Introduction

The Covid-19 virus appeared in Wuhan, China, in December 2019 and spread rapidly all over the world at a surprisingly fast rate. Many health experts believe the transmission of the new coronavirus to humans is likely caused by bats or pangolins (Ajibo, 2020). Due to the high infectious effect of the virus, the disease has been transmitted to many countries in a short time and, on 11 March 2020, the World Health Organization declared that Covid-19 as a pandemic because of its alarming spread and serious concern (Cirakli et al., 2021). In the last century, diseases such as the Russian flu in 1889, the Spanish flu in 1918, Severe Acute Respiratory Syndrome (SARS) in 2002, and the Ebola outbreak in 2014 have changed the way that both the world and people live. The Covid-19 pandemic is likely to have similar lasting effects (Morgan et al., 2021).

Covid-19, which soon spread all over the world, negatively affected not only the health sector but also socio-economic life. This pandemic primarily leads to many negative effects on most of the world’s economies such as closing of the economies, triggering a global crisis in health, and also destruction of social life due to strict quarantine measures. Hospitals and health workers around the world face catastrophic challenges associated with the Covid-19 pandemic. The economic dimension of the pandemic has a wide impact on a broad range of areas. For example, it has led to the temporary closure of many businesses in the service sector, brought the aerospace sector to a standstill with the closure of countries’ borders, and the retail sector to a standstill with the closure of large shopping centers. The main objective of the study is to provide policymakers and governments of nations with a better perspective by providing an overview of the observed and likely impacts of community movements on the Covid-19 pandemic. Mobility means people’s every kind of movement in public transportation, shopping malls, health institutions, parks, etc. It is important to determine the countries where this mobility is more effective in terms of the number of cases. Human mobility differs between countries. Therefore, the reason for the increase in the number of cases will be different for each country and will require different measures. The increase in the number of cases of countries has significant effects on both the health system and the economic sphere. Therefore, it is of great importance to identify measures that should be taken before the number of cases becomes severe. In the following sections of the study, the “Literature Review”, “Methodology”, and “Results” sections will be included, respectively.

Literature Review

Human mobility is about how people move in space and plays a crucial role in the transmission dynamics of infectious diseases in the spatiotemporal context. One of the main aims of this study is to provide a perspective in terms of revealing what opportunities and challenges exist for analyzing, modeling and predicting the spread of infectious diseases as a result of intensification of human mobility. There are many studies in the literature that analyze the relationship between mobility and Covid-19 from different perspectives (Hu et al. 2021; Martin & Bergmann 2021;  Palma et al. 2022).

The world has experienced many pandemics from past to present: smallpox, yellow fever, cholera, scarlet fever, typhoid, diphtheria, polio, whooping cough, measles, and influenza. Many infectious diseases in the past have shaped societies, social and economic life. Smallpox, for example, was one of the first outbreaks recorded in the USA. European immigrants brought the variola virus with them when they emigrated to the USA in the 1600 s, virtually wiping out the Native American population (Turner, 2020). In the past, such epidemics have been given remarkably little attention in the behavioral social sciences or even in the medical branches established in the social sciences (Huremović, 2019). The 1918 flu pandemic was one of the largest infectious outbreaks that spread around the world in less than 6 months, killing tens of millions of people (Patterson & Pyle, 1991). In the twentieth century, flu outbreaks in 1957 and 1968 resulted in death of nearly one million people (Ghendon, 1994).

In 1957, the world experienced a new influenza A (H2N2), the Asian flu. The virus originated in Singapore and then spread all over the world from Hong Kong and China. The next pandemic occurred about a decade later and originated in the USA as the H3N2 virus, a variation of the H2N2 virus. This flu contained two genes from an avian flu virus along with the enzyme from the 1957 H2N2 virus. H3N2 has mutated as a seasonal flu virus every year and still maintains a mutation state (Turner, 2020). The subsequent epidemic, known as severe acute respiratory syndrome (SARS), was life threatening in late 2002 as an outbreak, leading to a form of atypical pneumonia. In March 2003, the active ingredient was identified and passed into the literature as SARS coronavirus (SARS-CoV) (Kumar et al., 2016). The next epidemic in the literature, Middle East respiratory syndrome-coronavirus (MERS-CoV), was identified in 2012 as a new coronavirus (CoV) from a male Saudi Arabian patient who died of severe pneumonia (Memish & Al-Tawfiq, 2014).

The Covid-19 outbreak shocked world economies and social life. As this pandemic spread around the world, many experts were particularly concerned about two issues. The first is that as supply chains deteriorate, global food stocks begin to run out. The other is whether the existing health system can carry this burden in such a pandemic. Recently, numerous studies have investigated the effects of Covid-19 in a very broad range.

Some studies have focused on the effects of Covid-19 on public and private public health policies (Benítez et al., 2020; Berardi et al., 2020; Bukuluki et al., 2020; Fouda et al., 2020; Kennelly et al., 2020; Tiirinki et al., 2020). Accordingly, Fouda et al. (2020) study aims to provide an overview of the Covid-19 situation, health policies, and economic impacts in Greece, Iceland, New Zealand, and Singapore in their study. The common specificity of countries with different characteristics is to managed to control the pandemic at an early stage in terms of the total number of positive cases. The health system of these countries managed to absorb the shock and reduce the case mortality rate of Covid-19. In parallel with previous studies, Li and Mutchler (2020) analyzed the effects of Covid-19 on specific age groups. The paper found that one in five Americans age 65 and older live in places where high infection rates and high risks of economic insecurity occur at the same time. In contrast, Dang and Viet Nguyen (2021) addressed the effects of Covid-19 on gender inequality. In doing so, it used data from a six-country survey covering countries in different geographical locations and different income levels, and concluded that women are 24% more likely to permanently lose their jobs than men due to an outbreak of the disease. Gibson and Olivia’s (2020) study, which analyzes the direct and indirect effects of the virus on life expectancy and poverty, show that long-term reduction in real income reduces life expectancy.

Some other studies have focused on the economic effects of Covid-19 (Dash et al., 2021; Jena et al., 2021; Norouzi et al., 2020; Sharif et al., 2020; Takyi and Bentum-Ennin, 2020). For example, Hossain’s (2021) study focused on the impact of the Covid-19 pandemic on activities within the sharing economy (SE). The study used various publications such as news articles, TV news, YouTube videos and blog posts as data sources. Key results of the study through content analysis show how the SE phenomenon copes with the changing environment caused by Covid-19. Qin et al. (2020) investigated the short-term impact of pandemic shock on global value chains (GVC). The most affected sectors include electronics and optical equipment, textiles, machinery, manufacturing, and wholesale trade, with the most affected countries being the USA, South Korea, Japan, and Germany. Seeking answers to the question of whether the Covid-19 crisis has an impact on climate policies, Mintz-Woo et al. (2020) in their study, focus on carbon pricing in the form of carbon taxes or emissions trading. In various ways, the case for introducing a carbon price during the Covid-19 crisis is stronger than normal conditions. Supply and demand shocks have already become unstable and carbon pricing will allow this instability to reduce production in the long-run. Investigating its potential impact on stock market performance in 13 African countries, Takyi and Bentum-Ennin (2020) used a new Bayesian structural time series model (a state-space model) to assess and measure the absolute and relative impact of Covid-19. Evidence from the countries concerned shows that the Covid-19 pandemic had a significant negative impact on the equity markets of eight countries, while the five countries do not see a significant impact on the equity markets of Covid-19.

Covid-19, like other virus outbreaks, is transmitted by coughing, sneezing, breathing droplets spread by speech, or by taking the hands to the nose, mouth, and eye after touching the surfaces where the virus is found. Therefore, our main goal in this study will be to focus on the effects of human mobility on case numbers in five large metropolises where increase the risk of transmission in the context of Turkey.

Methodology

Wavelet theory is a method that allows separating the data into different frequency components and examining each matched component separately on the scale. The foundations of the wavelet theory were based on the work of the French mathematician Jean-Baptiste Joseph Fourier. This method called the Fourier transform allows the analysis of series on a frequency basis. However, when analyzing the time series, it was seen as a deficiency to consider only the frequency. The studies of Morlet and Grossmann laid the foundations of wavelet theory. They preferred to emit shorter waves at higher frequencies instead of examining geological mobility by emitting pulses equal to each other (Mallat, 2008).

If we examine a constant function defined as \(\varphi \epsilon {L}^{1}\left(R\right)\cap {L}^{2}(R)\); in the function, \(\varphi \epsilon {L}^{1}\left(R\right)\) alone may be sufficient, but the limitation of wavelet transform is guaranteed by assuming \(\varphi \epsilon {L}^{2}(R)\). In the form of \({\varphi }_{(b,a)};b \epsilon R and a \epsilon R\) (Carmona et al., 1998);

$${\varphi }_{\left(b,a\right)}\left(p\right)=\frac{1}{a}\varphi \left(\frac{x-b}{a}\right), x \epsilon R$$
(1)

In Eq. (1), \(\varphi\) can also be characterized as a sample of the original wave (\(\varphi\)) scaled by \(a\) and centered by b \(b\) around time. The continuous wavelet transformation (CWT) of this wave that has an end can be expressed as follows:

$${Y}_{p}\left(b,a\right)= \langle p, {\varphi }_{\left(b,a\right)}\rangle = \frac{1}{a}\int p\left(x\right)\varphi \left(\frac{\stackrel{-}{x-b}}{a}\right)dx$$
(2)

The \({Y}_{p}\left(b,a\right)\) value contains information about the p \(p\) signal on the x \(x\) scale around the b \(b\) point. In the equation, b \(b\) stands for the scale parameter, while a \(a\) stands for the position parameter. While p(x)\(p(x)\) is the function to be transformed, \({\varphi }_{\left(b,a\right)}(p)\) is the main wavelet function.

The wavelet spectrum of continuous data is calculated by the modules of the wavelet coefficients. Cross wavelet spectrum, on the other hand, is the process of finding common effects by multiplying the coefficients found after the wavelet transformations of two variables. For example, let the wavelet transforms of two variables defined as (P) and (R) are WP and WR, respectively.

$${W}_{PR}={W}_{P}{W}_{R}$$
(3)

If (P = R) is considered, the power spectrum of the wavelet is WPP = \({W}_{PP}={\left|{W}_{P}\right|}^{2}={WPS}_{P}\). In this case, the cross wavelet power is also as follows:

$${XWP}_{PR}=\left|{W}_{PR}\right|$$
(4)

Wavelet coherence indicates where two non-stationary variables have linear correlations in a given frequency band and which time period this frequency band indicates (Kılıç & Yıldırım, 2017).

The study examines the relationship between daily regional movement trends in different categories such as retail and recreation locations, grocery stores and pharmacies, parks, public transport stations, workplaces and housing in Brazil, the UK, and the USA, and the number of Covid 19 cases detected daily. The data consists of daily data covering the periods from 28/02/2020 to 08/02/2021, and this data is derived from Our World in Data database (https://ourworldindata.org/) and Google Mobility Reports. In order to observe the relationship between variables, the cross wavelet transform method was used using the MATLAB package program. While creating the methodology of this study, Iqbal et al. (2020) and Fareed et al. (2020) were supported by the studies.

Popularized by the work of Torrence and Compo (1988), CWT uses the wavelet coherence approach to outline the dynamic link between bivariate time series. In order to rationally explain wavelet coherence, cross wavelet power and cross wavelet transform are used. The cross wavelet transform helps to examine the correlation between two variables, and which variable affects the other variable. Making use of wavelet theory can provide some advantages while performing time series analysis. Time series that do not have a normal distribution can be used with wavelet theory. Also, the stationarity assumption can be relaxed by wavelet analysis. While performing the analysis, the series can be handled with both the time dimension and the frequency dimension. In this way, localized events in time can be detected more easily. In addition, the strength of the relationship between the variables can be determined in the short, medium, and long term (Grinsted et al., 2004; Vacha & Barunik, 2012).

Results

The colors in the bar on the right of the figures represent the increasing importance from blue to yellow (Fig. 1). The yellow colored islets represent regions where the power spectrum is concentrated. If the direction of the arrows in the figure points to the right, we understand that the two variables are in phase and there is a positive correlation relationship. If the arrows point to the left, we can state that the variables are out of phase and negatively correlated (Iqbal et al., 2020: 5). If the direction of the arrow is up, the independent variable leads the dependent variable. The opposite is true if the direction of the arrow is downward (Xuefeng et al., 2022). In the figures, the horizontal axis represents the time period, and the vertical axis represents each frequency band. The frequency progression continues as degrees of exponents of two. The arrows in the yellow area show the effect during the frequency period in the corresponding date range.

Fig. 1
figure 1

Covid-19 relationship with mobility change in grocery and pharmacies

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There are partial findings showing that mobility in the grocery shopping in Brazil affects the number of Covid-19 cases. This result shows that there is a correct directional relationship between mobility in grocery shopping and the number of cases. End of April, at the beginning of May, and in July the direction of the arrows shows that the mobility of grocery shopping affected the number of Covid-19 cases on average 128-day frequency in the significance area (yellow area in district convex area for Brazil). In areas that are slightly distorted to the left, it is observed that the two series move out of phase and have a negative correlation. In June and May in the UK, a change in mobility increased the number of Covid-19 cases at a frequency representing 128–256 days. In November, there is a simultaneous and positive correlation between these two variables at an average frequency of 128 days. In December 2020 and January 2021, the change in mobility affected Covid-19 case numbers at the 64-daily frequency. From February to September in the USA, a positive correlation was observed between the two variables at a frequency of 16–32 days. In December 2020 and January 2021, it is observed that mobility changes in grocery stores and pharmacies with an average frequency of 256 days affect the number of Covid-19 cases.

In Fig. 2, the change in mobility in parks in Brazil appears to have had a significant impact on the change in the number of Covid-19 cases. In the period from early April to the middle of May, the change in mobility in parks and gardens affects the number of Covid-19 cases at 32–64 day frequencies. However, from May to the end of August, the change in mobility in parks is observed to affect Covid-19 cases at an average frequency of 128 days. The fact that the direction of the arrows is right up during this period means that there is both a strong correlation and causality from mobility to Covid-19. Similar movements to this result are seen in December. In the UK, however, the impact of mobility changes in parking spaces on Covid-19 case numbers is very low. In May, the region with a positive correlation between two variables (mobility in parks and the number of Covid-19 cases) corresponds to the frequency band 256–524. In the same frequency band, there is a small area that indicates that mobility affects the number of cases in November. From February to June, mobility variation in parking spaces in America has a simultaneous positive correlation with Covid-19 case numbers at a frequency of 16–32 days. In periods other than this period, there is an out-of-phase relationship.

Fig. 2
figure 2

Covid-19 relationship with mobility change in parking spaces

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In Fig. 3, in Brazil, it is observed that the relationship between variables at an average frequency of 128 days in the period from June to October has a positive correlation and they move simultaneously. In the period corresponding to July, mobility in residences led to the number of Covid-19 cases. In the UK, it is seen that mobility change in the 128-day frequency band in May led to the number of Covid-19 cases. In November, February, December 2020, and February 2021 period, the average 128-day frequency band of the two variables appears to have simultaneous and positive correlation. In America, the variables of mobility change and number of cases show simultaneous positive correlations at frequencies of 128–256 days from April to the end of December and at frequencies of 32–64 days between November 2020 and February 2021.

Fig. 3
figure 3

Covid-19 relationship with mobility change in residences

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Figure 4 shows the relationship between mobility variation of retail locations for the respective countries and Covid-19 case numbers. From April to October, one can say that mobility has an effect on Covid-19 cases at a frequency that covers the range of 128–256 days, according to the relationship between these variables in Brazil. From February to July 2020, however, in the UK, there is simultaneous positive correlation between the two variables at 128–256 daily frequencies, and largely mobility leads the number of cases. A similar correlation relationship is also observed at 64–128 day frequencies in periods covering the end of 2020 and February 2021. In February and August 2020 in the USA, it has a simultaneous and positive correlation with an average frequency of 32 days, and covid cases appear to affect mobility. Between April and September 2020, there is a simultaneous and positive correlation between the two variables at 128-day frequencies.

Fig. 4
figure 4

Covid-19 relationship with mobility change in retail locations

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April and July periods for Brazil in Fig. 5 show a correlation between two variables in the 32–64-day frequency band range. Due to the change in the Covid-19 outbreak in April, it is observed that the change in mobility has increased. In the UK, there is no significant relationship between the mobility change in public transport stations and the number of cases in low frequency bands. In between February and August 2020 in America, covid cases with an average frequency of 32 days affect mobility at public transport stations, and there is a simultaneous positive correlation. In January 2021, it was observed that mobility affects the number of cases at 128–256 daily frequencies.

Fig. 5
figure 5

Covid-19 relationship with mobility change at public transport stations

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In Brazil, the relationship between workplace mobility and Covid-19 case numbers occurred at low frequencies in some periods, while no significant interaction was observed at high frequency values (Fig. 6). During from February to May, Covid-19 cases were observed to affect mobility in workplaces. But from August to October period, the shift in mobility at work in the 64-day frequency band was found to affect Covid-19. In the UK, when the impact of mobility changes at work on the number of cases was examined, it was concluded that the relationship was largely out of phase and that there was a negative correlation. Between February and June periods of 2020 in America, the 32-day frequency Covid-19 affects workplace mobility, and they appear to have a simultaneous positive correlation. It is seen that mobility at frequencies of 64 days in the period of July 2020 and September 2020 and at a frequency of 256 days around January 2021 affects Covid-19.

Fig. 6
figure 6

Covid-19 relationship with mobility change at work

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Conclusion

The Covid-19 outbreak has significantly affected the entire world from a health, social and economic point of view. This article explored the effects of interventions implemented by policymakers on health and non-health outcomes in terms of mobility and number of cases. As the number of cases and death rates reached frightening figures, governments took various measures to restrict mobility to control Covid-19 disease. As a result, such a situation has led to a break in the economic chain, especially in the transport, tourism, and retail sectors, which has led to the closure of many economic sectors and therefore to an increase in unemployment rates.

The results of the paper on a country-by-country basis can be summarized as follows: mobility in grocery stores and pharmacies can be said to have an impact on the number of cases in all three countries. However, it seems that this result occurs in America with a frequency of 16–32 days, with a frequency of 128 days for the other two countries. Brazil is the country where mobility in parks has the strongest impact. February–April 2020 and November 2020–February 2021 periods, while the average frequency period in the countries in the effect of mobility in the residence pointed to 256 days, this decreased to 32–64 days period in the period of November 2020–February 2021 period. This result means that people’s mobility in residences increases with the lengthening of restrictions and affects an increase in the number of cases. The lowest frequency country in retail outlets is America. While the lowest frequency in public transport was detected for Brazil, no significant results were found for the UK. The impact of mobility at work has a negative correlation for the UK and a positive correlation for other countries.

This study provides an analysis within the framework of public health strategies such as isolation, quarantine, social distance, and community containment that have historically been adopted for the control of outbreaks during periods when vaccines and antivirals were not available. In this context, according to the results of the study, policymakers should tighten their measures, especially for regions where frequency values are low and correlation is present. such pandemics are transmitted through respiratory droplets. For this reason, a certain social distance can be applied to avoid transmission in places with low frequency. In this way, transmission can be reduced. In places where the transmission rate is high, social distance rules include a process that goes from reducing the number of people to isolation. Brazil has been the country most affected by the rate of transmission by mobility. Considering the fact that Brazil has a lower per capita income compared to other countries, it has been observed that strict measures are not implemented from time to time, taking into account the negative effects of macroeconomic variables such as unemployment and inflation. It is considered important that one of the most important results we need to draw from the Covid-19 experience we have is this issue. Regardless of whether it is a developed or developing country, in order to act jointly against the disease all over the world, overcoming the negative economic tables that may arise in countries with low per capita income with the support of all countries of the world can be considered as a method that can help in ending pandemics. In the early stages of the Covid-19 pandemic, the president of Brazil, J. Bolsonaro and British Prime Minister B. Johnson have not implemented strict policies. Therefore, one can analyze countries that implement stricter policies for later study.