key: cord-0877955-vj1zsiu1 authors: Borah, Manash Jyoti; Hazarika, Bipan; Panda, Sumati Kumari; Nieto, Juan Jose title: Examining the correlation between the weather conditions and COVID-19 pandemic in India: A mathematical evidence date: 2020-11-18 journal: Results Phys DOI: 10.1016/j.rinp.2020.103587 sha: c979c4169aa681e7629bede5a6793161afb84565 doc_id: 877955 cord_uid: vj1zsiu1 In this article, for the analysis of Covid-19 progression in India, we present new insights to formulate a data-driven epidemic model and approximation algorithm using the real data on infection, recovery and death cases with respect to weather in the view of mathematical variables. The impact of environmental conditions on virus transmission has always been an important discussion topic among the investigators. Studies pertinent to West Nile Virus studies in the United States and Europe declare the connection between climate conditions and SARS-CoV and imply that weather variable might even be the source of metabolic pathways between SARS-CoV and humans. The environment is very strongly correlated with pneumonia-related improvements in mortality rates and death rates. The spread of the virus infections is affected by multiple factors, such as clouding, temperature, humidity and density of population. Correlation between the weather conditions and COVID-19 in Jakarta, Indonesia and claimed essential findings in this direction. In the Indian perspective, COVID-19 investigation is very restricted, in particular, the impact of climate change on the COVID-19 pandemic. Undoubtedly the present study will serve as new insight in this direction and will be useful for further analysis to arrive at a precise conclusion. In statistical methods, among the most critical problems when concerned with data is the correlation coefficient. The coefficient of correlation r (Pearson's Coefficient), proposed by Karl Pearson in 1885, is now one of the most commonly used indices. It has been proven to be a powerful tool in data processing, psychological disorders, market research, pattern classification, and in particular for problems in strategic decisions. Gerstenkorn and Manko [13] , formulated the correlation coefficients of intuitionistic fuzzy sets (shortly, IFSs), which were subsequently studied by Szmidt and Kacprzyk [34] , Bustince and Burillo [8] , further expanded November 11, 2020. the principles of correlation and correlation coefficient for interval-valued intuitionistic fuzzy sets (shortly, IVIFSs). Hung and Wu [15] suggested a strategy for using centroid to find the correlation coefficients of IFSs. IFSs also seems to be vital importance, so in this direction, several reports have addressed the A-IFS correlation. In most other papers (Gersternkorn and Mańko [13] , Hong and Hwang [14] , Hung and Wu [15] ), a pro and con type of relationship is represented. However, no account has been taken of its third term describing an A-IFS, the hesitation margin in addition to the membership and non-membership degrees shown to be significant from the perspective of similarity, distance or entropy measures (cf. Szmidt and Kacprzyk, e.g., [31, 32, 33, 34, 35] ). Molodtsov [25] introduced the concept fuzzy soft set theory in 1999, and it was greatly extended in wide directions by Maji et. al., [20, 21, 22] . Numerous researchers subsequently worked on several aspects of fuzzy soft sets, which are intuitive fuzzy soft sets [23] , interval-valued fuzzy soft sets [40] , intuition-valued fuzzy soft sets [16] etc. Correlation coefficient analysis is one of the important components of fuzzy soft sets. Das et al. [12] investigated the problem of measuring the correlation between the hesitant fuzzy soft sets. For similarity measurements of soft sets and related implementations, readers can also see [5, 6, 7] . 2019-nCoV terrifies the world. The virus first seen in Wuhan, China, has spread through continents. The increase in deaths in Italy, Spain, the US, and other countries has worried advanced and emerging economies countries alike. The smallest creature, invisible to the eye, questions the existence of humankind. Covid-19 combat is still in its early stages. Researchers [1, 4, 24, 27, 28, 29] are currently working on multiple investigative paths. The first case of the novel coronavirus disease 2019 (COVID-19) was identified at the end of 2019 in the city of Wuhan China, which is the provincial capital of Hubei. After acquiring pneumonia without a specific cause and the available vaccine or therapies be not successful for that. Furthermore, the virus is shown to be transmitted from person -to -person. The spread not only across the city of Wuhan but also across the other cities of China. Besides, the disease mutates to other areas of the globe, including Europe, North America and Asia-pacific regions. It is known that it takes 2 to 14 days for symptoms to emerge. The symptoms entail coughing, difficulty breathing and fever. The World Health Organization There are 190,006 diagnosed cases and a death rate of 15,309. The fatality rate for India is relatively low, at 3.09. On March 22, 2020, India implemented a 14-hour volunteer public curfew accompanied by a nationwide lockdown since March 24, 2020, in response to many other steps such as quarantine of suspicious cases, social distance guidelines for public health, regular personal hygiene and wearing face masks when leaving home for critical services. India's government is considering several lockdowns to avoid the virus from spreading. Initially, in lockdown 1.0 (March 25, 2020, to April 14, 2020), the whole nation was under total lockdown except for essential public services, and lockdown 2.0 (April 15, 2020, to May 3, 2020) was enacted with relaxation in regions where the virus has consisted and lockdown 3.0 (May 4, 2020, to May 17, 2020) with more relaxation in areas where there would be fewer cases of corona-virus. Lockdown 4.0 (May 18, 2020, to May 31, 2020) with certain significant exemptions, allowing for all commercial development and sizeable international movement. With further relaxation after this Unlock 1.0 (June 1, 2020, to June 30, 2020) and Unlock 2.0 (July 1, 2020, to July 31, 2020) are introduced. Intend to note that, on these lockdowns, the number of cases has been decreased. Human-to-human replication, meteorological parameters are believed to be important influences in the feasibility, propagation, and range of virus spread (Chan et al. [9] , Van Doremalen et al. [38] ). Zhu and Xie [42] studied the correlation among temperature and COVID-19 contamination in China and reported a positive linear relationship between average temperatures and the number of COVID-19 cases when the temperature is below 3 • C,. Also, Tosepu et al. [37] explored the relation in between the weather and the COVID-19 pandemic in Indonesia and concluded that the mean temperature of ( • C), is associated with the COVID-19 pandemic. Ma et al. [18] evaluated the influence of temperature and humidity variation on COVID-19 deaths, and asserted that these parameters affect COVID-19 mortality. Chen et al. [10] explored the correlation between meteorological parameters and COVID-19 severity spread worldwide and concluded that air density, temperature, and relative humidity are effective variables. Wang et al. [39] analysed the impact of temperature on COVID-19 spread and reported that COVID-19 transmission is strongly impacted by temperature. The most general objective of this research is to examine the correlation between both the meteorological parameters and pandemic COVID-19. In order to increase the possibility of success against this life-threatening pandemic, the dynamic aspects of SARS-CoV-2 invasion involve cooperation of scientists from multiple disciplines including medical, scientific, and engineering areas [2, 17, 26, 30, 36, 45, 46, 47, 48, 49, 50, 51] . We structure our article as follows: Some preliminary findings are given in section 2. The definition of correlation between the AIFSSs was discussed in section 3. We also suggested the idea of the correlation between the intuitionistic fuzzy soft-points of the Atanassov. In section 4 and 5, we present an application followed by a discussion on A-IFSSs pertinent to Covid-19. In this section we recall some basic concepts and definitions regarding fuzzy sets and fuzzy soft sets. [41] Let X be a universe of discourse, then a fuzzy set is defined as, Atanassov continued to expand the Fuzzy set to the IFS, as shown: The number µ A (x) and ν A (x) represent, respectively, the membership degree and non-membership degree of the element x to the set A. If A and B are two intuitionistic fuzzy sets of the set X, Then Definition 2.5. [11] Suppose now that we have a random sample x 1 , x 2 , x 3 , ..., xn ∈ X with a sequence of paired data that correspond to the membership values of fuzzy sets A and B defined on X, then the correlation coefficient r f (A, B) is given as: Definition 2.6. [22] Let U be an initial universe and F be a set of parameters. LetP (U ) denote the power set of U and A be a In our studies, we consider all Attanssov's intuionistic fuzzy sets inP (U ), of [19] i.e our new definition is is defined asr Proof. (i) Obvious. (ii) For t = 1, 2, 3, ..., n; i = 1, 2, 3, ..., m and j = 1, 2, 3, ..., p. Let G B = F A , then i = j and p = m. Thereforẽ Similarly,r 2 (F A , G B ) = 1, andr 3 (F A , G B ) = 1. (iii) Obvious. Therefore,r 1 (ẽ 1 (F A ),ẽ 3 (G B )) = −1.00;r 2 (ẽ 1 (F A ),ẽ 3 (G B )) = −1.00;r 3 (ẽ 1 (F A ),ẽ 3 (G B )) = −0.180. Proposition 3.7. Letẽ i (F A ) andẽ j (G B ) be two A-IFSSs over in (U, E). Then Proof. (i) Obvious. (ii) For t = 1, 2, 3, ..., n; i = 1, 2, 3, ..., m and j = 1, 2, 3, ..., p. Letẽ j (G B ) =ẽ i (F A ), then i = j and p = m. Thereforẽ (iii) Obvious. Now India has become largest affected country of Covid-19 in Asia. It is easy to see that the virus scattered across the country We used the following algorithms. Step(i) To collect maximum, minimum and average temperature data of five states from timeanddate dot com in tabular form. Step(ii) To convert Step (i) data to decimal form. Step(iii) To collect maximum, minimum and average humidity data of five states from timeanddate.com in tabular form. Step(iv) To convert Step (iii) data to decimal form. Step(v) To Collect data of five states from crowdsourced database of COVID-19 India dot org. Step(vi) To convert Step (v) data to decimal form. Step(vii) Find the correlation between A-IFSSs of Step (ii) and Step (vi). Step(viii) Arranged Step(ii) data as average, maximum and minimum then find the correlation between A-IFSSs of arranged data and Step (vi). Step(ix) Arranged Step(ii) data as minimum,average and maximum then find the correlation between A-IFSSs of arranged data and Step (vi). Step(x) Find the correlation between A-IFSSs of Step (iv) and Step (vi). Step(xi) Arranged Step(iv) data as average, maximum and minimum then find the correlation between A-IFSSs of arranged data and Step (vi). Step(xii) Arranged Step(iv) data as minimum,average and maximum then find the correlation between A-IFSSs of arranged data and Step (vi). Step(xiii) finally expressed Step (vii), Step (viii), Step (ix), Step (x), Step (xi) and Step (xii) in tabular form. The data from the table 3 has been summarized in the line graph (FIGURE 1) below. The data from the table 7 has been summarized in the line graph (FIGURE 3) below. Average and Maximum) and the number of total cases (as Active, Recovered and Decreased) in each state is evaluated. Similar way, we have found the correlation between humidity and the total number of cases. The data from the table 3 and 5 has been Table 1 ,2,4 and Table 6 . Moreover, Table 8 presents the result of correlation analysis. The results indicate that the temperature and humidity are maximum, the active cases and deceased are inverse correlation. The correlation is inverse, which implies that as the temperature and humidity are lower, the number of cases increase. Again the temperature is maximum than the Recovered cases are positive correlation and humidity is average than the recovered cases are positive correlation. The weather parameters are an important factor in determining the occurrence rate of Covid-19 in India. Our findings provide preliminary evidence that the Covid-19 pandemic may be partially suppressed with temperature and humidity increases in India. A few words about possible extensions of the preceding conclusions: • Fixed point method for correlation between the weather conditions and 2019-nCoV model of type SEIARM in USA via fuzzy sets. • Fixed point method for correlation between the weather conditions and 2019-nCoV model of type SCIRD in Brazil via fuzzy sets. • Fixed point method for correlation between the weather conditions and 2019-nCoV model of type SIDARTHE in India via fuzzy sets. Competing Interest: The authors declare that they have no competing interests. Data Availability: No data were used to support this study. Authors Contributions: MJB, BH and PSK formulated the problem. BH and PSK developed the theory and performed the computations. BH, PSK and JJN drafted and aligned the manuscript sequentially, thereafter verified the analytical methods. The four authors read and approved the final manuscript. 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Nieto has been partially supported by the Agencia Estatal de Investigacion (AEI) of Spain, co-financed by the European Fund for Regional Development (FEDER) corresponding to the 2014--2020 multi year financial framework, project MTM2016-75140-P; Xunta de Galicia under grant ED431C 2019/02; and Instituto de Salud Carlos III, grant COV20/00617.