1/ I want to share a special moment with all who happen to be looking this way. This is the happiest I've been since April 27, when I posted on medRxiv a preprint with title "Individual variation in susceptibility or exposure to SARS-CoV-2 lowers the herd immunity threshold".
2/ In that preprint we study two mathematical models of the COVID-19 pandemic: one accounting for individual variation in susceptibility to infection; the other accounting for individual variation in exposure to infection (heterogeneous connectivity).
3/ We describe how both models tell us that herd immunity thresholds are expected to be lower when individual variation is higher. Many colleagues have posted very insightful comments on our work and here I want to highlight @joel_c_miller and @BallouxFrancois.
4/ They made a similar note on the heterogeneous connectivity model. Contact networks are not static and can be modified substantially by social distancing measures. This is very relevant if we want to project epidemic trajectories following relaxation of interventions.
5/ We have been studying this with models that extend those released in April and fitting data until now. I think we have just found the most elegant formulation for the problem and the results are looking beautiful. We'll write it up and share when suitable.
6/ For now I can only share my deepest hope, genuine happiness a most sincere Merry Christmas!

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More from @mgmgomes1

9 Dec
TWIMC: I've been Mathematician and Mother for ~30 years (now also Grandmother) and this is what matters. I spent the last 10 years studying individual variation on characteristics that are under selection but that have no heritability repercussions in the time scale under study.
In these studies I have "used" (please make a note of this word) primarily host-pathogen systems but my curiosity for completely different systems was particularly vivid last year and I was happily moving away from infectious diseases when the pandemic started.
Early in the Covid pandemic I started being approached by reporters who wanted to understand what was happening and what to expect over times to come. To respond to them I started studying the data and interpreting it in light of my models.
Read 11 tweets
4 Oct
1/ Reducing transmission is not the only way of preventing deaths. From health records we can predict who is at risk of severe or fatal disease (medrxiv.org/content/10.110…, PLoS Medicine in press) and offer them shielding.
2/ Shielding was less than optimal in the first wave, because (at least in Scotland) it was implemented too late. But we are better prepared now.
3/ The policy option of shielding the vulnerable for a short time while allowing the epidemic to run to completion among the young and fit should not be ruled out (medrxiv.org/content/10.110…).
Read 4 tweets
4 Oct
1/ Heterogeneous susceptibility and exposure to infection are under selection by the force of infection. Highly susceptible and highly connected individuals tend to be infected earlier and removed from the susceptible pool earlier.
2/ Mean susceptibility and mean connectivity in residual susceptible pool decrease over time lowering cumulative attack rate (CAR). Models that do not account for complete variation in those characteristics are biased towards overpredicting CAR and herd immunity threshold (HIT).
3/ Correcting models by accounting for observed factors is insufficient. To ensure that variation (observable and unobservable) is captured completely we build a distribution into the models and infer its variance by fitting to epidemic curves.
Read 4 tweets
29 Sep
1. The evidence favouring the heterogeneity model over the homogeneity model is overwhelming, whether we base this on fit penalized by complexity (DIC or similar criteria), forward predictive performance, or the Bayes factor.
2. We show that decreasing mean IFR to 0.3%, consistent with recent estimate for England, does not change fit of the model or inference that slowing and reversal of epidemic was largely attributable to build-up of herd immunity but gives a more plausible value of 15% for the HIT.
3. If you believe that the IFR during this period was 1.1%, and you don't believe the estimate of 4% for the HIT that is obtained by specifying this IFR value, you have to diagnose something else that is wrong with the model;
Read 4 tweets
28 Sep
Latest on individual variation in susceptibility or exposure to #SARSCoV2 and #COVID19 with Marco Colombo, Joe Mellor, Helen Colhoun and Paul McKeigue:
Trajectory of COVID-19 epidemic in Europe medrxiv.org/content/10.110…
We show that relaxing the assumption of homogeneity in the modelling code released by Flaxman et al (Nature) to allow for individual variation in susceptibility or connectivity gives a model that has better fit to the data and more accurate 14-day forward prediction of mortality.
Allowing for heterogeneity in 11 European countries reduces estimate of "counterfactual" deaths that would have occurred if there had been no interventions from 3.2 million to 262,000, explaining most of the slowing and reversal of COVID-19 mortality by build-up of herd immunity.
Read 5 tweets
19 Sep
@PieterTrapman @mlipsitch 1/ Unclear what you mean by these numbers, but a week later I finally had a couple of hours on a Saturday to have a look. Running the models in our July preprint I am now comparing the 70% lower-risk group with the whole population. Here is what I find (explanations follow).
@PieterTrapman @mlipsitch 2/ I run each of the 3 models until the pandemic is over (one year is sufficient for these models). Then I calculate the proportion of the 70% lower-risk group that has been infected and divide by the portion of the entire population that has been infected.
@PieterTrapman @mlipsitch 3/ This metric varies wildly across models even though all assumed a gamma distribution with mean=1 and coefficient of variation estimated by fitting to first wave of confirmed cases in specific countries. I calculate HIT for each case and find this to be conserved across models.
Read 9 tweets

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