Selection for infectivity profiles in slow and fast epidemics, and the rise of SARS-CoV-2 variants
- Centre for Interdisciplinary Research in Biology (CIRB), Collège de France, CNRS INSERM, PSL Research University, France
- Mathematical Modelling of Infectious Diseases Unit, Institut Pasteur, Université de Paris, UMR2000, CNRS, France
- WHO Collaborating Centre for Infectious Disease Epidemiology and Control, School of Public Health, Li Ka Shing Faculty of Medicine, The University of Hong Kong Pokfulam, Hong Kong Special Administrative Region, China
- Laboratory of Data Discovery for Health, Hong Kong Science and Technology Park New Territories, Hong Kong Special Administrative Region, China
- Institute of Ecology and Environmental Sciences of Paris (iEES-Paris, UMR 7618) CNRS, Sorbonne Université, UPEC, IRD, INRAE, France
Figures
Figure 1
Variation of the selection coefficient as a function of transmission, for several infectivity profiles of emerging variants.
The Panels A and B show several variant infectivity profiles with the same effective reproduction number as historical strains (A) or an effective reproduction number increased by +10% (B). For …
Figure 2 with 1 supplement
Epidemiological and evolutionary trajectories of several types of emerging variants competing with historical strains.
The Panels A and B show epidemiological dynamics (daily cases number of historical strains in black, of variants in colours). Historical strains display several slightly different curves when …
Figure 2—figure supplement 1
The relationship between estimated growth rate of the variant and historical strains across time in the simulation study, in the scenario of progressive decline of from 1.5 to 0.5.
The three panels are three daily sample sizes to assess variant frequency (30,000, 10,000, 3000). This is shown for variants with no R advantage , and four infectivity profiles: shorter mean …
Figure 3 with 3 supplements
Inference of the R advantage and relative mean generation time in the simulation study.
The plots show the correlation between inferred and true quantities. The three colors show different sample sizes used to infer variant frequency: 1000 daily, 10,000 daily, and 1000 daily grouped by …
Figure 3—figure supplement 1
The daily basic reproduction number of the historical strains and variant ( and , identical thick lines), together with the effective reproduction number inferred from daily case and frequency data (thin lines), in the example simulation shown on Figure 2B for an emerging variant with +10% effective reproduction number and same distribution of generation time.
These realized effective reproduction number present a trend similar to the true basic reproduction number inputted to the simulation with three differences. First, the realized effective …
Figure 3—figure supplement 2
Inference of the R advantage and relative mean generation time in two additional simulation studies: (i) where the lag between symptom onset and case detection is longer (mean 6days instead of 2.2days) shown as points (“longer lag”), (ii) where the distribution of generation time is different from the assumptions of the model shown as open squares (“different gtd”).
In (ii), secondary infections are not possible in the first two days of infection, then the timing of infections follows a shifted gamma distribution. The plots show the correlation between inferred …
Figure 3—figure supplement 3
Inference of the R advantage and relative mean generation time (mgt) in the additional simulation study where the level of transmission is assumed to sharply decline from to .
Here, we varied the number of days for which number of cases and variant frequency data are available after the sharp decline from 10 (top panel) to 30days (bottom panel). The plots show the …
Figure 4
Data used for inference.
A and B: Dynamics of the Alpha variant frequency in England (A) and of the Delta variant frequency in England (B), estimated through SGTF. These frequencies are shown together with the dynamics of …
Figure 5 with 3 supplements
Inference of the infectivity profiles of the Alpha and Delta variants.
(A) Geometric intuition for how the relationship depends on the mean generation time for hypothetical variants with R advantage and relative mean generation time of and (as in Figures 1 …
Figure 5—figure supplement 1
The relationship between the selection coefficient and level of transmission RH(t) for the Alpha variant spreading in England.
Panel A shows the estimated selection coefficient with 90% confidence intervals (these intervals can be very wide so 90% instead of 95% was chosen for readability). Panel B shows the estimated RH(t) …
Figure 5—figure supplement 2
The effective reproduction number of historical strains RH(t) estimated on the English data, for the period when the Alpha variant emerged and replaced historical strains, then the period when the Delta variant emerged and replaced the Alpha variant and other strains.
The two periods are separated by the dashed vertical line. Black points show the maximum likelihood estimates, red shaded areas the 95% confidence interval.
Figure 5—figure supplement 3
Negative log-likelihood of the fully optimized model as a function of overdispersion in number of cases and in emerging variant frequency.
Overdispersion is represented by two factors: a factor reducing the number of cases, thus increasing the variance of the error in cases number compared to a Poisson, and a factor reducing the sample …
