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

Chandrika Prakash Vyasarayani; Anindya Chatterjee

We have first studied this model in some detail, seeking useful approximate solutions. For a weakly growing outbreak that affects a small proportion of the total population, and under a further simplification that neglects self-recovery and assumes perfect quarantining, the method of multiple scales yields an analytical expression for the complete progression of the outbreak, from infinitesimal initiation to final saturation. For moderate growth rates, a long wave approximation for the same parameters provides a nonlinear first order ODE for the same progression. With imperfect quarantining and nonzero self-recovery the long wave approximation for the full progression of the outbreak is given by a second order ODE. Finally, although the underlying DDE system is technically infinite dimensional, we have shown that a six-state Galerkin-based reduced order model for the system does an excellent job of capturing a wide range of solutions, i.e., the dynamics is effectively low-dimensional.