key: cord-0880264-p2eq0bp9
authors: Viswanath, N. C.
title: Analysis of the Second COVID-19 Wave in India Using a Birth-Death Model
date: 2021-05-19
journal: nan
DOI: 10.1101/2021.05.19.21257447
sha: 9ed75f705f847a77a095f16481345d009cf7ce88
doc_id: 880264
cord_uid: p2eq0bp9

India is witnessing the second wave of the COVID-19 disease from the first half of February 2021. The method in [5] is applied here to analyze the second wave in India. We start with fitting a birth-death model to the active and total cases data for the period from 13th to 28th February 2021. This initial dataset is expanded step by step by adding the two future weeks' data to it until 14th May 2021. This resulted in six models in total. The efficacy of each model is tested in terms of predictions made for the next two weeks. The infectivity rates are found to be ever-increasing in the case of the five initial models. The infectivity rate for the sixth model, which is based on the data from 13th February to 14th May 2021, shows a decreasing nature with an increase in time. This indicates a decline in the second wave, which may start from 4th June 2021 according to the fitted parameters.

According to Ranjan et al. [3] , a rise in the number of COVID-19 cases in India started from 13 th February 2021 which indicated the start of the second wave of the disease progression. Using a SIR model [2] , they predict a peaking of the same in mid-May 2021.

[4] applied a generalized birth-death model [1] for modeling the total and actively infected COVID-19 cases in several countries. This turned out to be a special case, of the standard SIR model [2] , in which the susceptible cases variable has no explicit role. [5] discussed application of the model in [4] when a rise in the number of cases occurs after a fall. Here we check the efficacy of the method in [5] in analyzing the second wave that occurred in India.

... (2) [5] discussed application of the above model when a rise in the number of cases occurs after a fall. Their idea was to fit equations (1) and (2) to a dataset after adjusting the total cases so that the total and active cases remain the same at the starting epoch. We follow the method in [5] for fitting equations (1) and (2) to the active and total cases data [7] . Fitting was done using the nlinfit function available in the MATLAB R2019b [6] software.

We consider 13 th February 2021 as a starting point. We fitted equations (1) and (2) using the method discussed in [5] for the data from 13 th to 28 th February 2021. Figure 1 shows the fit. Figure 2 is the comparison of the predictions by the fitted model with actual data for the next two weeks (from 1 st to 14 th

March 2021). Figure 2 shows that the accuracy of the prediction decreases as time increases.

Next, we expanded the prediction dataset by adding the actual data of the next two weeks to it. Figure 3 shows the fit for the data from 13 th February to 14 th March 2021. The parameters for this fit are: a = 0.0895802716; b = -0.0046661410; ‫ܫ‬ ሺ 0 ሻ = 128946; ߤ = 0.0782528444. Again the parameter b turns out to be negative. Prediction for the next two weeks, which is from 15 th to 28 th March 2021, is given in Figure   4 . It shows a decent prediction, whose accuracy begins to decrease as time increases.

We then considered the data from 13 th February to 31 st March 2021. Figure 5 shows the fit whose parameters are given by: a = 0.0784394479; b = -0.0135156063; According to [4] , a point of inflection on the curve (1) of actively infected cases where its decline starts is given by

The parameters for the final fit give ‫ݐ‬ ௦

as equal to 111.9, which indicates the decline of active cases may start from 4 th June 2021. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted May 19, 2021. ; https://doi.org/10.1101/2021.05.19.21257447 doi: medRxiv preprint

A Contribution to the mathematical theory of epidemics

Characterization of the Second Wave of COVID-19 in India

Analysis and Prediction of COVID-19 characteristics using a birth-and-death model

Prediction of COVID-19 Active and Total Cases After a Fall and Rise of Cases

Update 3)