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

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

x y z w as functions of time. These are basically the daily increments in the populations of various kinds. Recall that y is the number of sick people in free society while w is the number of positive cases, reported in official records. Hence y is a measure of the actual strength of the epidemic while w is a measure of the strength as interpreted from available data. The Figure is given below. is the author/funder, who has granted medRxiv a license to display the (which was not peer-reviewed) The copyright holder for this preprint .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 We can see that the peak in y (green) comes significantly before the peak in w (grey). The time interval between the two peaks is approximately 8 days, which corresponds to Ï„2 + Ï„3. To further bolster this conjecture, we increase Ï„2 to 4 (which makes an even more virulent epidemic with 20 percent of x remaining after 100 days) and reduce Ï„3 to 1. The plot is given below. This time, there is a 5-6 day separation between the two peaks, as we would expect. Other runs, not shown here, with different values of k0 and Ï„'s also bring out the truth of the conjecture that the peak in w occurs a time approximately Ï„2 + Ï„3 after the peak in y. Thus, the numerical values of the parameters are actually not too important so far as this prediction is concerned. Note that Ï„1, technically also a delay term, does not enter here. The lag between actual and reported results is entirely on account of the two delays which are novel to the Coronavirus. Going back to Figure 6 , we can see that when y has peaked, w is still strongly in the ascending region. This implies that, in the initial stages where the numbers of reported cases are increasing strongly, the disease is actually much closer to its peak and spreading much faster than the numbers would indicate. Hence, measures such as lockdowns and enforced social isolation, is the author/funder, who has granted medRxiv a license to display the (which was not peer-reviewed) The copyright holder for this preprint .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 which reduce the spread of the disease by reducing k0, need to be implemented as soon as there is a significant growth in the numbers being reported. Waiting for the disease to get "closer to peak" before implementing lockdowns can actually be a sub-optimal policy as that will enforce the curbs after the disease has already spread like wildfire. There is however a brighter side to this picture, which is that when w has peaked, y is well into the trailing region. Thus, the epidemic is closer to the end that we would otherwise imagine on the basis of a raw interpretation of the data. (As a parenthetical note, this disparity between the actual and reported case histories would have been impossible to obtain from a traditional S-I-R model, which validates our unconventional choice of basic variables.)