key: cord-0744260-qlvbv6bn
authors: Manik, Souvik; Mandala, Manoj; Pal, Sabyasachi; Patra, Subhradeep; Acharya, Suman
title: Impact of climate on COVID-19 transmission: A study over Indian states
date: 2022-03-17
journal: Environ Res
DOI: 10.1016/j.envres.2022.113110
sha: 4967eb9b8e12adeab7d8ddaeb2343b6556fcd5b3
doc_id: 744260
cord_uid: qlvbv6bn

Corona Virus Disease 2019 (COVID-19) started in Wuhan province of China in November 2019 and within a short time, it was declared as a worldwide pandemic by World Health Organisation due to the very fast worldwide spread of the virus. There are a few studies that look for the correlation with infected individuals and different environmental parameters using early data of COVID-19 but there is no study so far that deals with the variation of effective reproduction number and environmental factors. Effective reproduction number is the driving parameter of the spread of a pandemic and it is important to study the effect of various environmental factors on effective reproduction number to understand the effect of those factors on the spread of the virus. We have used time-dependent models to investigate the variation of different time-dependent driving parameters of COVID-19 like effective reproduction number and contact rate using data from India as a test case. India is a large population country that is highly affected due to the COVID-19 pandemic and has a wide span of different temperature and humidity regions and is ideal for such study. We have studied the impact of temperature and humidity on the spread of the virus of different Indian states using time-dependent epidemiological models SIRD, and SEIRD for a long time scale. We have used a linear regression method to look for any dependency between the effective reproduction number with the relative humidity, absolute humidity, and temperature. The effective reproduction number shows a negative correlation with both relative and absolute humidity for most of the Indian states, which are statistically significant. This implies that relative and absolute humidity may have an important role in the variation of effective reproduction number. Most of the states (six out of ten) show a positive correlation while two (out of ten) show a negative correlation between effective reproduction number and average air temperature for both SIRD and SEIRD models.

The first case of COVID-19 was reported in India on 30 January 2020 (Delhi, 2020) . Till 10 October 2021, India had 33.9 million total confirmed cases which were highest in Asia (Worldometer, 2020a) and the second-highest in the world (Worldometer, 2020a). During the above-mentioned period, India had 33.2 million recoveries, and 0.45 million were deceased (Worldometer, 2020a) . Study with India is interesting as it is the world's second-largest population with about one-sixth of the world's total population (Worldometer, 2020b) .

The second wave of COVID-19 started in India on 11 February 2021. The second wave had a significant impact with daily cases nearly four times than during the first wave peak (Ranjan et al., 2021) . In India, the second wave was caused mainly by the (MoHFW, 2021a) . WHO cautioned that the Indian variety, B.1.617, was rapidly spreading in India, accounting for more than 28% of positive test samples. The Indian strain (B.1.617) of SARS-CoV2 was found to be more infectious compared to other SARS-CoV2 variants (WHO et al., 2021) .

The spread of an epidemic depends on a large number of factors. Earlier, it was found that humidity is one of the driving factors to explain the seasonality of influenza (Shaman and Kohn, 2009) . Similar seasonal variability would be expected for COVID-19 and other coronaviruses like SARS. The spread of COVID-19 (SARS-CoV-2) was found to be correlated with temperature and latitude (Poole, 2020) . A study of the seasonality of many other viruses, like seasonal Influenza, suggests that the cool season in the northern hemisphere favours disease propagation more than the warm season in the northern hemisphere (Poole, 2020) . Earlier, it was shown that 50% of the influenza virus transmission variability can be explained by absolute humidity but a detailed study was not possible for limited data (Shaman and Kohn, 2009) . Meteorological parameters (temperature, relative humidity, and absolute humidity) may play an important role in influencing infectious diseases such as severe acute respiratory syndrome (SARS) and influenza.

At the beginning of the spread of the COVID-19 disease, it was widely believed that summer will cause the virus to reduce (Bukhari and Jameel, 2020) . Results of other coronaviruses (such as SARS coronavirus) also indicated that the virus may be less effective with rising temperature and humidity (Chan et al., 2011) . A rigorous study is necessary with a large amount of data to explore the effect of temperature and humidity on the spread of COVID-19.

Several social or non-meteorological factors could influence the correlation study between meteorological factors and COVID-19 transmissions, such as governmental interventions, social interactions, lock-downs, herd immunity, vaccinations, population density, personal hygiene, defence mechanisms, and cultural activities. Different studies focused on the impact of social interaction on COVID-19 spread Calbi et al., 2021; Block et al., 2020; Oraby et al., 2021) . Well-timed lock-downs have been found to split the peak of hospitalizations into two smaller distant peaks, extending the overall pandemic duration. Lock-down is the most rigorous public health measure which can be taken to minimize contact rate and viral transmissions in a community (Oraby et al., 2021) . It was found that during the second wave, the 2021 assembly election played a major role in the COVID-19 spread rate in India (Manik et al., 2021) .

In the present paper, we investigate the influence of average air temperature, absolute humidity, and relative humidity on the effective contact rate and reproduction number of COVID-19. There are a few studies that look for the correlation with infected individuals and different environmental parameters using early data of COVID-19 (Arumugam et al., 2020; Chiyomaru and Takemoto, 2020; Pirouz et al., 2020; Notari, 2021; Sajadi et al., 2020) but so far there is no study that deals with the variation of effective reproduction number and environmental factors. Effective reproduction number is the driving parameter of the spread of a pandemic and it is important to study the effect of various environmental factors on the effective reproduction number to understand the effect of those factors on the spread of the virus. Our study is unique as we deal with time-dependent models and look for the impact of temperature and humidity on effective reproduction number.

We have done a rigorous study for different Indian states which are strongly affected during the second wave of COVID-19. Coronavirus spread has been influenced by a variety of parameters including the use of masks, personal hygiene, social distance, vaccination, etc. We have assumed that these factors remained constant for these states throughout the study and that their impact on the result is minimal. India also represents a wide variety of temperatures and humidity regions, which is ideal for our study. In this paper, we have looked at the variety of different driving parameters of the pandemic like effective contact rate ( ) and effective reproduction number (ℝ(t)) using time-dependent mathematical models SIRD and SEIRD for different Indian states.

In Sect. 2, we summarise different mathematical models of the pandemic. Sect. 2.1 carries a brief introduction of the SIRD model. A short introduction of the SEIRD model is given in Sect. 2.2. We have discussed the data analysis and methodology in the Sect. 3. In Sect. 4, we present our findings. The temperature dependence of the effective reproduction number is discussed in the Sect. 4.1 and the humidity dependence of the effective reproduction number ℝ( ) is discussed in Sect. 4.2. In Sect. 5, we discuss our findings, and in Sect. 6 we summarise our results.

Different mathematical models are designed to simulate the effect of the disease from different perspectives (Gupta et al., 2020a; Piccolomini and Zama, 2020; Pribylova and Hajnova, 2020; Ndiaye et al., 2020; Notari, 2021) . These help us to get an idea about the spread rate of a disease over the population. We have used the time-dependent epidemiological models SIRD and SEIRD. The spread rate depends on a large number of parameters such as mean incubation time (Bhattacharjee, 2020; Baum, 2020) , mean infectious period, social distancing, and risk of international spread (Bogoch et al., 2020; Zhao et al., 2020) . The most important part of these models is to calculate the basic reproduction number ( 0 ) which is the contagiousness of the disease. 0 is defined as the average number of people who can be affected by a single infected person over a course of time. 0 > 1 indicates that the spread is increasing, 0 = 1, indicates that the spread is stable and 0 < 1, indicates that the spread is expected to stop. We have studied the effective reproduction number ℝ( ) for India using different models. We have also studied the evolution of ℝ( ) using the same models for different individual states of India. 

There are several models for studying contagious disease transmission in a large population. The simplest compartmental model that can explain the evolution of an outbreak at the population level is the Susceptible-Infected-Recovered (SIR) model. The SIRD model (Ndiaye et al., 2020; Manik et al., 2021) is the extended version of the SIR model. We have used this model to study different time-dependent parameters like effective reproduction number (ℝ), contact rate ( ), recovery rate ( ), and mortality rate ( ). At any time , ( ) be the total number of susceptible individuals, ( ) be the total number of infected individuals, ( ) be the total number of recovered, and ( ) be the total number of deceased individuals. The SIRD model assumes that the population is mixed homogeneously. Though India is a big country, it may be safely assumed that the mixing was nearly homogeneous. The population is classified into four categories at time : susceptible, infectious, recovered, and deceased. The total population, , is assumed to remain constant during the study. Natural birth and death are often ignored in simple compartmental models because the spread rate of COVID-19 is typically considerably faster than the dynamics of birth and death. Furthermore, it is supposed that everyone who is exposed to the virus becomes infected immediately, with no latent period between exposure and infection.

Different compartments of the SIRD model are shown in Fig. 2 . The infant entered susceptible class once the maternal antibodies no longer existed in the body. Since a susceptible has enough contact with an infective to allow transmission, they are known as an infective class , which means they are infectious in the sense that they can transmit the virus. Once the infectious phase is elapsed, the individual falls into one of two classes: , which is made up of people who gained immunity through infection, or , which is made up of deceased people. Here, is the contact rate and is the recovery rate and is the mortality rate. ( ), ( ), ( ) and ( ) can be expressed in fractional form:

The schematic diagram showing different compartments of SIRD, and SEIRD model. is the contact rate, is the recovery rate, is the incubation period, and is the mortality rate.

from the conservation law,

SIRD model can be expressed by following set of differential equations.

from the equation 4, we may write

We use equation (5) to find

Now we use equation (6) to find

The effective reproduction number ℝ(t) can be expressed as

In Fig. 3 , we have shown a variety of different parameters for the SIRD model for a few selected Indian states. In the second, third, and fourth row, the variation of effective contact rate ( SIRD ( )), the variation of recovery rate ( SIRD ( )), and the variation of mortality rate ( SIRD ( )) are shown. The fifth row represents the variation of effective reproduction number (ℝ SIRD ( )) for the SIRD model.

The Susceptible-Exposed-Infected-Recovered-Deceased (SEIRD) model (Li, 2018) is the extended version of the SEIR model. At any time , ( ) be the total number of susceptible individuals, ( ) be the total number of exposed individuals, ( ) be the total number of infected individuals, ( ) be the total number of recovered individuals, and ( ) be the total number of deceased individuals from the epidemic. In the SEIRD model, we have considered the average incubation period of 1∕ as a constant. We presume that the individuals who recovered from the disease can not become susceptible again.

Various compartments of the SEIRD model are shown in Fig. 2 . The Exposed ( ) compartment in the SEIRD model is an extension to the SIRD model. The susceptible ( ) moves into the exposed compartment ( ) when a susceptible individual comes across significant interaction with an infective individual ( ). The individual enters the class at the end of the latent phase and becomes capable to spread the infection. Finally, at the end of the infectious time, the person moves to either the recovered compartment or the deceased compartment (for detail, see section 2 of Manik et al. (2021) ).

The parameter is the product of the average number of contacts per person and per unit time by the probability of disease transmission in contact between susceptible and infectious individuals. is the recovery rate and is the mortality rate. The compartment of the exposed individuals in the SEIRD model makes the model slightly more delicate. The SEIRD model is a compartmental model used to understand the mathematical modeling of infectious diseases in a large population. If is the total population size then in fraction form

From the conservation of the total number of individuals, we have the relation

These quantities change by discrete amounts but if the minimal possible change is relatively low, we can consider ( ), ( ), ( ), ( ) as differentiable functions. For any time ≥ 0, the SEIRD model can be expressed by the differential equations

We use the discrete form of equations (13) to (17). We use equation (14) to find

We use equation (16) to find

Now we use equation (17) to find

The effective reproduction number ℝ(t) can be given by

In Fig. 3 , we have shown the variation of different parameters for the SEIRD model for a few selected Indian states. In the second and third row, the variation of effective contact rate ( SEIRD ( )) and the variation of recovery rate ( SEIRD ( )) are shown. The fourth row shows the variation of mortality rate ( SEIRD ( )) and the fifth row shows the variation of effective reproduction number (ℝ SEIRD ( )) for the SEIRD model.

We have used the COVID-19 data maintained by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University to track reported cases of Coronavirus in real-time . The time-series data of different Indian states can be accessed from this source 1 . We have obtained weather data from "World Weather Online" using a python based API from 1 February 2021 to 10 October 2021. We have taken state population data from the "India Census" site 2 . We have used standard python packages i.e., Numpy, Scipy, Pandas, Matplotlib, Epitools (Manik et al., 2022a) for the entire work. Since environmental variables are not expected to have an immediate effect on COVID-19 cases, we have acquired weather data including temperature and relative humidity 7 days before the reported cases. We have also calculated absolute humidity, the actual amount of water vapour in the atmosphere, depending on the air temperature, ( ; in • ) and relative humidity, (RH; in %) (Auler et al., 2020) . The absolute humidity (AH; in ∕ 3 ) is the weight of water vapour per unit volume of air and is estimated using the ClausiusâĂŞClapeyron equation and can be described as follows (Gupta et al., 2020b 

where corresponds to absolute humidity, is the relative humidity, and is the average temperature. We have selected the ten most affected Indian states for which the total confirmed COVID-19 cases were maximum during the time-span of COVID-19 second wave in India (2 February 2021 to 10 October 2021). The lower threshold of total confirmed individuals was 0.56 million during the above-mentioned period for those selected states. We have studied the variation of confirmed, recovered, and deceased individuals for Indian states Maharashtra, Kerala, Karnataka, Tamil Nadu, Andhra Pradesh, Uttar Pradesh, West Bengal, Delhi, Rajasthan, and Gujarat. These states are located at different corners of the country with a wide variability of different atmospheric parameters. The effective contact rate ( ( )), recovery rate ( ( )), mortality rate ( ( )) and effective reproduction number (ℝ( )) are estimated from the mathematical equations discussed in Sect. 2 for different states of India. We have also studied the evolution of these parameters using time series data. Since some of the states have wide variability of different atmospheric parameters, we have taken average values of different meteorological parameters across different cities for every state. We have calculated the values of transmission coefficients using SIRD and SEIRD models (for details, Sect. 2.1, 2.2) for different states (Maharashtra, Kerala, Karnataka, Tamil Nadu, Andhra Pradesh, Uttar Pradesh, West Bengal, Delhi, Rajasthan, and Gujarat) of India. To minimize the effect of noise, we have used a three-day rolling mean variation of transmission coefficients for our study. For the SIRD model, we have used equation (7), (8), (9) and (10) to calculate the effective contact rate ( ( )), recovery rate ( ( )), mortality rate ( ( )) and effective reproduction number (ℝ( )) respectively. For the SEIRD model, we have used equation (18), (19), (20) and (21) to calculate ( ), ( ), ( ), and ℝ( ) respectively. We have optimized the values of all transmission coefficients by removing all negative values. Linear regression is carried out between the 7-days rolling mean of the various meteorological variables and the effective reproduction number (ℝ( )) to understand the effect of meteorological parameters on the spread of COVID-19. We have used the ordinary least squares (OLS) or linear least-squares method to fit the linear model and to estimate the intercept and slope of the fitted regression lines. We have estimated the Pearson correlation coefficient (r-value) and the two-tailed p-value (for a hypothesis test in which the null hypothesis is that the slope is zero) based on the Wald test with t-distribution using SciPy's stats.linregress module (Virtanen et al., 2020) . If the p-value is low (generally ≤ 0.05), then the correlation is statistically significant and if the p-value > 0.05 then the correlation is not statistically significant. We have estimated the regression coefficient 2 as the square of the r-value which represents the coefficient of determination for the linear regression model.

We have used time series data for infected, recovered, and deceased individuals of COVID-19 . The impact of temperature and humidity on ℝ( ), ( ), and ( ) is studied in detail for a large population, which is very relevant to the practical scenario. In the first row of Fig. 1 , we have shown the daily variation of the confirmed cases for India. In the second row of Fig. 1 , the variation of the deceased individuals is shown. From this figure, two different waves of the COVID-19 in India are visible. The second wave is nearly four times the first wave and provides ideal time to investigate the correlation of the spread rate of the virus with environmental parameters for a large population. The shaded region shows the duration of our current study.

In Fig. 3 , we have shown the variation of different parameters related to a pandemic for eight different Indian states which are strongly affected by the coronavirus. We have shown the variation of driving parameters of a pandemic for the states Maharashtra, Kerala, Karnataka, Tamil Nadu, Andhra Pradesh, Uttar Pradesh, West Bengal, Delhi, Rajasthan, and Gujarat. These states belong to different corners of the country with wide variability for different meteorological parameters like temperature and humidity and formed an ideal sample of states to study the impact of temperature and humidity on the spread of the virus. In Fig. 3 , the first row shows the variation of the number of infected, recovered, and deceased individuals with time, the second row shows the variation of effective contact rate ( ) with time, the third row shows the variation of recovery rate ( ), the fourth row shows the variation of mortality rate ( ) and the fifth row shows the variation of effective reproduction number ℝ( ) for different Indian states.

In the SEIRD model, there is more fluctuation for few states in the plot of effective contact rate and effective reproduction number in Fig. 3 , compared to the SIRD model. The results from both SIRD and SEIRD are significant and show a similar type of trend. Since the SEIRD model has an additional compartment (Exposed) in comparison to the SIRD model, it is more realistic and shows relatively more variability compared to SIRD model. Fig. 4 shows the variation of average temperature ( ), relative humidity ( ), and absolute humidity ( ) for different Indian states for which the study is executed. The figure shows a wide range of temperature and humidity since selected states represent different regions of the country. 

We have studied the dependence of effective reproduction number ℝ( ) on temperature for different Indian states. The linear regression method is used to find the correlation and the regression coefficient 2 . Table 1 shows the result of the linear regression method for different models for the study period. The positive sign indicates the correlation between effective reproduction number (ℝ( )) and average temperature ( ) with a positive slope and the negative sign indicates a correlation between ℝ( ) and temperature with a negative slope. The correlation with negative slope indicates that the effective reproduction number (ℝ( )) will decrease with the increase of the temperature. For the 

, which indicate that for these two states the COVID-19 spread is reduced by increasing temperature. Six states out of ten, show a positive correlation between ℝ( ) and

for both SIRD and SEIRD models, which implies that effective reproduction number increases with the increase of average air temperature. For the states of Gujarat and Uttar Pradesh the correlation is not conclusive.

The first column of Fig. 5 represents the variation of the effective reproduction number ℝ( ) with average temperature for different Indian states (Maharashtra, Kerala, Karnataka, Tamil Nadu, Andhra Pradesh, Uttar Pradesh, West Bengal, Delhi, Rajasthan, and Gujarat). The variation of ℝ( ) with is estimated for two different time-dependent Table 1 Value of regression coefficient 2 with p-value using different models for different Indian states from ℝ(t) vs plot with seven days running average. The '+' sign implies positive correlation and '-' sign implies negative correlation between ℝ(t) and . models SIRD and SEIRD. A positive correlation is found for the states of West Bengal, Tamil Nadu, Maharastra, Andhra Pradesh, Kerala, and Karnataka for both models, whereas the states Delhi, and Rajasthan shows a negative correlation between ℝ( ) and . For the state of Gujarat and Uttar Pradesh, the correlation results are not conclusive. The state of Gujarat shows a positive correlation with for the SIRD model and a negative correlation for the SEIRD model, which is less significant than the SIRD model. For Uttar Pradesh, the SIRD model shows a positive correlation and the SEIRD model showed a negative correlation, both correlations are statistically less significant (p-value>0.05).

Humidity plays a crucial role as a driving environmental parameter on the spread of a virus. We have investigated whether there is any dependence of relative and absolute humidity on the spread rate of COVID-19. We have studied the correlation of effective reproduction number ℝ( ) with relative humidity ( ) and absolute humidity ( ) with a seven-day running average. We have used the linear regression method to look for any correlation between ℝ( ) with and . We find out the correlation coefficient 2 . We have summarised the result of variation of the ℝ( ) with average and for different states of India in Table 2 . For the SIRD model, all ten states show a negative correlation between ℝ( ) with . The SEIRD model also shows that all states follow a negative correlation except Delhi. Except for Delhi, the negative correlation is highly significant for both models.

The second column of Fig. 5 shows the correlation of the ℝ( ) with for ten Indian states which are strongly Table 2 The summary of regression coefficient 2 with p-value using different models for different Indian states from ℝ(t) vs plot with seven days running average. The '+' sign implies positive correlation and '-' sign implies negative correlation between ℝ(t) and . Table 3 The summary of regression coefficient 2 with p-value using different models for different Indian states from ℝ(t) vs plot with seven days running average. The '+' sign implies positive correlation and '-' sign implies negative correlation between ℝ(t) and .

affected by COVID-19. Most of the states show a negative correlation between ℝ( ) and , which implies that the relative humidity might be playing a role to control the spread of the virus.

We have looked for the correlation between ℝ( ) and . The result of correlation study of ℝ( ) with is summarized in Table 3 . For the time-dependent SIRD model, eight states out of ten states show a negative correlation between ℝ( ) and

, which are statistically significant (p-value<0.05). For the SEIRD model also most of the states show a negative correlation between ℝ( ) and

. For the state of Tamil Nadu, the correlation is positive for both the models SIRD and SEIRD but the correlation is statistically less significant (p-value>0.05). For the state of Delhi, we have not found a conclusive result, though the SEIRD model shows a positive correlation with a higher p-value than the SIRD model. For the state of Kerala, we have found a positive correlation between ℝ( ) and for both the models SIRD and SEIRD.

The third column of Fig. 5 shows the correlation of ℝ( ) with for ten Indian states which are strongly affected by the COVID-19. Most of the states show a negative correlation between ℝ( ) and

, which implies that the effective reproduction number decreases with an increase in absolute humidity. Absolute humidity may be playing a role to control the spread of the virus.

Earlier a mixed result was found between correlation of COVID-19 transmission and temperature using the early phase of the COVID-19 data in different global locations. A positive correlation was found for several studies in New York (Bashir et al., 2020) and Jakarta (Tosepu et al., 2020) . A negative correlation was observed for multiple worldwide studies (Arumugam et al., 2020; Chiyomaru and Takemoto, 2020; Pirouz et al., 2020; Notari, 2021; Sajadi et al., Figure 5 : Correlation between the effective reproduction number ℝ( ) and 7 days moving average of the different meteorological parameters. The best fitted linear regression lines are shown with the orange (SEIRD) and the blue (SIRD) colors. The shaded region for both the fitted regression lines depict 95% confidence interval. 2020; Wu et al., 2020; Xie and Zhu, 2020) in California (Gupta et al., 2020b) , Italy (Livadiotis, 2020) , Ghana (Iddrisu et al., 2020) , Japan (Ujiie et al., 2020) , Spain (Abdollahi and Rahbaralam, 2020; Tobias and Molina, 2020) , and China (Oliveiros et al., 2020; Qi et al., 2020; Shi et al., 2020; Sil and Kumar, 2020) . For the countries like Nigeria (Taiwo and Fashola, 2020) , Spain (Briz-Redon and Serrano-Aroca, 2020), Iran (Ahmadi et al., 2020; Jahangiri et al., 2020) , and in a worldwide study (Jamil et al., 2020) no correlation was found.

Global research of 166 nations (excluding China) found a negative correlation between temperature and COVID- 19 cases, with a temperature increase of 1 • resulting in a 3.08% drop in cases (Yu et al., 2020) . Another worldwide study with 100 nations (up to 18 March 2020) with wide temperature variation from -33.9 to 34.3 • , suggested a negative correlation between daily COVID-19 cases and temperature (Meyer et al., 2020) . A significant negative correlation was reported earlier between daily COVID-19 cases and temperature (−10 • to 10 • ) for provinces of China . Several studies investigated the effect of humidity on the spread of the virus, but the results were inconclusive for few countries. There was no definite correlation between humidity and COVID-19 transmission in studies from Africa, Indonesia, Jakarta, New York, the USA, and a global study of 100 nations (Meyer et al., 2020; Bashir et al., 2020; Adekunle et al., 2020; Tosepu et al., 2020) . A weak positive correlation was found between average relative humidity and COVID-19 cases in Saudi Arabia (Alkhowailed et al., 2020) . A significant positive correlation between relative humidity and new COVID-19 cases was reported for the United States (Chien and Chen, 2020) . A negative correlation between the relative humidity and COVID-19 cases was reported for Spain (Paez et al., 2021) , where transmission reduced by 3% for every 1% increase in humidity. Earlier, it was found that high temperature and humidity reduce the COVID-19 confirmed cases, deaths and improve recovery (Sarkodie and Owusu, 2020) . UV index, wind speed, pressure, and precipitation also may have an impact on virus transmission (Manik et al., 2022b) . Several studies emphasise the correlation between air pollution and COVID-19 transmission (Lembo et al., 2021; Conticini et al., 2020; Al Huraimel et al., 2020) . A significant correlation was found between different air pollutant agents and greenhouse gas elements with the cumulative positive number of cases and deaths (Lembo et al., 2021) . We have used the time-dependent models SIRD and SEIRD to study the evolution of different time-dependent driving parameters of a pandemic like effective reproduction number and effective contact rate for different Indian states which are strongly affected by COVID-19 for a long time scale of nearly eight months. During the time of our study, the infected cases are very high and we have focused on the most destructive second wave in India, which broke down all the health systems drastically. We have also studied the evolution of time-dependent recovery rate and mortality rate. The mortality rate has shown several spikes in the diagram which implies the significant impact of the virus on the population.

One of the main aspects of the study is to look for a correlation between driving parameter of a pandemic the effective reproduction number with temperature and humidity using different time-dependent models. The correlation between the temperature and effective reproduction number indicates that for most of the Indian states a positive correlation between the effective reproduction number and air temperature is observed. The positive correlation between the effective reproduction number and the average air temperature is prominent for the states of West Bengal, Tamil Nadu, Karnataka, Kerala, Andhra Pradesh, and Maharastra. A negative correlation is observed for the states Delhi and Rajasthan for both SIRD and SEIRD models. For the state of Madhya Pradesh, the correlation between the effective reproduction number and the average air temperature is negative for the SEIRD model, which is statistically significant (p-value<0.05).

The study of the correlation between the effective reproduction number and the humidity has provided some important outcomes. We have used both relative and absolute humidity to look for the correlation with effective reproduction number. All ten states show a negative correlation between effective reproduction number and relative humidity with high statistical significance for the time-dependent SIRD model. For the state of Delhi, the negative correlation significance is relatively low for the SIRD model which shows a positive correlation for the SEIRD model with higher statistical significance. The SEIRD model also showed a negative correlation between the effective reproduction number and relative humidity for all the states except Delhi.

The correlation between the absolute humidity and effective reproduction number shows a similar type of trend in correlation like relative humidity. All of the states except Tamil Nadu and Kerala show a negative correlation between the absolute humidity and effective reproduction number for the SIRD model. The state of Tamil Nadu shows a positive correlation with a high p-value, which is statistically less significant. For the SEIRD model in the state of Delhi, Kerala, and Tamil Nadu, the correlation between the effective reproduction number and absolute humidity is positive, the rest of the states show a negative correlation. The p-value for the states Kerala and Tamil Nadu is high which implies less statistical significance.

We have looked for the evolution of different driving parameters of a pandemic using time-dependent epidemiological models SIRD and SEIRD for different Indian states. We have studied the correlation between effective reproduction number with average temperature, relative humidity, and absolute humidity of different Indian states. We have found that most of the Indian states show a negative correlation between effective reproduction number and relative and absolute humidity for time-dependent models SIRD and SEIRD, which implies that humidity may have an impact on the spread of the virus. The correlation between temperature and effective reproduction number suggests that for most of the Indian states effective reproduction number increases with the increase of average air temperature. There also exist several factors like personal hygiene, vaccination, social interaction, etc., which also play a crucial role in the spread of the virus. Environmental variables, particularly temperature and humidity, may play a role in epidemic spread, but their impact is marginal when compared to other social factors such as social interaction, governmental interventions, lock-downs, population density, herd immunity, personal hygiene, migration patterns, defence mechanisms and so on.

Temperature and humidity alone can not account for the majority of the variation in disease transmission. Therefore, countries should put more emphasis on healthcare policies and vaccination.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Not applicable

Not applicable

We are giving consent for publication of this article in Environmental Research.

We have used data from https://data.covid19india.org/ and https://github.com/CSSEGISandData/ COVID-19.

Effect of temperature on the transmission of covid-19: A machine learning case study in spain

Spatio-temporal analysis of meteorological factors in abating the spread of covid-19 in africa

Investigation of effective climatology parameters on covid-19 outbreak in iran

Sars-cov-2 in the environment: Modes of transmission, early detection and potential role of pollutions

Impact of meteorological parameters on covid-19 pandemic: A comprehensive study from saudi arabia

Ambient temperature and covid-19 incidence rates: An opportunity for intervention

Evidence that high temperatures and intermediate relative humidity might favor the spread of covid-19 in tropical climate: A case study for the most affected brazilian cities

Correlation between climate indicators and covid-19 pandemic in new york, usa

Covid-19 incubation period: An update

Statistical investigation of relationship between spread of coronavirus disease (covid-19) and environmental factors based on study of four mostly affected places of china and five mostly affected places of italy

Social network-based distancing strategies to flatten the covid-19 curve in a post-lockdown world

Pneumonia of unknown aetiology in Wuhan, China: potential for international spread via commercial air travel

International trade as critical parameter of covid-19 spread that outclasses demographic, economic, environmental, and pollution factors

Can commercial trade represent the main indicator of the covid-19 diffusion due to human-to-human interactions? a comparative analysis between italy, france, and spain

A spatio-temporal analysis for exploring the effect of temperature on covid-19 early evolution in spain

Will coronavirus pandemic diminish by summer?

The consequences of covid-19 on social interactions: an online study on face covering

The effects of temperature and relative humidity on the viability of the sars coronavirus

Meteorological impacts on the incidence of covid-19 in the u.s. Stochastic Environmental Research and Risk Assessment 34

Global covid-19 transmission rate is influenced by precipitation seasonality and the speed of climate temperature warming

Can atmospheric pollution be considered a co-factor in extremely high level of sars-cov-2 lethality in northern italy? Environmental pollution 261

Update on novel coronavirus: one positive case reported in kerala. Ministry of Health and Family Welfare 1601095

An interactive web-based dashboard to track covid-19 in real time

Seir and regression model based covid-19 outbreak predictions in india

Effect of weather on covid-19 spread in the us: A prediction model for india in 2020

Effects of weather and policy intervention on COVID-19 infection in Ghana. arXiv e-prints

The sensitivity and specificity analyses of ambient temperature and population size on the transmission rate of the novel coronavirus (covid-19) in different provinces of iran

No evidence for temperature-dependence of the covid-19 epidemic

Air pollutants and sars-cov-2 in 33 european countries

An Introduction to Mathematical Modeling of Infectious Diseases

Statistical analysis of the impact of environmental temperature on the exponential growth rate of cases infected by covid-19

Epitools: A python package for modelling and forecasting epidemic

Impact of environmental factors on covid-19 transmission: an overview

Effect of 2021 assembly election in india on covid-19 transmission

Evidence that higher temperatures are associated with a marginally lower incidence of covid-19 cases

Genome sequencing by insacog shows variants of concern and a novel variant in india, ministry of health and family welfare, government of india

Guidelines for international arrivals, ministry of health and family welfare, government of india

Comparative prediction of confirmed cases with covid-19 pandemic by machine learning, deterministic and stochastic sir models

Temperature dependence of covid-19 transmission

Role of temperature and humidity in the modulation of the doubling time of covid-19 cases

Modeling the effect of lockdown timing as a covid-19 control measure in countries with differing social contacts

A spatio-temporal analysis of the environmental correlates of covid-19 incidence in spain

Preliminary analysis of covid-19 spread in italy with an adaptive seird model

Relationship between average daily temperature and average cumulative daily rate of confirmed cases of covid-19

Seasonal influences on the spread of sars-cov-2 (covid19), causality, and forecastabililty (3-15-2020)

Seiar model with asymptomatic cohort and consequences to efficiency of quarantine government measures in covid-19 epidemic

Covid-19 transmission in mainland china is associated with temperature and humidity: A time-series analysis

Characterization of the second wave of covid-19 in india

Temperature, Humidity, and Latitude Analysis to Estimate Potential Spread and Seasonality of Coronavirus Disease 2019 (COVID-19)

Impact of meteorological factors on covid-19 pandemic: Evidence from top 20 countries with confirmed cases

Absolute humidity modulates influenza survival, transmission, and seasonality

Impact of temperature on the dynamics of the covid-19 outbreak in china

Does weather affect the growth rate of covid-19, a study to comprehend transmission dynamics on human health

Covid-19 spread and average temperature distribution in nigeria

Is temperature reducing the transmission of covid-19 ?

Correlation between weather and covid-19 pandemic in jakarta, indonesia

Effect of temperature on the infectivity of covid-19

Scipy 1.0: fundamental algorithms for scientific computing in python

Covid-19 weekly epidemiological update

Worldometer, 2020a. Coronavirus cases. Worldometer

Worldometer, 2020b. Countries in the world by population

Effects of temperature and humidity on the daily new cases and new deaths of covid-19 in 166 countries

Association between ambient temperature and covid-19 infection in 122 cities from china

Effects of temperature and humidity on the daily new cases and new deaths of covid-19 in 166 countries

Preliminary estimation of the basic reproduction number of novel coronavirus (2019-ncov) in china, from 2019 to 2020: A data-driven analysis in the early phase of the outbreak

J o u r n a l P r e -p r o o f

xThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:J o u r n a l P r e -p r o o f