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

Chandrika Prakash Vyasarayani; Anindya Chatterjee

If social distancing is practiced, then we expect m to decrease and thus β to be lower, even thoughβ may remain the same. For this reason, in the later portions of this paper, we will consider time-varying β while holding other parameters constant. For a fast-spreading pandemic, we assume α = 0 for simplicity, which makes R a slave as well, and we need to only retain the equations for S and I. Finally, by choice of units of time, we can let σ = 1. This is equivalent to nondimensionalizing τ which has units of time, as well as γ and β which have units of 1/time. Our equations now arė Infected individuals E(t) remain asymptomatic and non-infectious for a time duration σ. Subsequently, these individuals become infectious and enter population I(t), but remain asymptomatic for a time duration τ . Upon showing symptoms, they enter population Q(t) and are quarantined with probability p for a time κ, beyond which they infect nobody. Some infectious asymptomatic individuals may become non-infectious on their own, with rate γ. After quarantine, the cured population R(t) could in principle lose immunity at a small rate α, but we take α = 0 for a fast-spreading pandemic.