A rambling mind

Personal Ravings

Solving log(x) = R(x-1) for a family of R values, with R up to 7

Implications of the R0 Reproduction Number in an unconstrained Delta variant environment

In my April 8th 2020 post about the R0 reproduction number and the use of SIR models to model the pandemic, I developed a chart which predicted the proportion of the population uninfected by the end of an unconstrained pandemic.

That chart allowed for an R0 up to 3, but the Delta variant that arrived in the UK a year later, in April 2021, has an R0 far higher than the original, possible 2.5 times as high, as much as R0=7, perhaps.

I have added to the scope of that previous post to develop a chart allowing R0 up to 7..

Repeated elements of the 164-compartment model flowchart with Uninfected, Vaccinated, double Vaccinated, Recovered and Deceased compartments for each group; and Incubation, Sick, Seriously Sick, and Better infective compartments per group, per variant and per vaccination status, with associated transition rates

“Freedom Day”, multiple vaccinations and the Delta variant

In this post, I run a development of my model which includes immunity waning (at a 150 day half-life), vaccine hesitancy by group, multiple vaccine inoculations (representing the typical two jabs required by most vaccines for best immunity) and also the possibility of vaccinated people not only to become infected, but also to pass on the virus even if not infected themselves.

Chart 318 for scenarios UK479 and UK465 with vaccinations and 2021 NPI relaxations up to June 21st with 4% and Aug 16th with 2% NPI effectiveness. v3 transmission k11 = 1, var_eff = 100%, fss and fmort as fort v1 and v2. Modelled 800 day outcomes to April 12th 2022 compared with reported active cases and deaths to June 4th. Serious cases for three variants.

Delta variant impact on June 21st easing – delay or reduce?

Having explored what pandemic advisers might be seeing and highlighting to decision-makers in Government, I run scenarios with different settings for the planned June 21st relaxation of lockdown, the last in the series of relaxations over the first half of 2021, following the January 3rd lockdown. These model scenarios show examples of what the relative consequences of the June 21st relaxation as planned, versus four other options:- cancellation of the June 21st step altogether, two different delays, of 28 and 56 days, and lastly a 50% reduction in the scope of the June 21st relaxation.

Recent variants with their identifiers, lineage, source country if known, total cases, and new cases since May 12th: source gov.uk

What are UK Government advisers seeing?

I have developed some model scenarios that show examples of what might be behind expert advice on the caution required with new SARS-Cov-2 variants. The scenarios indicate the importance of the UK vaccine programme, as we face variants with potentially different characteristics of transmission, severity of infection and responsiveness to vaccines. Understanding those variant characteristics is vital for projections.

Chart 18 for scenarios UK433 & UK439: v3 transmission k11 = 1, comparing var_eff and fss fmort effects. Modelled 800 day outcomes to April 12th 2022 compared with reported deaths to May 23rd. Serious cases for all variants, with 2021 NPI relaxations up to June 21st 2021.

Why the UK Government is worried about new variants

I have developed some model scenarios that show examples of what might be behind expert advice on the caution required with new SARS-Cov-2 variants. The scenarios indicate the importance of the UK vaccine programme, as we face variants with potentially different characteristics of transmission, severity of infection and responsiveness to vaccines.

Chart 303 for the grouped model UK929: modelled 800 day outcome for all variants for serious cases and deaths, with 2021 NPI relaxations up to June 21st 2021

Exploring new variants, vaccines and NPIs

There has been increasing concern recently about SARS-Cov-2 variants that might escape vaccines to some extent, as well as having different transmission rates (as the Kent variant does), and causing different severity of illness with higher mortality. I have added a vaccination efficacy modifier, var_eff, by variant, as a multiplier to the standard vaccination efficacy, vac_eff, to help model such potential variants that have a partial or total capability to escape vaccines, and this post shows examples of how that works, using a third variant introduced to the model on January 1st 2021. In addition, I have completed adding fSS (the fraction of people becoming seriously sick from each variant) and fmort (fatality of the variant) by Covid variant.

Chart 19 for the grouped model UK957: modelled 800 day outcome compared with reported data to April 21st for active cases and deaths, with 2021 NPI relaxations up to June 21st 2021

Tuning the age and vulnerability model

In my latest post on March 26th I described a new Coronavirus group model, based on work I had done as a UK case study in support of Prof. Alex de Visscher’s paper, in conjunction with Dr. Tom Sutton, on “Second-wave Dynamics of COVID-19: Impact of Behavioral Changes, Immunity Loss, New Strains, and Vaccination” which has now been published for peer review as a pre-print on Springer’s site at https://www.researchsquare.com/article/rs-195879/v1. I have now added the latest UK vaccination progress figures, and the UK Government’s announced intentions for the near future regarding Non Pharmaceutical Interventions (NPIs). I have also updated mortality and infection characteristics for the four different population groups in the model.

Chart 209 showing modelled and reported cumulative cases and deaths to 800 days in the groups model

Age and vulnerability related Coronavirus modelling

In my most recent post on February 12th, I described modelling work I had done in support of Prof. Alex de Visscher’s paper, in conjunction with Dr. Tom Sutton, on “Second-wave Dynamics of COVID-19: Impact of Behavioral Changes, Immunity Loss, New Strains, and Vaccination” which has now been published for peer review as a pre-print on Springer’s site at https://www.researchsquare.com/article/rs-195879/v1. I have now added vaccination and multiple variants I had already added to our previous model into the new grouped population model, and this blog post reports on progress with that new model.

Chart 17 model output for deaths, active cases and Seriously Sick to 800 days. 2nd virus variant from September 23rd, day 235. 3rd variant from January 1st 2021, Day 335. 250k vacs/day from January 1st (day 335) and 400k vacs/day from February 1st (day 366) and thereafter. 15% NPI reduction on March 7th, model Day 401.

NPIs, variants and vaccine models

This paper reports some parametric Coronavirus model runs I have made that compare, in particular, how the UK vaccine programme allows some NPI relaxation compared with a case with no vaccination. The outcome is that the vaccine programme in the UK has the potential to reduce the imposition of NPIs on March 7th by about 15%, without costing lives, this being the next time we in the UK are due for a major NPI review, potentially involving the return of schools at around March 7th.

Repeated elements of the 12-compartment model flowchart with repeated Incubation, Sick, Seriously Sick, and Better compartments, all infective, with transfer rates

The timing of multiple Coronavirus variants

Since my most recent posts on December 23rd and January 5th I have adjusted my model algorithms to model more than two variants, so that once better data is available on new variant characteristics, I can respond more quickly. The scenarios I have modelled show that presented with the threat of new variants, early proactive, preventative and decisive action in necessary as soon as a variant is identified. If a new variant is allowed to multiply and grow before appropriate Non Pharmaceutical Interventions are introduced (just as in the first days of the UK pandemic in March 2020, and with our UK March 23rd response) control of the virus is quickly lost.

Loading…

Something went wrong. Please refresh the page and/or try again.


Follow My Blog

Get new content delivered directly to your inbox.

%d bloggers like this: