COVID-19 disease spread modeling by QSIR method: The parameter optimal control approach.

BACKGROUND: At present, India is in the decreasing phase of the second wave of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). But India as a country is in the second position in a high number of confirmed cases (33,678,786) in the world (after the United States of America) and third position in the number of COVID-19 deaths (after the United States and Brazil) at 465,082 deaths. Almost above numbers are dominantly seen in the second wave only. Thus, future long-term projections are required to mitigate the impact.
METHODS: The conventional SIR model was modified so that a new compartment Q(quarantine) is added to the conventional SIR model to analyze the COVID-19 impact. The parameter optimal control technique was used to fit the curve by estimating the infection, susceptible, etc.
RESULTS: The model predicts the cumulative number of cases of 2.6928E7 with a confidence interval of 95%, CI[2.6921E7,2.6935E7], and an accuracy of 99.3% on May 25, 2020(480th day from 30 to 01-2020). The estimated R0 is 1.1475. The model's mean absolute error(E MAE ) is 1.79E4, and the root-mean-square error is (E RMSE ) is 3.19E4. The future projection are,3.48E7(Lockdown), 3.80E7(periodic-lockdown), 4.52E7(without lockdown). The whole model accuracy is 99%, and projection accuracy is about 94% up to 01-Nov-2021, The goodness of fit value 0.8954.
CONCLUSION: The model is over-estimating corona cases initially and then showed a decreased trend. As the number of days increases, the model accuracy decreases; thus, more control points of the cost function are required to fit the model best.

Introduction

The Novel Coronavirus first emerged on January 27, 2020, in Kerala, India. The COVID-19 evolved gradually and appeared to 171 cases by March 18, 2020. So from March 24, 2020, the country-wide lockdown was implemented. The lockdown that was imposed throughout the country was lifted in stages starting from June 8, 2020, in the name of Unlock 1.0 and then progressed up to Unlock 6.0. The per-day new cases are less in number up to the month of June. Later on the virus showed exponential growth in India and reached approximately 97000/per day new cases in mid-September. Because of mitigation strategies such as restricting the transport, stopping mass gatherings, creating awareness on Covid-19 spread by government and new normal such as face mask and social distancing and sanitizer use decreased and the number of new cases decreased and in control. Still, India imposed face masks mandatory. We can't conclude that the Covid-19 spread was in favor of wearing masks. According to WHO wearing a face mask alone is not sufficient. Though India followed all kinds of restrictions, because of the lifting of the lockdown, India saw the worst spread of the virus than it did in the first wave from February 2021. The second wave was started in Maharashtra, India, from the month of march and progressed up to May 2021 due to several socio-economic and administrative reasons. The second wave dynamics have a massive impact on human health and the economy of the country. In the second wave, new cases reached up to 4 lakhs. To mitigate the effects of the COVID-19 s wave, the government took a lot of preventive measures such as quarantine,, social distancing, vaccination drive along with treatments such as plasma therapy. As a part of controlling the spread of the virus, vaccines such as Covishield, Covaxin are introduced. With a great effort, the vaccination drive achieved a total number of Figure 100 crore. Along with mitigation strategies, the industrial revolution 5.0 created a huge impact on the health care industry by introducing new technologies such as Covi-19 tracking, digital monitoring, optimizing the supply chain, performing an automatic treatment, etc. The revolutions like IoT, , which is very useful in transferring data without any human interface, create a better treatment rapidly. Medical 4.0, IoMT , also ease the monitoring of Covid-19 patients by making the bridge between the medical health monitoring things to the network through Artificial intelligence, Machine learning, Big data network, and cloud storage, etc., and reduce the re-admission into hospital post-Covid.

All these efforts were succeeded in reducing the spread of coronavirus in the second wave. Thus, we are on the verge of ending the second wave and also probably the end of the pandemic. Still, we never know how pandemics may turn endemic. Since the nature of the virus and its mutations are changing rapidly over time, resulting in various strains which are totally different from early-stage dynamics. , Significant strains like U.S strain L452R and indigenous strain E484Q are dominantly seen in states like Maharashtra, Karnataka in India. The mutated strains like E484Q and L452R had high transmission rates. So there is a need to construct new models to tackle the further waves due to unexpected mutations of the virus. Many attempts have been made on epidemiology models to predict active cases, including simple SIR and logistic growth models and complex models like MSIR and SEIR models. The accuracy of these models may differ based on their assumptions and parameters. However, all these attempts are made in the early stage of the spread of COVID- 19. In this paper, the main focus is given to the second wave, and an attempt was made to predict the probable time to end the pandemic. Previous research , like SIS, SEIR, exponential growth, logistic growth models did not take into account the quarantine, lockdown, and social distancing strategies , and re-infections, vaccination effects to control the pandemic. Thus, by considering all the above assumptions, the nature of the second wave and future projection of cases was done. The approximate end of the pandemic was also predicted.

Methodology

In this analysis, a new compartment is added to the SIR model. Q is the newly added compartment named, here Quarantine means only people who are not affected by corona, and the following self-isolation because of lockdown guidelines. Persons with already Covid-19 positive are not considered in chamber Q. Where S to Q won't exchange when there is a lockdown or self-isolation, those people will not be affected by COVID-19 for a brief period. At the same time, some people will go from quarantine compartment to susceptible because of the end of lockdown or violation of lockdown. Thus, here two rates are defined such that the people exchange between Q and S. The below Fig. 1 shows the flow between two compartments (see Fig. 2).

Fig. 1

Exchange of flow between compartments Q(Quarantine) and S(Susceptible) without lockdown and lockdown cases.

Fig. 2

Generalized flow chart of QSIR compartment model.

Where α is the susceptible rate, and δ is the quarantine rate.

Assumptions

Birth and death rates are neglected. Simulations are taken from 1st corona case. i.e., January 27, 2020.

The fraction of people always goes from Q to S with a rate α in both with and without lockdown cases. But in lockdown, the fraction of people will go from S to Q with a rate δ.

The first lockdown was implemented for 100 days, from 170th to 270th day. i.e., up to unlock 6.o till November 30.

The vaccination rate is considered from real-time data.

The second lockdown is taken from the 460th day to the 480th day.

The future projection was made with three cases. The first one is the Total lockdown and second one is periodic lockdown of 15 days will be implemented for every one month. The last one is no further lockdown will be implemented at all, and it is assumed that only curfew will be implemented(In curfew, δ C is lesser than δ).

Re-infections are considered with a period of 120 days.

Mathematical equations

Initially, all the parameters are divided with the population size P0. The rates δ and γ are chosen from the trial and error method, and β and α are estimated by parameter optimal control approach.

Parameter optimal control

Here the parameter to optimize is the cumulative number of cases, and control vectors are β and α. The cost function is defined asWhere θ is the cumulative number of corona cases up to certain period from the start of simulation.

θ0 is the observed cumulative number of cases taken from real-time data.

Steps to parameter optimal control

In the first step, choose β and α as an initial guess.

Run the differential equation to a required time

Calculate the cost function F

Run the simulation again by taking β = β ​+ ​dβ and α = α ​+ ​dα

Calculate cost function again F then calculate the gradient similarly

Then the required β.and α is β = β-C 1  × (dF) and α = α-C 2  × (dF) where C1 and C2 are constants.

Repeat the procedure until the best fit of the curve is achieved.

For the detailed method of optimal control, please refer., The estimated β and α are 0.4590 and 0.0106.

The below figure shows the values of model parameters in different conditions.

Reproduction number

The basic reproduction number is the same as the SIR model since the infection compartment was not had any intervention of the quarantine compartment. Here basic reproduction number tell us that how many people are infected by every single individual infected person. The above formula was calculated from the next-generation matrix method. , , The estimated R0 for this method is 1.147.

Error estimation and goodness of fit

The error is estimated from two formulas.

Mean absolute error (E): it the average error by only considering maginited and leaving direction and Root mean square error: It is the average of squared error and particularly useful when we have large errors between observed and predicted

Here accuracy of the whole model is defined as (E)and accuracy at a particular day is simply. .

Goodness of fit from Normalized mean square error:Here the p(i) is the per day active number of cases of the model, and o(i) is observed per day active cases. is the mean of observed.

It is the measure of fit from observed value, which is most useful in predicting the future.

Results

Accuracy of model

The real time data of Covid-19 cases from 30-Jan-2020 to 25-May-2021 was taken to model the spread of Covid-19. Table 1 shows the α, β, γ, δ values in different conditions stated in the assumption section.

Table 1

Values of Quarantine, susceptible, infected and recovered rates at different conditions.

Name	1–170	170–270	270–380	380–460	460–480	480-end(Lockdown)	480-end(Periodic Lockdown)	480-end(No Lockdown)
α	0.102	0.102	0.102	0.102	0.102	0.102	0.102	0.102
β	0.4595	0.4595	0.4595	0.4595	0.4595	0.4595	0.4595	0.4595
γ	0.4	0.4	0.4	0.4	0.4	0.4	0.4	0.4
δ	0	0.004	0.0001	0.004	0.0001	0.004	0.0006(cerfew) −0.004(lockdown)	0.0001

The vaccination rate is considered from real-time data, which is shown in the below Fig. 3 .

Fig. 3

Plot of vaccination rate calculated from Real-time data.

The predicted cumulative number of cases as of date May 25, 2021, was 2.6928E7 with CI[2.6921e7,2.6935e7], and observed cases from real-time data was 2.6752E7; the model accuracy is 99.3%. From the below Fig. 4 , the model predicts that the maximum per day active cases in the first wave was 103688 on the 7-Sept-2020 (224th day from 30-Jan-2020). The observed cases are 97950 on the 14-Sept-2020 (231th day from 30-Jan-2020), and there is an offset of 7 days with an accuracy of 94.36%. The maximum per day active cases in the second wave was 3.8385E5 on the 18-May-2021 (473rd day from 30-Jan-2020). The observed cases are 4.1418E5 on the 7-May-2021 (463rd day from 30-Jan-2020), and there is an offset of 10 days with an accuracy of 92.7%.

Fig. 4

Figure showing Actual vs. Modeled Per day cases from Jan-2020 to May-2021.

From the above Fig. 5 , the cumulative cases of actual and model are 3.44E7,3.48E7, CI[3.47E7,3.49E7] with an error percentage of 1%.

Fig. 5

Cumulative corona cases plot from Jan-2020 to Nov-2021.

The mean absolute error of model E is 1.79E4, and root-mean-square error E is 3.19Ee4. The goodness of fit value is 0.8954.

Future projection

The below Fig. 6 shows the prediction of the future with three cases. The predicted number of days required to end the pandemic with continued lockdown is about 600 days(Oct-2021), and the cumulative number of cases at the end of the pandemic is 3.4890E7. And if the periodic lockdown of 15 days for every one month is implemented, then the pandemic will end after approximately 720 days(Jan-2022), cumulative cases at the end of the pandemic is 3.80E7 and if a complete nationwide lockdown is not imposed, then there will be a whopping increase in the number of cases and the rate of spread of the virus. The pandemic will be continued up to approximately 825 days(May-2022), and cumulative cases will be 4.5E7.

Fig. 6

Future projection of per day new cases till the end of the pandemic.

The detailed data was given in Table 2 at the appendix.

Discussion and conclusion

From the model data, the per day active cases are overestimated with change of 6% in first wave, and then in the second wave, the model underestimated about a change of 8%. As the number of days increasing, the accuracy is decreasing with underestimating trend. This trend suggests that only one optimal control point of cost function is not sufficient to predict the cases accurately. It indicates that more cost function points are required to estimate the cases accurately. From projection, the end of the pandemic, even in the worst-case scenario is on May 2022. From the figure, the model shows that there is a drastic decrease in cases after Aug-2021. The main reason for this is an increase in the vaccination rate.

Though the model predicts the active cases with utmost accuracy, the future projection may not be justified because the spread of the virus depends on several factors, such as different pathogenic mutations of the virus, which is highly random and unpredictable and effectiveness of vaccination and preventive measures. Even for the people vaccinated, the mutations affected them drastically. The only way to control the spread is self-quarantine and isolation. Since the lifting of lockdown clearly shows an increment in cumulative active cases, one needs to take care and follow the preventive measures, and the rate at which vaccines are being jabbed must increase. This analysis was done on the whole country, but in a real case scenario, the state-to-state dynamics change spatially and temporally, so adding compartments that account for the spatial progress of COVID-19 adds much more benefits to the future projection.

Limitations of model

The sensitivity of the model highly depends on the values of α, β, γ, δ even in a small increment leads to change on prediction of the model.

Even vaccination rate is taken from real-time data, and the Covid-19 needs multiple shots. Thus, there is a lag inherently in the model.

Re-infection is taken with a constant duration, but Re-infection dynamics will significantly vary in Spatio-temporal pattern. This is a major cause for the varying number of waves and active cases in different countries.

The initial guesses will affect the number of iterations to optimize, so care has to be taken in choosing the initial guesses.

The values of γ, δ are estimated from the trial and error, which is a difficult task when we are modeling for multiple countries. The values will vary with a significant change in order.

Research support

This research received no external financial or non-financial support.

Relationship

There is no additional relationship to disclose.

Patents and intellectual property

There are no patents to disclose.

Other activities

There are no other activities to disclose Data Statement The data required to reproduce the above findings are available to download from https://github.com/CSSEGISandData/COVID-19 https://ourworldindata.org/coronavirus/country/india.

Declaration of competing interest

The authors declare that they have no conflict of interest.

Date	Actual	Predicted-with lockdown	CI95_Lower bound	CI95_Upper bound	Predicted-without lockdown	CI95_Lower bound 2	CI95_Upper bound 3	Predicted-periodic lockdown	CI95_Lower bound 4	CI95_Upper bound 5
‘26-May-2021′	26948874	26743500.5	26650206.3	26836794.7	26743500.5	26421336.9	27065664.1	26743500.5	26650206.3	26836795
‘27-May-2021′	27157795	27095131.3	27001837.1	27188425.5	27095131.3	26772967.7	27417294.9	27095131.3	27001837.1	27188425
‘28-May-2021′	27369093	27440107.7	27346813.5	27533401.9	27440107.7	27117944.1	27762271.3	27440107.7	27346813.5	27533402
‘29-May-2021′	27555457	27777952.8	27684658.6	27871247.1	27777952.8	27455789.2	28100116.4	27777952.8	27684658.6	27871247
‘30-May-2021′	27729247	28108220.9	28014926.7	28201515.1	28108220.9	27786057.3	28430384.5	28108220.9	28014926.7	28201515
‘31-May-2021′	27894800	28430517.7	28337223.5	28523811.9	28431191.1	28109027.5	28753354.7	28430891.8	28337597.6	28524186
‘01-Jun-2021′	28047534	28744498.6	28651204.3	28837792.8	28747134.8	28424971.2	29069298.4	28745961.6	28652667.3	28839256
‘02-Jun-2021′	28175044	29049839.7	28956545.5	29143133.9	29056287.6	28734124	29378451.2	29053413.4	28960119.1	29146708
‘03-Jun-2021′	28307832	29346287.4	29252993.2	29439581.6	29358899.4	29036735.8	29681063	29353266.3	29259972.1	29446561
‘04-Jun-2021′	28441986	29633625.9	29540331.7	29726920.1	29655203.4	29333039.9	29977367	29645544	29552249.8	29738838
‘05-Jun-2021′	28574350	29911673	29818378.8	30004967.3	29945413.5	29623249.9	30267577	29930270.1	29836975.9	30023564
‘06-Jun-2021′	28694879	30180292.2	30086998	30273586.4	30229737.2	29907573.6	30551900.8	30207481.6	30114187.4	30300776
‘07-Jun-2021′	28809339	30439390	30346095.7	30532684.2	30508376.3	30186212.7	30830539.9	30477226.9	30383932.7	30570521
‘08-Jun-2021′	28909975	30688898.9	30595604.7	30782193.1	30781510	30459346.4	31103673.6	30739549.8	30646255.5	30832844
‘09-Jun-2021′	28996473	30928808.8	30835514.5	31022103	31049330.6	30727167.1	31371494.2	30994522.8	30901228.5	31087817
‘10-Jun-2021′	29089069	31159143.4	31065849.2	31252437.6	31312022.6	30989859.1	31634186.2	31242225.4	31148931.2	31335520
‘11-Jun-2021′	29182532	31379954.5	31286660.2	31473248.7	31569757.7	31247594.1	31891921.3	31482739.2	31389445	31576033
‘12-Jun-2021′	29274823	31591316.5	31498022.3	31684610.7	31822691.8	31500528.2	32144855.4	31716143.9	31622849.7	31809438
‘13-Jun-2021′	29359155	31793334	31700039.8	31886628.2	32070975.6	31748812.1	32393139.2	31942527	31849232.8	32035821
‘14-Jun-2021′	29439989	31986137.8	31892843.6	32079432	32314753.8	31992590.2	32636917.3	32161982.1	32068687.9	32255276
‘15-Jun-2021′	29510410	32169882.6	32076588.4	32263176.8	32554164.3	32232000.7	32876327.9	32374607.7	32281313.4	32467902
‘16-Jun-2021′	29570881	32344750.2	32251456	32438044.4	32789347.1	32467183.5	33111510.6	32580513.9	32487219.7	32673808
‘17-Jun-2021′	29633105	32510936.9	32417642.6	32604231.1	33020430.2	32698266.6	33342593.8	32779810	32686515.7	32873104
‘18-Jun-2021′	29700313	32668655.5	32575361.2	32761949.7	33247536.5	32925372.9	33569700	32972608.9	32879314.7	33065903
‘19-Jun-2021′	29762793	32818136.5	32724842.2	32911430.7	33470787.6	33148624	33792951.2	33159030.8	33065736.6	33252325
‘20-Jun-2021′	29823546	32959622.4	32866328.2	33052916.6	33690300.3	33368136.8	34012463.9	33339198.9	33245904.7	33432493
‘21-Jun-2021′	29881772	33093360.5	33000066.3	33186654.8	33906178.5	33584014.9	34228342.1	33513232.1	33419937.9	33606526
‘22-Jun-2021′	29935221	33219613.5	33126319.3	33312907.7	34118531.8	33796368.3	34440695.4	33681260.4	33587966.2	33774555
‘23-Jun-2021′	29977861	33338648.5	33245354.3	33431942.7	34327463.5	34005299.9	34649627.1	33843413.9	33750119.7	33936708
‘24-Jun-2021′	30028709	33450741.3	33357447.1	33544035.5	34533079.5	34210915.9	34855243.1	33999829.7	33906535.5	34093124
‘25-Jun-2021′	30082778	33556150.5	33462856.3	33649444.7	34735446.2	34413282.6	35057609.8	34150618.5	34057324.3	34243913
‘26-Jun-2021′	30134445	33655145.8	33561851.6	33748440	34934640.8	34612477.2	35256804.4	34296063.6	34202769.4	34389358
‘27-Jun-2021′	30183143	33748010.7	33654716.5	33841304.9	35130762.6	34808599	35452926.1	34436449.2	34343155	34529743
‘28-Jun-2021′	30233183	33835013.3	33741719.1	33928307.5	35323879.8	35001716.2	35646043.3	34572022.6	34478728.4	34665317
‘29-Jun-2021′	30279331	33916422.9	33823128.7	34009717.1	35514063.2	35191899.6	35836226.7	34703019.8	34609725.6	34796314
‘30-Jun-2021′	30316897	33992494.8	33899200.5	34085789	35701354.3	35379190.8	36023517.9	34829644.8	34736350.5	34922939
‘01-Jul-2021′	30362848	34063499.8	33970205.5	34156794	35885835.5	35563671.9	36207999.1	34952118.5	34858824.3	35045413
‘02-Jul-2021′	30411634	34129691.2	34036397	34222985.5	36067556.2	35745392.6	36389719.8	35070629.2	34977335	35163923
‘03-Jul-2021′	30458251	34191308	34098013.7	34284602.2	36246536.4	35924372.8	36568700	35185336.5	35092042.3	35278631
‘04-Jul-2021′	30502362	34248603	34155308.8	34341897.2	36422846	36100682.4	36745009.6	35296424	35203129.8	35389718
‘05-Jul-2021′	30545433	34301807.4	34208513.2	34395101.6	36596508.6	36274345	36918672.2	35404037.4	35310743.2	35497332
‘06-Jul-2021′	30585229	34351168.1	34257873.9	34444462.3	36767615.9	36445452.3	37089779.5	35508357.4	35415063.1	35601652
‘07-Jul-2021′	30619932	34396880.9	34303586.6	34490175.1	36936114.3	36613950.8	37258277.9	35609467.4	35516173.2	35702762
‘08-Jul-2021′	30663665	34439168.3	34345874	34532462.5	37102057.1	36779893.5	37424220.7	35707511.1	35614216.8	35800805
‘09-Jul-2021′	30709557	34478230.8	34384936.5	34571525	37265443.3	36943279.7	37587606.9	35802593.2	35709299	35895887
‘10-Jul-2021′	30752950	34514273.6	34420979.4	34607567.8	37426316.8	37104153.3	37748480.4	35894737.7	35801443.5	35988032
‘11-Jul-2021′	30795716	34547489.3	34454195.1	34640783.6	37584703.3	37262539.7	37906866.9	35983962.8	35890668.6	36077257
‘12-Jul-2021′	30837222	34578039.5	34484745.3	34671333.8	37740518.3	37418354.7	38062681.9	36070229.6	35976935.4	36163524
‘13-Jul-2021′	30874376	34606116.2	34512822	34699410.4	37893849.6	37571686	38216013.2	36153602.4	36060308.2	36246897
‘14-Jul-2021′	30907282	34631902.8	34538608.6	34725197	38044798.8	37722635.2	38366962.4	36234155.5	36140861.2	36327450
‘15-Jul-2021′	30946147	34655566	34562271.8	34748860.2	38193433.4	37871269.8	38515597	36311946.6	36218652.4	36405241
‘16-Jul-2021′	30987880	34677252.1	34583957.9	34770546.4	38339753.7	38017590.2	38661917.3	36387000.8	36293706.5	36480295
‘17-Jul-2021′	31026829	34697103.8	34603809.6	34790398	38483783.2	38161619.6	38805946.7	36459358.7	36366064.5	36552653
‘18-Jul-2021′	31064908	34715254.9	34621960.7	34808549.2	38625538.7	38303375.1	38947702.3	36529061.4	36435767.2	36622356
‘19-Jul-2021′	31106065	34731832.7	34638538.5	34825126.9	38765041.8	38442878.2	39087205.4	36596155.1	36502860.8	36689449
‘20-Jul-2021′	31144229	34746954.8	34653660.5	34840249	38902297.2	38580133.6	39224460.8	36660680.4	36567386.2	36753975
‘21-Jul-2021′	31174322	34760730.8	34667436.5	34854025	39037298.1	38715134.5	39359461.7	36722675.8	36629381.6	36815970
‘22-Jul-2021′	31216337	34773273.1	34679978.9	34866567.3	39170127	38847963.5	39492290.6	36782223.8	36688929.6	36875518
‘23-Jul-2021′	31257720	34784684.6	34691390.4	34877978.9	39300852.5	38978689	39623016.1	36839400.3	36746106	36932694
‘24-Jul-2021′	31293062	34795056.9	34701762.7	34888351.2	39429499.7	39107336.1	39751663.3	36894262.3	36800968	36987556
‘25-Jul-2021′	31293062	34804476.5	34711182.3	34897770.7	39556108	39233944.4	39878271.5	36946874.1	36853579.9	37040168
‘26-Jul-2021′	31371901	34813020.1	34719725.8	34906314.3	39680669.1	39358505.5	40002832.7	36997281	36903986.8	37090575
‘27-Jul-2021′	31411262	34820760.4	34727466.1	34914054.6	39803189	39481025.4	40125352.6	37045535.7	36952241.5	37138830
‘28-Jul-2021′	31440951	34827764.7	34734470.5	34921058.9	39923668.6	39601505	40245832.1	37091690.2	36998396	37184984
‘29-Jul-2021′	31484605	34834098.2	34740804	34927392.4	40042151.1	39719987.5	40364314.7	37135814.2	37042519.9	37229108
‘30-Jul-2021′	31528114	34839817.6	34746523.4	34933111.8	40158620.6	39836457.1	40480784.2	37177954.5	37084660.3	37271249
‘31-Jul-2021′	31572344	34844976.9	34751682.6	34938271.1	40273084.5	39950920.9	40595248	37218168.1	37124873.9	37311462
‘01-Aug-2021′	31613993	34849626.2	34756332	34942920.4	40385559.6	40063396	40707723.2	37256515.7	37163221.5	37349810
‘02-Aug-2021′	31655824	34853811.5	34760517.3	34947105.8	40496052.3	40173888.7	40818215.9	37293054.2	37199759.9	37386348
‘03-Aug-2021′	31695958	34857575	34764280.8	34950869.2	40604568	40282404.4	40926731.6	37327840.4	37234546.2	37421135
‘04-Aug-2021′	31726507	34860957.9	34767663.6	34954252.1	40711179.3	40389015.8	41033342.9	37360952.7	37267658.5	37454247
‘05-Aug-2021′	31769132	34863997.3	34770703.1	34957291.5	40815953.8	40493790.2	41138117.3	37392465.8	37299171.6	37485760
‘06-Aug-2021′	31812114	34866727	34773432.8	34960021.2	40918953.4	40596789.9	41241117	37422450.3	37329156.1	37515745
‘07-Aug-2021′	31856757	34869177.7	34775883.5	34962472	41020245.9	40698082.3	41342409.5	37451007.4	37357713.2	37544302
‘08-Aug-2021′	31895385	34871376.3	34778082.1	34964670.5	41119858.3	40797694.7	41442021.9	37478219.7	37384925.4	37571514
‘09-Aug-2021′	31934455	34873346.9	34780052.7	34966641.1	41217801.6	40895638	41539965.2	37504159.9	37410865.7	37597454
‘10-Aug-2021′	31969954	34875111.8	34781817.6	34968406	41314098.8	40991935.2	41636262.4	37528899.8	37435605.5	37622194
‘11-Aug-2021′	31998158	34876691.1	34783396.9	34969985.3	41408766	41086602.4	41730929.5	37552504.3	37459210.1	37645799
‘12-Aug-2021′	32036511	34878103.6	34784809.4	34971397.8	41501846.5	41179682.9	41824010.1	37575041.5	37481747.3	37668336
‘13-Aug-2021′	32077706	34879365.9	34786071.7	34972660.2	41593353.2	41271189.6	41915516.8	37596567.6	37503273.4	37689862
‘14-Aug-2021′	32117826	34880493.3	34787199.1	34973787.5	41683314.7	41361151.1	42005478.2	37617139	37523844.7	37710433
‘15-Aug-2021′	32156493	34881499.3	34788205.1	34974793.6	41771752.3	41449588.7	42093915.9	37636807	37543512.8	37730101
‘16-Aug-2021′	32192576	34882397	34789102.8	34975691.2	41858724.2	41536560.6	42180887.8	37655628.1	37562333.8	37748922
‘17-Aug-2021′	32225513	34883197.7	34789903.5	34976491.9	41944289.8	41622126.2	42266453.4	37673655.2	37580361	37766949
‘18-Aug-2021′	32250679	34883911.4	34790617.2	34977205.6	42028454.1	41706290.5	42350617.7	37690926.8	37597632.6	37784221
‘19-Aug-2021′	32285857	34884547.4	34791253.1	34977841.6	42111276.9	41789113.3	42433440.4	37707490.2	37614195.9	37800784
‘20-Aug-2021′	32322258	34885114	34791819.8	34978408.2	42192805.3	41870641.7	42514968.9	37723387.2	37630093	37816681
‘21-Aug-2021′	32358829	34885618.6	34792324.3	34978912.8	42273070.7	41950907.1	42595234.2	37738637.5	37645343.3	37831932
‘22-Aug-2021′	32393286	34886067.5	34792773.3	34979361.7	42352072.6	42029909	42674236.2	37753255	37659960.8	37846549
‘23-Aug-2021′	32424234	34886466.7	34793172.4	34979760.9	42429820.8	42107657.2	42751984.4	37767255.6	37673961.4	37860550
‘24-Aug-2021′	32449306	34886821.4	34793527.1	34980115.6	42506340.7	42184177.2	42828504.3	37780658.7	37687364.4	37873953
‘25-Aug-2021′	32474773	34887136.3	34793842.1	34980430.6	42581643.3	42259479.7	42903806.9	37793480.7	37700186.4	37886775
‘26-Aug-2021′	32512366	34887415.8	34794121.6	34980710	42655726	42333562.4	42977889.6	37805736.1	37712441.9	37899030
‘27-Aug-2021′	32558530	34887663.6	34794369.4	34980957.8	42728613.1	42406449.5	43050776.7	37817444.3	37724150	37910738
‘28-Aug-2021′	32603188	34887883.3	34794589.1	34981177.5	42800325.5	42478161.9	43122489.1	37828623.6	37735329.3	37921918
‘29-Aug-2021′	32649947	34888077.8	34794783.6	34981372	42870855.4	42548691.8	43193019	37839287.9	37745993.7	37932582
‘30-Aug-2021′	32695030	34888249.9	34794955.7	34981544.2	42940218.8	42618055.2	43262382.4	37849454.9	37756160.7	37942749
‘31-Aug-2021′	32737939	34888402.1	34795107.9	34981696.3	43008396.9	42686233.3	43330560.5	37859137.2	37765842.9	37952431
‘01-Sep-2021′	32768880	34888536.5	34795242.3	34981830.7	43075385.7	42753222.1	43397549.3	37868349.4	37775055.1	37961644
‘02-Sep-2021′	32810845	34888655.1	34795360.9	34981949.3	43141188.5	42819024.9	43463352.1	37877107.5	37783813.2	37970402
‘03-Sep-2021′	32857937	34888759.7	34795465.4	34982053.9	43205805.5	42883641.9	43527969.1	37885426.8	37792132.5	37978721
‘04-Sep-2021′	32903289	34888851.8	34795557.6	34982146	43269256.8	42947093.2	43591420.3	37893325.1	37800030.9	37986619
‘05-Sep-2021′	32945907	34888932.9	34795638.7	34982227.1	43331505.4	43009341.8	43653669	37900812.9	37807518.7	37994107
‘06-Sep-2021′	32988673	34889004.2	34795710	34982298.5	43392563.2	43070399.6	43714726.7	37907906.7	37814612.5	38001201
‘07-Sep-2021′	33027621	34889066.9	34795772.7	34982361.2	43452455.6	43130292.1	43774619.2	37914624.3	37821330	38007918
‘08-Sep-2021′	33058843	34889122.1	34795827.8	34982416.3	43511229.7	43189066.2	43833393.3	37920985.3	37827691.1	38014279
‘09-Sep-2021′	33096718	34889170.5	34795876.2	34982464.7	43568894.5	43246730.9	43891058.1	37927004.5	37833710.3	38020299
‘10-Sep-2021′	33139981	34889213	34795918.8	34982507.2	43625462.2	43303298.6	43947625.8	37932696.9	37839402.7	38025991
‘11-Sep-2021′	33174954	34889250.3	34795956	34982544.5	43680935.1	43358771.5	44003098.7	37938075.7	37844781.5	38031370
‘12-Sep-2021′	33208330	34889283	34795988.7	34982577.2	43735308.4	43413144.8	44057472	37943153.5	37849859.3	38036448
‘13-Sep-2021′	33236921	34889311.6	34796017.3	34982605.8	43788575.4	43466411.9	44110739	37947942.2	37854648	38041236
‘14-Sep-2021′	33264175	34889336.6	34796042.4	34982630.8	43840771.4	43518607.9	44162935	37952457.6	37859163.4	38045752
‘15-Sep-2021′	33289579	34889358.5	34796064.3	34982652.7	43891880.2	43569716.6	44214043.8	37956710	37863415.8	38050004
‘16-Sep-2021′	33316755	34889377.7	34796083.4	34982671.9	43941903	43619739.4	44264066.6	37960711.4	37867417.2	38054006
‘17-Sep-2021′	33347325	34889394.4	34796100.1	34982688.6	43990819.2	43668655.6	44312982.8	37964471.4	37871177.2	38057766
‘18-Sep-2021′	33381728	34889408.9	34796114.7	34982703.1	44038653.9	43716490.4	44360817.5	37968006.9	37874712.7	38061301
‘19-Sep-2021′	33417390	34889421.6	34796127.4	34982715.8	44085388.8	43763225.2	44407552.4	37971330.3	37878036.1	38064625
‘20-Sep-2021′	33448163	34889432.6	34796138.4	34982726.9	44130998.5	43808834.9	44453162	37974452.6	37881158.4	38067747
‘21-Sep-2021′	33478419	34889442.2	34796148	34982736.4	44175479.5	43853315.9	44497643.1	37977385.8	37884091.5	38070680
‘22-Sep-2021′	33504534	34889450.5	34796156.3	34982744.7	44218757.1	43896593.5	44540920.7	37980136.1	37886841.9	38073430
‘23-Sep-2021′	33531498	34889457.7	34796163.5	34982751.9	44260818	43938654.4	44582981.6	37982713.6	37889419.4	38076008
‘24-Sep-2021′	33563421	34889463.9	34796169.7	34982758.1	44301662	43979498.4	44623825.6	37985128.5	37891834.3	38078423
‘25-Sep-2021′	33594803	34889469.2	34796175	34982763.4	44341282.8	44019119.2	44663446.4	37987390	37894095.7	38080684
‘26-Sep-2021′	33624419	34889473.8	34796179.6	34982768	44379697.7	44057534.1	44701861.3	37989507.8	37896213.6	38082802
‘27-Sep-2021′	33652745	34889477.8	34796183.6	34982772	44416897.5	44094733.9	44739061.1	37991489.8	37898195.6	38084784
‘28-Sep-2021′	33678786	34889481.2	34796187	34982775.4	44452876.6	44130713	44775040.2	37993343.4	37900049.1	38086638
‘29-Sep-2021′	33697581	34889484.1	34796189.9	34982778.3	44487656.4	44165492.8	44809820	37995076.8	37901782.6	38088371
‘30-Sep-2021′	33716451	34889486.6	34796192.4	34982780.8	44521268.8	44199105.2	44843432.4	37996698.4	37903404.2	38089993
‘01-Oct-2021′	33739980	34889488.7	34796194.5	34982783	44553701.5	44231537.9	44875865.1	37998213.8	37904919.6	38091508
‘02-Oct-2021′	33766707	34889490.6	34796196.4	34982784.8	44584982.9	44262819.3	44907146.4	37999628.6	37906334.3	38092923
‘03-Oct-2021′	33791061	34889492.1	34796197.9	34982786.4	44615131.1	44292967.5	44937294.7	38000947.7	37907653.5	38094242
‘04-Oct-2021′	33813903	34889493.5	34796199.3	34982787.7	44644164.2	44322000.6	44966327.8	38002176.2	37908882	38095470
‘05-Oct-2021′	33834702	34889494.6	34796200.4	34982788.8	44672101.8	44349938.2	44994265.4	38003318.7	37910024.5	38096613
‘06-Oct-2021′	33853048	34889495.6	34796201.4	34982789.8	44698960.3	44376796.8	45021123.9	38004379.7	37911085.5	38097674
‘07-Oct-2021′	33871881	34889496.4	34796202.2	34982790.6	44724766.3	44402602.7	45046929.9	38005364.1	37912069.9	38098658
‘08-Oct-2021′	33894312	34889497.1	34796202.9	34982791.3	44749546	44427382.4	45071709.5	38006276.3	37912982.1	38099571
‘09-Oct-2021′	33915569	34889497.7	34796203.5	34982791.9	44773319.4	44451155.8	45095483	38007120.6	37913826.4	38100415
‘10-Oct-2021′	33935309	34889498.2	34796204	34982792.4	44796114.2	44473950.6	45118277.8	38007901.1	37914606.9	38101195
‘11-Oct-2021′	33953475	34889498.6	34796204.4	34982792.9	44817963.3	44495799.7	45140126.9	38008622.2	37915327.9	38101916
‘12-Oct-2021′	33971607	34889499	34796204.8	34982793.2	44838884.6	44516721	45161048.2	38009287.2	37915993	38102581
‘13-Oct-2021′	33985920	34889499.3	34796205.1	34982793.5	44858897	44536733.4	45181060.6	38009899.8	37916605.6	38103194
‘14-Oct-2021′	34001743	34889499.6	34796205.4	34982793.8	44878019.1	44555855.6	45200182.7	38010463.2	37917169	38103757
‘15-Oct-2021′	34020730	34889499.8	34796205.6	34982794	44896283.4	44574119.8	45218447	38010980.9	37917686.6	38104275
‘16-Oct-2021′	34037592	34889500	34796205.8	34982794.2	44913714.2	44591550.7	45235877.8	38011456	37918161.7	38104750
‘17-Oct-2021′	34053573	34889500.1	34796205.9	34982794.4	44930340.8	44608177.2	45252504.4	38011891.6	37918597.3	38105186
‘18-Oct-2021′	34067719	34889500.3	34796206	34982794.5	44946197.2	44624033.6	45268360.8	38012290.7	37918996.5	38105585
‘19-Oct-2021′	34081315	34889500.4	34796206.2	34982794.6	44961315.5	44639151.9	45283479	38012656.3	37919362	38105950
‘20-Oct-2021′	34094373	34889500.5	34796206.2	34982794.7	44975728.8	44653565.3	45297892.4	38012990.9	37919696.6	38106285
‘21-Oct-2021′	34108996	34889500.5	34796206.3	34982794.8	44989463.6	44667300	45311627.2	38013296.9	37920002.6	38106591
‘22-Oct-2021′	34127450	34889500.6	34796206.4	34982794.8	45002547.8	44680384.2	45324711.3	38013576.5	37920282.3	38106871
‘23-Oct-2021′	34143236	34889500.7	34796206.4	34982794.9	45014996.9	44692833.3	45337160.5	38013831.7	37920537.5	38107126
‘24-Oct-2021′	34159562	34889500.7	34796206.5	34982794.9	45026826.8	44704663.2	45348990.4	38014064.1	37920769.9	38107358
‘25-Oct-2021′	34175468	34889500.8	34796206.5	34982795	45038062.4	44715898.8	45360225.9	38014275.7	37920981.5	38107570
‘26-Oct-2021′	34189774	34889500.8	34796206.6	34982795	45048722.6	44726559.1	45370886.2	38014467.9	37921173.7	38107762
‘27-Oct-2021′	34202202	34889500.8	34796206.6	34982795	45058833.3	44736669.7	45380996.8	38014642.5	37921348.3	38107937
‘28-Oct-2021′	34215653	34889500.8	34796206.6	34982795.1	45068410.1	44746246.5	45390573.7	38014800.8	37921506.6	38108095
‘29-Oct-2021′	34231809	34889500.9	34796206.6	34982795.1	45077480	44755316.4	45399643.5	38014944.2	37921650	38108238
‘30-Oct-2021′	34246157	34889500.9	34796206.6	34982795.1	45086061.1	44763897.5	45408224.7	38015074.1	37921779.9	38108368
‘31-Oct-2021′	34260470	34889500.9	34796206.7	34982795.1	45094174.6	44772011	45416338.2	38015191.8	37921897.6	38108486
‘01-Nov-2021′	34273300	34889500.9	34796206.7	34982795.1	45101838.2	44779674.6	45424001.8	38015298.4	37922004.2	38108593