Transmission Dynamics of COVID-19 and Impact on Public Health Policy

B Shayak; Mohit Manoj Sharma; Richard H Rand; Awadhesh Kumar Singh; Anoop Misra

Recall that in our model the free evolution of the disease starts after 15 days, and that in the base case (no lockdown) the peak of y occurs at 45 days, the peak of w occurs at 53 days, and the fraction of x remaining at 100 days is 31 percent. For the first run, we implement a very early lockdown from t = 20 to t = 35. is the author/funder, who has granted medRxiv a license to display the (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.03. 29.20047035 doi: medRxiv preprint This is an ineffective move -the disease remains quiescent during the lockdown but explodes after the restrictions are lifted. A similar phenomenon also happens for a range of early lockdowns, thus nullifying their effect completely. This runs contrary to the perception that locking down at the earliest signs of spread is the strategy to adopt -it is good if the lockdown can be indefinite but inutile when there are external constraints on its duration. Similarly, a lockdown at too late a stage (after the disease has peaked) is also useless, for obvious reasons. We find that the optimal time of imposing the lockdown is such that the centre of the lockdown period corresponds to the peak in y in the absence of the lockdown. For the next run, we impose lockdown from t = 37 to t = 52, straddling the y-peak at t = 44. The results are presented below. This well-timed lockdown cripples the flow of the disease before it approaches its peak. Moreover, the disease does not restart its virulent spread after the curbs are eased. The remaining fraction of x at the end of the 100-day period turns out to be 53 percent. Instead, if we impose the 15-day lockdown with its centre coinciding with the (no lockdown) peak in w, i.e. from t = 45 to t = 60, then too the flow of the disease is choked but the remaining fraction of x reduces to 45 percent, which is a nearly 1/5 drop from the previous case. In the next plot, we vary the starting point of the 15-day lockdown from the 20 th day to the 55 th day and plot the remaining percentage of x at the end of the 100-day period. We can see a clear maximum in is the author/funder, who has granted medRxiv a license to display the (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.03. 29.20047035 doi: medRxiv preprint this percentage when the lockdown is timed to straddle and hence stamp out the peak in y; the percentage decreases rapidly on both sides of the maximum. Another feature of the bottom panel of Fig. 10 is extremely important. We see from the grey curve that the rate of detected cases dw/dt keeps increasing even after the lockdown has been imposed. Indeed, in a qualitative sense, w in the presence of the lockdown proceeds smoothly to a peak and then tails off, just as it would have in the absence of the lockdown (there is a spike at the instant the lockdown is lifted but that is probably a numerical artefact and unlikely to manifest in practice). This might mislead one to believe that the lockdown has been ineffective. However, the actual decrease, and a very significant one at that, has taken place in a quantity (y) which cannot be measured directly. The height of the peak in w with the lockdown in place (about 0.007) has also reduced drastically relative to that without the lockdown (Fig. 7 , height about 0.019) -once again, a comparison with an unmeasurable quantity. Thus we see that the lockdown serves its purpose even if this is no