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

Chandrika Prakash Vyasarayani; Anindya Chatterjee

We suppose that normal living entails some specific β, and the public cannot indefinitely maintain high social distancing, i.e., significantly lower β. Yet it may be possible to lower β early in the outbreak, and then go back to the normal β later, when it is safe. The benefits are illustrated using simulations in figure 8 , where the chosen τ , γ and p correspond to a critical β = 1 (recall equation (66)). Now, suppose that normally β = 1.04. The disease will spread, and saturate at S(∞) ≈ 0.92, as per equation (48). Yet, for the same β = 1.04, a larger uninfected population of S * could be stable (equation (49)). That S * , in principle, could be reached using an artificially low β ≈ 1.02. If we change β from 1.04 to 1.02 early in the outbreak, and hold β = 1.02 until a steady state is reached, then finally returning to β = 1.04 could yield a stable solution. The outbreak would be arrested, and the total number of affected people would be cut almost in half. In figure 8 , β is switched from 1.04 to 1.02 at two different instants T c , for two different simulations, and then switched back to 1.04 later. In each such switched case, although finally β = 1.04, the steady value S(∞) corresponds to β = 1.02. In contrast, if β = 1.04 had been held throughout, almost twice as many people would have been infected. A further numerical study is presented in figure 9 . Here we vary both T c as well as T o , the time of switching back to β = 1.04. The parameters of figure 8 are used except for T c and T o . We see that the percentage of people affected can be cut almost in half for sufficiently low T c provided T o is large enough. If T o is made smaller, then there is a special value of T c when S(∞) is highest for the chosen T o , but the gains may be suboptimal.