Speed and strength of an epidemic intervention

Jonathan Dushoff; Sang Woo Park

Here, K(τ, t) is the infection kernel describing how infectious we expect an individual infected τ time units ago to be in the population. In general, K(τ, t) will depend on population characteristics that may change through time t -notably, the proportion of the population susceptible, S(t). Since we are interested in invasion and control, we will generally neglect changes in K(τ, t) through time. Thus, we will assume K(τ, t) ≡ K(τ ). Importantly, this (Park et al., 2019) . The infection kernel after applying each intervention strategyK(τ ) is shown in red. (A) The effect of a constant-strength intervention with θ = 1.5. A constant-strength intervention reduces the density by a constant proportion:K(τ ) = K(τ )/θ; when the strength of intervention matches the strength of epidemic (θ = R), the resulting distribution is equivalent to the intrinsic generation-interval distribution (K(τ ) = g(τ )). (B) A constant-speed intervention with φ ≈ 0.0267/day is applied to the same kernel. A constant-speed intervention reduces the density exponentially: K(τ ) = K(τ ) exp(−φτ ); when the speed of intervention matches the speed of epidemic (φ = r), the resulting distribution is equivalent to the initial backward generation-interval distribution (K(τ ) = b(τ )).