2.4. Time-independent ascertainment rate

Motivated by the possibility that variants of concern may have different pathological characteristics to each other or elicit different test-seeking responses, we estimate ascertainment rates for each variant class. Unlike the previous section these rates are constant for each variant in each region and age band. We let V={w,A,Δ,o1,o2} to denote the wild-type, Alpha, Delta, Omicron BA.1 and Omicron BA.2 variants, respectively, and ϕ=(ϕw,ϕA,ϕΔ,ϕo1,ϕo2) where ϕv denotes the time-independent rate for variant class v. Recalling that pv(t) is the proportion of infections caused by variants of class v, we use a revised estimate of M(t) that weights the contribution of each variant class by its proportion

We can then estimate by taking the value that minimizes the absolute error between M(t) and M~(t) taking only the time points T′ up to March 1st 2021 when SGTF positive tests were associated with the Delta variant. Specifically, the time-independent ascertainment rates are estimated by numerically solving