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

Chandrika Prakash Vyasarayani; Anindya Chatterjee

The above policy implications seem simple and robust. We emphasize that the benefit is not merely in lowering the rate at which people get infected, but also in the total number of people infected by the end of the outbreak. The intuitive key to understanding this reduction caused by social distancing lies in stability under fresh, but small, infection. Here, stability implies that with a small infected population, the outbreak will not grow very much (recall figure 2(a) versus 2(b)). Under identical conditions, a larger infected population could cause the outbreak to grow: the assumption is that once the infected numbers are contained, a fresh large influx of infected people will be avoided. If β is lowered with social distancing, the outbreak saturates at a high S(∞), and the infected population goes to near-zero values. Subsequently, under the assumption of no subsequent large influx of infected people, β can be increased within the stability boundary, and the outbreak does not grow significantly further. In contrast, the benefits from reducing the time to quarantine, τ , require greater sustained institutional alertness but may be stronger.