page source you'll be able to see all the calculations.

Here you can reset the data in this post to three different scenerios. The first uses current official data only. The second modifies current data with educated guesses about what isn't being properly reported/communicated by the government. The third extends the second into a massive outbreak worse than New South Wales.

New Zealand is currently having upwards of 200 cases of COVID-19 per day (recently much less, but we've been up to about 200 before). [1] If you want to simulate a much greater outbreak, you can use 5000 here which is approximately how many cases per day we would have if our outbreak was equivalent to the outbreak in New South Wales.

I don't know what proportion of those cases were vaccinated. I thought they were going to publish that data, but I cannot find it. I have to make an educated guess. At some point in time, more cases were vaccinated than not, and the anti-COVID-vax community made a stink about that. But of course the unvaccinated cases were still proportionately much higher than their baseline proportion in the greater population. I will be conservative and estimate half.

[1][guess]

[computed]

Most current cases are isolating in thier homes and not spreading COVID. The only cases that are in the community are people who don't yet know they have COVID — they are infectious but aren't yet showing symptoms. In these cases, each case is infectious for two days before symptoms. We can model it as two cases overlapping at a time.

Thanks to exceptional contact tracing work, most people start self-isolating even before they become infectious. I'm making a wild guess as to what percentage of people don't (usually because of not being found by the contact tracers). If you want to simulate a much bigger outbreak (such as New South Wales), set this to 100 percent since contract tracing in such a case will not be able to keep up.

[guess]From the above, we get the following results:

[computed]

[computed]

The population is divided into three groups: Ineligible (12 and under), Eligible and Vaccinated, and Eligible but Unvaccinated. Some of the data below combines two of the three groups in different ways. For instance, the unvaccinated population includes the ineligible. This makes a big difference for when we compute the relative risks between venues that require (or don't require) vaccine passports.

[3][computed from data at 1]

[computed]

[1]

[computed] (This includes children under 12 years of age who are ineligible for the vaccine)

[computed]

[computed]

The odds of someone being infectious depends on what group they are in. We divide the number of infectious people in such a group by the total number of people in the group.

[computed]1 in {{ 1 / unvaccinated_infectious_odds }} [computed]

[computed]

1 in {{ 1 / vaccinated_infectious_odds }} [computed]

[computed]

1 in {{ 1 / passported_infectious_odds }}

(Passported people include all vaccinated people plus all ineligible people) [computed]

[computed]

1 in {{ 1 / anybody_infectious_odds }} [computed]

If somebody is infectious and interacts significantly with somebody who isn't, the transmission rate (secondary attack rate) is about 16.6%. With Omicron, this will probably be higher in the future.

[5]If you are vaccinated, you have 95% protection against the symptoms of COVID-19 compared to the unvaccinated [1]. Now, I don't personally believe that based on other studies claiming that the vaccine wears ouff pretty quickly, but I am apparently wrong because the official government statement on this fact is "Clinical trials found that the Pfizer vaccine gave 95% protection against the symptoms of COVID-19", and I have to take the official word on this.

[1][computed]

Given all of the above, we can calculate the odds of catching COVID-19 given a significant encounter with someone. We multiply the odds they are infectious with the overall transmission chance, and if you are vaccinated we multiply again with the vaccine mitigation.

Unvax to Unvax | 1 in {{ 1 / (unvaccinated_infectious_odds * transmission_chance) }} |
---|---|

Unvax to Vax | 1 in {{ 1 / (unvaccinated_infectious_odds * transmission_chance * vaccine_mitigation ) }} |

Vax to Unvax | 1 in {{ 1 / (vaccinated_infectious_odds * transmission_chance ) }} |

Vax to Vax | 1 in {{ 1 / (vaccinated_infectious_odds * transmission_chance * vaccine_mitigation ) }} |

Anybody to Unvax | 1 in {{ 1 / (anybody_infectious_odds * transmission_chance ) }} |

Anybody to Vax | 1 in {{ 1 / (anybody_infectious_odds * transmission_chance * vaccine_mitigation ) }} |

Passported to Vax | 1 in {{ 1 / (passported_infectious_odds * transmission_chance * vaccine_mitigation ) }} |

COVID-19 sucks. But in New Zealand, only 51 people have died and 13,252 people have recovered (the remaining 1102 cases are still in process).

[1][1]

So the chance of dying if you catch COVID-19 is {{ 100 * odds_of_dying }}%.

Combining the odds of catching COVID-19 with the odds of dying from it, we get the following.

Unvax to Unvax | 1 in {{ 1 / (unvaccinated_infectious_odds * transmission_chance * odds_of_dying) }} |
---|---|

Unvax to Vax | 1 in {{ 1 / (unvaccinated_infectious_odds * transmission_chance * vaccine_mitigation * odds_of_dying ) }} |

Vax to Unvax | 1 in {{ 1 / (vaccinated_infectious_odds * transmission_chance * odds_of_dying ) }} |

Vax to Vax | 1 in {{ 1 / (vaccinated_infectious_odds * transmission_chance * vaccine_mitigation * odds_of_dying ) }} |

Anybody to Unvax | 1 in {{ 1 / (anybody_infectious_odds * transmission_chance * odds_of_dying ) }} |

Anybody to Vax | 1 in {{ 1 / (anybody_infectious_odds * transmission_chance * vaccine_mitigation * odds_of_dying ) }} |

Passported to Vax | 1 in {{ 1 / (passported_infectious_odds * transmission_chance * vaccine_mitigation * odds_of_dying ) }} |

Most venues have a choice of allowing only vaccinated people (via a vaccine passport) or allowing everybody. How much riskier is a venue which allows everybody?

We don't know how many people one encounters per venue visit, nor how intensely they mix, but it doesn't matter. Because we are comparing venue to venue, these unknowns will cancel each other out. We can simply create two mock venues and divide.

In our venue that allows everybody, we presume we have {{ permissive_venue_vaccinated }} vaccinated people and {{ permissive_venue_unvaccinated }} unvaccinated people (based on the population ratio), making 100 people.

In our other venue that requires vaccine passports, we presume we have {{ passported_venue_vaccinated }} vaccinated people and {{ passported_venue_unvaccinated }} vaccine-ineligible (thus unvaccinated) people, making only {{ passported_venue_vaccinated + passported_venue_unvaccinated }} people. Because the eligible unvaccinated are excluded, there are less customers in total.

We compute the odds on each venue as such: (number vaccinated * vaccinated odds + number unvaccinated * unvaccinated odds)

Permissive Venue | {{ permissive_venue_odds }} |
---|---|

Passport-restricted Venue | {{ passported_venue_odds }} |

The relative risk of being in a passported venue is {{ passported_venue_odds / permissive_venue_odds }}.

The risk reduction of excluding the unvaccinated is {{ 100 * (1 - passported_venue_odds / permissive_venue_odds) }}%

So far {{ vaccinated_population }} people have been vaccinated. {{ vaccinated_population_one_dose}} have had at least one dose.

[1]So far {{ vaccine_severe_side_effects }} severe side effects have been reported.

[2]
So the odds of a severe side effect, per person vaccinated (not per dose) are {{ vaccine_severe_side_effects / vaccinated_population_one_dose }}. (We use the larger population of people who have gotten a single dose to be conservative). This is **1 in {{ 1 / (vaccine_severe_side_effects / vaccinated_population_one_dose) }}**.

So far {{ vaccine_doses }} doses of vaccine have been administered.

[1]
On a per-jab basis, we have {{ vaccine_severe_side_effects / vaccine_doses }} chance of a severe side effect, or **1 in {{ 1 / (vaccine_severe_side_effects / vaccine_doses) }}**.

So far only 1 person has died from the vaccine, but up to 127 reports of death following vaccine have been filed. 55 were determined to be unlikely to be caused by the vaccine. 57 were deemed to have insufficient information. 14 are still under investigation. These numbers are NOT AT ALL CLEAR. Why such long investigations? Why so much insufficient information? It might well be that we have up to 72 deaths caused by the vaccine! I'm going to start this number at the 1 known death, but use your judgement and put in the number of people you think died from the vaccine.

[2]
So the odds of dying from the vaccine, per person vaccinated (not per dose) are {{ vaccine_deaths / vaccinated_population_one_dose }}. (We use the larger population of people who have gotten a single dose to be conservative). This is **1 in {{ 1 / (vaccine_deaths / vaccinated_population_one_dose) }}**.

On a per-jab basis, we have {{ vaccine_deaths / vaccine_doses }} chance of death, or **1 in {{ 1 / (vaccine_deaths / vaccine_doses) }}**.

Vaccine passport venues are only about {{ 100 * (1 - passported_venue_odds / permissive_venue_odds) }}% safer than general permissive venues.

General odds of catching symptomatic COVID-19 per encounter with anybody: 1 in {{ 1 / (anybody_infectious_odds * transmission_chance ) }}

General odds of dying per encounter with anybody: 1 in {{ 1 / (anybody_infectious_odds * transmission_chance * odds_of_dying ) }}

General odds of having a severe side effect from being vaccinated, overall: 1 in {{ 1 / (vaccine_severe_side_effects / vaccinated_population_one_dose) }}

General odds of dying from the vaccine, overall: 1 in {{ 1 / (vaccine_deaths / vaccinated_population_one_dose) }}

Number of encounters required before odds of catching COVID-19 surpass odds of having a severe side effect from the vaccine: {{ (vaccine_severe_side_effects / vaccinated_population_one_dose) / (anybody_infectious_odds * transmission_chance ) }}

Number of encounters required before odds of dying of COVID-19 surpass odds of dying from the vaccine: {{ (vaccine_deaths / vaccinated_population_one_dose) / (anybody_infectious_odds * transmission_chance * odds_of_dying ) }}

We have NOT EVEN TOUCHED UPON the personal factors that affect your risk of death or severe disease such as age and health factors. These factors can make a difference of 10,000-fold!

If you are young, healthy and reclusive (interacting with few people), getting vaccinated is a suckers bet. You're odds are much better by not getting vaccinated. But if you feel it is your duty to vaccinate in order to stop the pandemic, you are certainly welcome to.

If you are old, or unhealthy, or highly social, getting vaccinated might be appropriate for you. Talk to your doctor.

[1] COVID-19: Data and statistics

[3] Adverse events following immunisation with COVID-19 vaccines: Safety Report #38 – 4 December 2021

[2] New Zealand Stats Population Clock

[4] Transmission potential was greatest in the first 2 days before and 3 days after onset of symptoms

[5] Household Transmission of SARS-CoV-2: A Systematic Review and Meta-analysis