Why estimating population-based case fatality rates during epidemics may be misleading

Lucas Böttcher; Mingtao Xia; Tom Chou

We use the estimated basic reproductive number R 0 = β 1 S(0)/(µ 1 + c) ≈ 2.91 [17] to fix β 1 S(0) = (µ 1 + c)R 0 ≈ 0.158/day. We also first assume that the susceptible population does not change appreciably before quarantine and set S(t) = S(0). Thus, we only need to solve for I(τ, t) in Eqs. (9) and (10). We solve Eqs. (9) and (10) numerically (see the Methods section for further details) and use these numerical solutions to compute D 0,1 (t), R 0,1 (t), and N 0,1 (t) (see Fig. 3(a) and (b) ), which are then used in Eqs. (14) and CFR d (t − τ res ). To determine a realistic value of the time lag τ res , we use data on death/recovery periods of 36 tracked patients [16] and find that patients recover/die, on average, τ res = 16.5 days after first symptoms occurred. We show in Figs. 3(c) and (d) that M 1 p (t) approaches the individual mortality ratioM 1 (∞) ≈ 0.1 of section II A. This occurs because the model for P (τ, t) and I(τ, t) are equivalent and we assumed that the initial distribution of τ for both quantities are given by ρ(τ ; 8, 1.25). However, the population-level mortality ratios CFR d (t, τ res ) and M 0 p (t) also take into account recently infected individuals who may recover before symptoms. This difference yields different mortality ratios because newly infecteds are implicitly assumed to be detected immediately and all have τ 1 = 0. Thus, the underlying infection-time distribution is not the same as that used to computeM 1 p (t) (see SI for further details). The mortality ratios CFR d (t, τ res ) and M 0 p (t) should not be used to quantify the individual mortality probability of individuals who tested positive after their incubation period. During the course of an outbreak, the measures CFR d (t, τ res ) and M 0 p (t) are subject to another confounding influence. Since D(t), R(t), and N (t) do not . CC-BY-NC-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (7)). The death and recovery rates are defined in Eqs. (4) and (5). We use a constant infection rate β1S(0) = 0.158/day, which we estimated from the basic reproduction number of SARS-CoV-2 [17] . To model quarantine effects, we set β1 = 0 for t > 50. We show the mortality-ratio estimates M 0 p (t) and M 1 p (t) (see Eq. (14)) and CFR d (t, τres) (see Eqs. (8), (11) , (12) , and (14)).