COVID-19 and Lockdown in India: Evaluation using Analysis of Covariance

Background: The lockdown in India has entered into its ninth month to curb the Coronavirus disease-19 (COVID-19) pandemic. The objective of the present study is to evaluate impact of different phases of lockdown on evolution of new cases of infection and deaths due to COVID-19. Methods: In this retrospective longitudinal study, the Indian data on new cases of infection and deaths due to COVID-19 were retrieved from John Hopkins University dashboard. The cases from 25 March to 31 October 2020 were analyzed using analysis of covariance for four phases of lockdown and �ve phases of unlockdown. Results: The coe�cients of regression for new cases did not differ signi�cantly for initial four phases of lockdown and unlock-1, while from unlock-2 the coe�cients showed signi�cant decrease till unlock-5. While death cases showed no signi�cant differences between coe�cients of regression for initial four phases of lockdown and unlock, but coe�cient of unlock-5 was signi�cantly lower than unlock-4. Conclusion: The trends of coe�cients of regression of new cases and deaths reveals positive effects of lockdown in �attening the epidemic curve. Though the pandemic is on downslope, till the availability of vaccines, non-pharmaceutical measures such as social distancing, wearing of masks need to be implemented.


Introduction
The global visibility of Coronavirus disease-19 deaths propelled Governments worldwide to impose lockdown.In developed nations, the cost of achieving this move is "merely" a substantial economic slowdown.But for India, a developing democracy with a mammoth population of 1.3 billion and a vulnerable economy, the cost of lockdown is more than economic recession.The loss of lives through violence, starvation, indebtedness and severe stress are invisible.[1] According to the World Health Organization report on 28 November 2020, there have been 61,299,371 con rmed cases of COVID-19, including 1,439,784 deaths globally.[2] As per Ministry of Health and Family Welfare, Government of India there are 453956 , 8802267 and 136696 active, recovered and death cases respectively in the country.[3] India has to face multiple challenges on the COVID-19 front.Physical distancing without total lockdown is unthinkable, especially in big and crowded cities.As per National sample survey reports, only 36% of Indians wash their hands with soap before meals.Furthermore, 160 millions do not have access to clean water to wash their hands.[4] To combat such scenarios and for optimum allocation of resources a number of mathematical models were suggested to forecast evolution of COVID-19 cases , mortality and length of hospital stays.[5] [6] [7] [8] In addition to provision of health services, coordination between various agencies including transport departments, police , food supply departments play a key role.[9].
The objective of the present study was to evaluate the effects of various phases of lockdown on the ongoing COVID-19 transmission and mortality in India.

Data analysis:
Nine linear regression models were tted for nine phases of lockdown, where time series data of new cases was taken as dependent variable and time as regressor.Similarly, nine linear regression models were tted for deaths.The linear regression model can be de ned as follows: where, is the intercept and is the coe cient of regression and e is the error term of the models.The coe cient of regression re ects the evolution of new cases or deaths of COVID-19.The higher the value of coe cient of regression means the higher the rate of evolution.The coe cients of regression of various phases of lockdown were compared.

Statistical Analysis
To compare the coe cients of regression of various phases of lockdown, analysis of covariance (ANCOVA) was performed.The ANCOVA evaluates whether the means of regression coe cient are equal across the various phases of lockdown.The statistical level of signi cance was considered at 5%.Microsoft Excel 2010 was used for creating database and analysis was performed on MATLAB 2016a (9.0.0.341360) [11] Results

Evolution of new cases of COVID-19
The plot of new cases per day of COVID-19 showed a biphasic trend (Fig. 1(a)).The nine linear regression models for new cases of COVID-19 were tted for nine different phases of lockdown (Fig. 2).The mean of the coe cients of regression increases from LD1 to ULD2, then it shows decreasing trends till ULD5 (Table 2).The comparison of coe cients of regression of different phases of lockdown was performed with analysis of covariance [F(8,203) = 1450.03;p < 0.001].The signi cant differences between various coe cients of regression of new cases can be interpreted from plots of con dence intervals (Fig. 3).The overlapping between limits of con dence intervals suggests no signi cant difference exists.We observed that the evolution of new cases of COVID-19 was the highest during the ULD2 phase (b = 1246; p < 0.001).

Evolution of death cases
Similarly, the plot of death cases per day of COVID-19 showed a biphasic trend (Fig. 1(b)).The nine linear regression models for death cases of COVID-19 were tted for nine different phases of lockdown (Fig. 4).
The mean of the coe cients of regression increases from LD1 to ULD2 with mid non-signi cant uctuations, then it shows decreasing trends till ULD5 (Table 2).The comparison of coe cients of regression of different phases of lockdown was performed with analysis of covariance [F(8,203) = 197.5;p < 0.001].The signi cant differences between various coe cients of regression of death cases can be interpreted from plots of con dence intervals (Fig. 5).We observed that the evolution of new cases of COVID-19 was the highest during the ULD2 phase (b = 13.15;p < 0.001).Gradually the evolution rate slows in ULD3 (b = 4.08; p = 0.48) and becomes negative in ULD4 (b = 0.26; p = 0.46) and ULD5 (b = 18.99; p < 0.001) phases.There were no signi cant differences between coe cients of regression of LD1, LD2, LD3, LD4, ULD1, ULD2, ULD3 and ULD4, but ULD5 differs signi cantly from ULD4.

Discussion
On 24 March 2020, a mammoth population of 1.3 billion was restricted to home with announcement of nationwide lockdown by the prime minister of India.The lockdown was aimed to break the chain of transmission and atten the epidemic curve to curb COVID-19 pandemic.There was suspension of all means of transportation including air, rail and road with the exception of essential services.The educational institutions, industrial establishments, hospitality services were locked.Essential services including food shops, hospitals, medical stores, ATMs, petrol pumps, re, police were exempted.[12] Subsequently various impositions were partially removed from LD2 and unlock phases have been continuing till now.India consists of 28 heterogeneous states with corresponding dynamics of the COVID-

[13]
As compared with the pre-lockdown period, the doubling rate of new cases was increased from three to eight days during the LD1.[12] The results showed that the rate of evolution of new cases did not differ signi cantly during the next four phases of lockdown.Singh BP et al. model effects of lockdown on the tempo of COVID-19 and found no signi cant differences between pre-lockdown rates and LD1 growth rates, but growth rates in LD1 and LD2 differ signi cantly.[14] Kumar D et al. showed as compared to prelockdown and LD1, the doubling time in LD2 was higher.On 14 April 2020, with the end of LD1, the LD2 was announced till 3 May 2020.[15] On 20 April 2020, government allowed some relaxations that include, opening of agricultural businesses such as dairy, aquaculture, plantations and shops selling farm products with proper maintenance of social distancing.Further, the cargo transportation vehicles were allowed.[12] The demographic pro le of initial 2500 COVID-19 sufferers revealed 59% belongs to age group of 20 -49 years, that constitute the working age group.[16] As on 4 May 2020, LD3 had been continued with some more relaxations as announced by the Ministry of Home Affairs, Government of India.Based on doubling rates, the lockdown areas in the whole country were divided into 'red zone', 'orange zone', and 'green zone' with high, moderate and low doubling rates respectively.In red zones, no movement of public was permitted, while in orange zones, private and hired vehicles are permitted.In green zones, buses with 50% carrying capacity were allowed.[12] Sahoo BK et al. suggested a mathematical model, where time dependent infection rate (depend on lockdown) was tted with Gompertz function and effects of lockdown were modeled.The initial infection rate was 0.15 per day which has come down to about 0.05 per day (about 3 times lower) after 6 weeks of lock down and the downward trend continues, as suggested in the present study.[17] Pai C used the SEIR Model (susceptible-exposed-infected-recovered model) to predict the impact of removal of lockdown on 3 rd May 2020.They predicted that peak of active infected cases would be around 43,000 in the mid of May, 2020 with 7 to 21% increase in peak value due to relaxation in lockdown strategies.[18] From 18 May 2020, LD4 continued and more power was given to states to demarcate zones.The average daily number of tests have increased from 1,717 (19)(20)(21)(22)(23)(24)(25) to 131,772 (25-31 May) with an estimated testing shortfall of 4.58 million tests nationally by 31 May 2020.[19] In view of economical impacts of lockdown, relaxations in ULD1 allowed shopping malls, religious places, hotels and restaurants to reopen.Still no inter-state travel was allowed and night curfew continued.Further as part of ULD2, a number of activities were allowed outside of containment zones, the only exception were educational institutions, international air travel, places of recreation such as swimming pools, gymnasiums, theatres, entertainment parks, bars, auditoriums and assembly halls.The inter-state borders were open.From ULD1 to ULD2 the rate of evolution increases, but after ULD2, the rate of evolution has been decreasing.Since ULD3, night curfews were removed and gymnasiums and yoga centers were allowed to open.With LD4, marriages and funeral ceremonies were allowed and religious, political, sports and academic gatherings up to 100 persons were allowed.[12] Vaishnav V et al. used a group method of data handling to assess the impact of relaxations during lockdown.They reported that apart from relaxations in LD3 and LD4, the increased testing capacity and migration of laborers were important reasons of increased positive cases.[20] During LD5, major relaxations include opening of cinema halls with 50% sitting capacity and reopening of hill stations, beaches and national parks.The results showed that the evolution of death cases due to COVID-19 closely parallels the evolution of new cases of infection .(Figure 3 and 5).However, Mate A et al used the SEIR model to compare a range of policies.After the initial lockdown, their simulations demonstrate that even policies that enforce strict physical distancing while returning to normal activity could lead to widespread outbreaks.However, "middle ground" policies that alternate weekly between total lockdown and physical distancing may lead to much lower rates of infection while simultaneously permitting some return to normalcy.[21] Nadim S et al. performed the dynamical analysis of the impact of lockdown on disease transmission.The impact of lockdown of susceptible individuals will always have a positive population-level impact for every 0 < r < 1 , where r is lockdown e cacy.The lockdown of susceptible individuals resulted in reduction of the basic reproduction number.[22] Finally, India was quick to implement lockdown and closing its international borders as praised by the World Health Organisation as "tough and timely".[23]

Conclusion
The timely lockdown in India has a key role in curbing the COVID-19 pandemic.Furthermore , the partial relaxations during an ongoing pandemic are appropriate measures to deal with medical as well as economical issues of the country.Now the pandemic is on its downslope, but till the availability of vaccine, non-pharmaceutical measures such as social distancing, wearing of mask and sanitization of hands need to be implemented.

Limitation Of The Study
The small number of time points for initial phases of lockdown, that is, LD1, LD2, LD3 and LD4 contains 21,19,14,14 days respectively.

Declarations
Ethics Declarations:    Shows coe cients of regression with 95% con dence interval of linear regression models of new cases of COVID-19 for nine phases of lockdown.
present study used de-identi ed data from public domain, thus exempted from ethical review by O ce of the Ethics Committee, SMS Medical College and attached Hospitals, Jaipur via letter no .430/MC/EC/2020 dated 26 Jun 2020.

Figures
Figures

Figure 4 Shows
Figure 4

Table 2
showing estimates of coe cients of regression of new cases of infection and deaths due to COVID-19 in various phases of lockdown and unlock in India