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

Lucas Böttcher; Mingtao Xia; Tom Chou

To estimate the mortality ratio of the population conditioned simply on being infected, we have to estimate the larger number of recovereds that went untested. As shown in Fig. S4 , the untested recovered fraction can be estimated by assuming that the death rate for the untested infecteds is zero and by writing an SIR model without death for the untested pool of infecteds dS(t) dt = −S(t) ∞ 0 dτ β(τ , t)(I * (τ , t) + I u (τ , t)), ∂I * (τ, t) ∂t + ∂I * (τ, t) ∂τ = −(µ(τ, t) + c(τ, t))I * (τ, t), ∂I u (τ, t) ∂t + ∂I u (τ, t) ∂τ = −c(τ, t)I u (τ, t), dR(t) dt = ∞ 0 dτ c(τ, t)(I * (τ, t) + I u (τ, t)),