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

Chandrika Prakash Vyasarayani; Anindya Chatterjee

which is equivalent to equation (16) . This means the steady state P in this general case will be exactly correct, unlike the previous subcase of p = 1 and γ = 0. However, note that this unique limiting P is for the specific solution that starts asymptotically at zero, at t = −∞. Since we now have a second order differential equation in the long-wave approximation, trying to approximate what is purportedly a single solution, we have a minor dilemma in interpreting the two degrees of freedom available in initial conditions for equation (62). One of those corresponds to an arbitrary time-shift, as noted earlier. That leaves one other initial condition. Since our derivation has not identified what this initial condition should be, we expect that it should be inconsequential. This does turn out to be the case, as seen next. For small P and smallṖ , equation (62) can be linearized to givë