New approximations, and policy implications, from a delayed dynamic model of a fast pandemic

Chandrika Prakash Vyasarayani; Anindya Chatterjee

In contrast, two solutions for β = 1 and τ = 1.2 are shown in figure 2 (b). Numerical solutions for two different initial functions show that the rapidly spreading phase of the disease and the saturation value of S are essentially identical, independent of the initial function. It is important to note that the relative time-shift between these two solutions is inconsequential. The underlying dynamical system is autonomous, and the use of asymptotic initial conditions at −∞ leaves a free parameter in the solution that allows time-translations (this will be explicitly clear in the analytical approximations later in the 6 . 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. (18) was P (t) = a 1 + t 1+τ , t ≤ 0. The two solutions in (b) are relatively time-shifted because the underlying system is autonomous, and one solution grows from smaller initial values; see main text for further discussion. (18) was