COVID Odyssey: NZ New Year Fear 42 Post #969~ Worldwide windup~ Verification of our formula for Ro

We verify our formula for Ro: For definitions and background please see the WELCOME menu. We also use the same formula to estimate Re. Re is the effective reproduction number when there is isolation. We assume that n =10 and that infectivity reduces by a factor of 1/r each day where r is the daily…

COVID Odyssey: NZ New Year Fear 41 Post #968~ Worldwide windup~ More simulations to confirm our formula

We confirm our estimates for Re and hence Ro worldwide. We have developed spreadsheets simulating the spread of COVID-19 based on a specific daily increase in case numbers (r). We extend our spreadsheet to utilise a range of values for r. As a result of the original simulations we have developed a formula for calculating…

COVID Odyssey: Worldwide Winter Windup 10 ~ Vaccine hesitancy ~ is herd immunity possible?

The vaccine hesitant includes a range of people ranging from people fearful of getting a jab, those fearful of the consequences of getting a jab, to anti-vaxxers. ‘Herd immunity’, also known as ‘population immunity’, is the indirect protection from an infectious disease that happens when a population is immune either through vaccination or immunity developed…

COVID Odyssey: Worldwide Winter Windup 9 ~ Ro > Re ~ How much greater is Ro?

We consider how much greater Ro  is than Re. We look at the following table: For definitions see: Welcome In New Zealand  both r = SQRT(2) and r = 1.429 provide good estimates for the total number of cases from 21 to 25 August 2021. See: COVID Odyssey: Winter Warning NZ 15 ~ Delta variant…

COVID Odyssey: Worldwide Winter Windup 8 ~ Ro ~ Estimating Re & Ro by 3 straight lines

We have estimated Re and Ro for COVID-19 using the linear equation y = 17r – 18, where r is a daily growth rate of infections (estimated over the next 5 days). We now add in two extra lines to complete the approximations. The three lines are: y = 17r – 18       …

COVID Odyssey: Worldwide Winter Windup 7 ~ Ro ~ Estimating Ro by a straight line

We estimate Re and Ro for COVID-19 using the linear equation y = 17r – 18, where r is a daily growth rate of infections (estimated over the next 5 days). i.e. We use the value calculated for y in the equation as an estimate for Re and Ro. Update: See: COVID Odyssey: Worldwide Winter…

COVID Odyssey: Worldwide Winter Windup 6 ~ Ro ~ Estimates for the Alpha and Delta variants

We have already estimated Ro for the original COVID-19 Outbreak in 2020 and for the Delta variant.  We have estimated Ro between 5 and 8 for the original COVID-19 Outbreak in 2020. We have estimated Ro between 9 and 12.7 for the original Delta COVID-19 Outbreak. We now estimate Ro for the 2020 Alpha variant. …

COVID Odyssey: Worldwide Winter Windup 5 ~ Revised estimates for Re worldwide

We revise our estimates for Ro worldwide. Previously we had the ranking below (see r1 and Re1 columns) for the 2020 outbreak (note: r1 is without weights; r2 is with weights): The above was calculated using: Note that n = 10 days and  r[d] is a daily increase (growth factor) calculated over the next 5…

COVID Odyssey: Winter Windup 16 ~ Methods used to estimate Ro

Originally posted on Green Bottles, Alan's Ark & COVID Odyssey: Alan Grace's vir[tu]al journey:
In this post we shall look at ways experts analyse the spread of COVID-19. My own mathematical techniques are simple but have produced some surprising results. Analysis can quite often involve solving systems of differential equations (see…

COVID Odyssey: Winter Windup 15 ~ Executive summary ~ Our formula for Ro

Updates for New Zealand Delta variant data and results see below. For earlier and other variants see: Welcome About COVID Odyssey: Winter Warning NZ 6 ~ Estimating the number of 2021 Cases ~ A simpler formula COVID Odyssey: Winter Warning NZ 2 ~ Delta variant ~ Lockdown 4 appears to be working For COVID-19 we…

COVID Odyssey: Winter Windup 14 ~ COVID-19 ~ Simulations to develop our formula for Ro

We have used simulations to develop our formula for Ro which is based on the daily rate of increase, r, for cases. For simulations using r = 1.4 and r = SQRT(2), for each simulation we generate 40 outbreaks using Excel and calculate statistics. Sample runs are included in this post. Our formula for Ro…

COVID Odyssey: Worldwide Winter Windup 4 ~ Is Ro 6 to 7.8 in early 2020?

For COVID-19 in early 2020, we have estimated Ro to be in the range 6 to 7.8. For the Delta variant we have estimated Ro to be in the range 9 to 12.7. Update. See: COVID Odyssey: Worldwide Winter Windup 5 ~ Revised estimates for Re worldwide We consider widening our range estimate for COVID-19…

COVID Odyssey: Winter Windup 13 ~ Is the COVID-19 Delta variant as infectious as measles?

Experts think the COVID-19 Delta variant is much more contagious than the flu and chickenpox, and on par with the measles. See: https://www.healthline.com/health-news/cdc-says-delta-variant-as-infectious-as-chickenpox-what-to-know-now We have found that Ro for the Delta variant is between 9 and 12.7. See: COVID Odyssey: Winter Windup 9 ~ COVID- 19 Delta Variant 2021 ~ Is Ro in the range…

COVID Odyssey: Worldwide Winter Windup 3 ~ COVID-19 in 2020 vs 2021 ~ Cases per million people

We look at cases per million people for the 31 countries with over one million cases on 6 August 2021 and compare the results estimated for the daily rate of increase, r, estimated a year earlier on 6 August 2020. We have looked at the spread of COVID-19 throughout the world early in 2020. We…

COVID Odyssey: Worldwide Winter Windup 2~ Be afraid, be very afraid of the Lambda variant

Be afraid, be very afraid of the Lambda variant. Strong likelihood of more dangerous COVID-19 variants – WHO. The eighth meeting of the Emergency Committee convened by the WHO Director-General under the International Health Regulations (2005) (IHR) regarding the coronavirus disease (COVID-19) took place on Wednesday, 14 July 2021 from 11:30 to 16:00 Geneva time…

COVID Odyssey: Worldwide Winter Windup ~ COVID-19 in 2020 vs 2021 ~ How many people may one person infect in your country?

We look again at the spread of COVID-19 throughout the world early in 2020. We look at case numbers up to 6 August 2020. As expected estimates for Re#2 (last column in the first table, calculated using our formula for Ro below), and hence Ro occurred very early in an outbreak in each country. Ro…

COVID Odyssey: Winter Windup 12 ~ Conclusion~ Ro = 6 to 7.8 in early 2020?

We revisit data for the spread of COVID-19 in early 2020. We see in China that a daily increase close to r~ 1.5 fits the case data well from 23 Jan to 28 January 2020. We have seen in New Zealand that a daily increase close to r~ 1.4 fits the case data well from…

COVID Odyssey: Winter Windup 11 ~ COVID-19 ~ Daily decline in infectivity

We have assumed that case numbers increase at a daily rate of r and infectivity decreases daily at a rate of 1/r. This simplifies the formula. However it is possible that infectivity decreases daily at a different rate. Below is a graph showing various rates: Below is data for the graph. Note: values have been…

COVID Odyssey: Winter Windup 10 ~ COVID-19 Delta variant ~ Conclusions 2021

The Delta variant of COVID-19 appears to be twice as infectious as the original 2020 outbreak. We have found that Ro for the Delta variant is between 9 and 12.7. Ro is the average number of people once person may infect over a period of n = 10 days when there is no quarantine or…

COVID Odyssey: Winter Windup 9 ~ COVID- 19 Delta Variant 2021 ~ Is Ro in the range 9 to 12.7?

The Delta variant of COVID-19 appears to be twice as infectious as the original 2020 outbreak. for the 2020 outbreak we estimated Ro = 6. In previous posts we simulated outbreaks using a value for Ro around 12.7 (actually Ro = SQRT(3)). In this post we consider also Ro = 9 (halfway between 6 and…

COVID Odyssey: Winter Windup 8 ~ COVID- 19 Delta Variant 2021 ~ Graphs

We look at graphs of the number of people that may be infected by one person having the Delta variant of COVID-19. The graphs are produced from our simulations for 1778 cases for Day 12 starting with 10 cases on Day 1 and using a daily increase of r = SQRT(3) with an infectious period…

COVID Odyssey: Winter Windup 7 ~ COVID-19 Delta Variant 2021 ~ Simulations

In the previous post we saw that for the Delta variant there could be a daily increase in the number of cases of r = SQRT(3). For background see: COVID Odyssey: Winter Windup 6 ~ COVID-19 Delta Variant 2021 ~ Does Ro = 12? This would give rise to the table below: We see from…

COVID Odyssey: Winter Windup 6 ~ COVID-19 Delta Variant 2021 ~ Does Ro = 12?

We look at the how many people one person with the Delta variant of COVID-19 may infect on average in 2021. By definition we let: r denote the effective Reproduction rate of COVID-19 for one day Ro (R0; R-Zero; R-Nought) denote the Reproduction number for COVID-19 without any quarantine or isolation Re denote the effective Reproduction number for COVID-19 (Re assumes isolation/quarantine is…

COVID Odyssey: Winter Windup 5 ~ Conclusions for NZ in 2020 ~ Back to the past: Re = 5.8 and Ro = 6

In this post we conclude that we need to go back to our original results for estimating Ro. By definition we let: r denote the effective Reproduction rate of COVID-19 for one day Ro (R0; R-Zero; R-Nought) denote the Reproduction number for COVID-19 without any quarantine or isolation Re denote the effective Reproduction number for COVID-19 (Re assumes isolation/quarantine is happening) a case be defined…

COVID Odyssey: Winter Windup 4 ~ The formula for calculating Ro

In this post we develop the formula we have used for calculating Ro, the number of people one person may infect on average over a 10-day symptomatic period (n = 10) given a daily increase r in the number of cases and a daily decrease of 1/r in infectivity. Note: The formula in this post…

COVID Odyssey: Winter Windup 3 ~ Carpe diem 2020 ~ Estimating Ro by simulations

In early 2020 we calculated that there was a daily increase in cases of r = 1.4 and we assumed infectivity decreased by 1/r each day over n = 10 days. We created simulations to estimate Ro, the number of people a person with COVID-19 was likely to infect on average. How do we choose…

COVID Odyssey: Winter Windup 2 ~ In early 2020 can one person infect 4 or 6 others on average?

Ro is the number of people that on average one person with COVID-19 may infect. Note: The formula in this post has been updated. See: COVID Odyssey: Winter Windup 5 ~ Conclusions for 2020 ~ Back to the past: Re = 5.8 and Ro = 6 Early in 2020 we arrived at the following table…

COVID Odyssey: Winter Windup ~ 2020 simulations revisited

We revisit the simulations undertaken in early 2020 to estimate the number of people one person with COVID-19 may infect on average over an n-day infectious period. We developed a formula calculating the numbers Ro and Re (with and without isolation respectively) given a daily rate (r) of increase in cases. We also produced a…

COVID-19 Worldwide in 2020~ How many people may one person infect on average? What can we expect when Ro = r^2.5?

We considered in the last post that Ro = r ^ 2.5 where r is a daily increase in case numbers for a number of days. In New Zealand in the initial outbreak r = 1.4 and hence we estimate now that Ro = 1.4 ^ 2.5. See: COVID-19~ Refining estimates for Ro~ Is Ro…

Update 2: COVID-19 in NZ in Early 2020~ Does Re = 5.8 and Ro = 6?

Two years ago today on 7 July 2021 we looked back at our analysis of COVID-19 in NZ in early 2020 as the breakout occurred in New Zealand. In New Zealand we discovered than a daily increase of r = 1.4 fitted the New Zealand cases numbers well. First look at our 7 July 2021…

Update: COVID-19 in NZ in Early 2020~ Does Re = 5.8 and Ro = 6?

We update our last post. The results are not very different. First look at our 7 July 2021 post for definitions: Warning: In this post below we have used r^5 to estimate Re. We have decided this may not be a good idea. A link to an updated post is here: Update 2: COVID-19 in…

COVID-19 in NZ in Early 2020~ Does Re = 5.8 and Ro = 6?

Two years ago today on 7 July 2021 we looked back at our analysis of COVID-19 in NZ in early 2020 as the breakout occurred in New Zealand. In New Zealand we discovered than a daily increase of r = 1.4 fitted the New Zealand cases numbers well. First look at our 7 July 2021…

COVID Odyssey: Autumn Addendum Post #971~ COVID Odyssey Time Capsule Addendum

COVID Odyssey Addendum Summer has ceased Autumn’s awesome My thoughts come least my mind’s caught numb I feel like an April fool I have sealed my time capsule Before adding my addendum Alan Grace 26 March 2022 The Time Capsule embargo was lifted briefly on 30 March to include this addendum. Future posts can be…

COVID Odyssey: NZ New Year Fear 6 Post #933~ Omicron will be dominant variant in NZ community in 2 to 4 weeks

What community variant? What on earth letter are we onWhen will we next have OmicronDelta is now dominantOmicron soon prominentPerhaps rename it Omnicron? Alan Grace14 January 2022 We have only had one known case of community spread of Omicron in New Zealand. NZ Herald today (14 Jan) on P1: Should we rename Omicron, Omnicron? Below…

COVID Odyssey: New Year Fear ~ Post #928: How sky high are these PI hypotheses?

Hi PI How the New Year drew near We dread the clear new fear Now sky high rear these PI hypotheses How soon ere PI appear Alan Grace 2 January 2022 We assume that the next upcoming COVID-19 VOC (Variant of Concern) may be called PI when it is eventually comes/ is identified. We look…

COVID Odyssey: Summer Surprise 2 ~ Post#924: NZ COVID-19~ OMICRON has reached NZ border

Yesterday Thursday 16 December it was officially announced at a televised media conference that the OMICRON variant has been detected at an MIQ facility in Christchurch. We extend our previous chart to include the OMICRON variant. The horizontal access shows potential values for Ro. For the previous chart see: COVID Odyssey: Worldwide Winter Windup 6…

COVID Odyssey: Spring Spruce up 7 ~ NZ COVID-19 Delta Poll 3 results~ When will New Zealand have 90% fully vaccinated?

We will discuss poll 3: See: https://www.neighbourly.co.nz/message/view/67022662 Here are the poll results: I believe the best choice is: 90% of the population over 12 fully vaccinated is not possible by February. First look at: COVID Odyssey: Worldwide Winter Windup 10 ~ Vaccine hesitancy ~ is herd immunity possible? COVID Odyssey: Spring Spruce up 6 ~…

COVID Odyssey: Winter Warning NZ 18 ~ Delta variant: NZ vs Norway~ How may % vaccination affect case numbers?

We use Norway data to estimate a worst-case scenario for Norway and New Zealand. We anticipate we could have 500,000 cases over a one-year period and 2100 deaths. Even using Norway’s actual case data provides a scary scenario for New Zealand. New modelling prepared for the Government by Professor Shaun Hendy suggests that New Zealand…

COVID Odyssey: Winter Warning NZ 15 ~ Delta variant outbreak 2021 ~ Estimating Ro and Re

We estimate under the current Lockdown Level 4 in Auckland one person may infect 6 to 6.3 other people in New Zealand in the current Delta variant outbreak of COVID-19. Without lockdown we have estimated one person with the Delta variant of COVID-19 may infect 9 to 12.75 other people. See: COVID Odyssey: Worldwide Winter…

COVID Odyssey: Winter Warning NZ 11 ~ Delta variant ~ Will NZ Cases exceed last year?

The total number of cases in this outbreak in New Zealand is likely to exceed the the total in the outbreak early in 2020 if the midpoint is in September. Update. See: COVID Odyssey: Winter Warning NZ 12 ~ Estimating the number of 2021 Cases ~ What will the total be? Yesterday the number of…

COVID Odyssey: Winter Warning NZ 10 ~ Delta variant ~ Analysis

We analyse the 2021 outbreak in New Zealand. We hope that the midpoint has been reached. By definition we let: r denote the effective Reproduction rate of COVID-19 for one day Ro (R0; R-Zero; R-Nought) denote the Reproduction number for COVID-19 without any quarantine or isolation Re denote the effective Reproduction number for COVID-19 (Re assumes isolation/quarantine is happening) a case be defined as a…

COVID Odyssey: Winter Warning NZ 6 ~ Estimating the number of 2021 Cases ~ A simpler formula

We have developed a simpler formula for estimating the number of cases in New Zealand for the current COVID-19 Delta variant outbreak.. Our formula is: C = r^d where r = 1.429 and d = the number of days since 10 August 2021. Here is the PDF version: NZCases2021r The effective reproduction rate (Re) is…