Abstract
The COVID-19 global pandemic has significantly impacted people throughout the United States and the World. While it was initially believed the virus was transmitted from animal to human, person-to-person transmission is now recognized as the main source of community spread. This article integrates data into physics-based models to analyze stability of the rapid COVID-19 growth and to obtain a data-driven model for spread dynamics among the human population. The proposed mass-conservation model is used to learn the parameters of pandemic growth and to predict the growth of total cases, deaths, and recoveries over a finite future time horizon. The proposed finite-time prediction model is validated by finite-time estimation of the total numbers of infected cases, deaths, and recoveries in the United States from March 12, 2020 to December 9, 2020.
Keywords: Finite-time estimation, finite-time modding, pandemic growth stability
I. Introduction
The first confirmed case of COVID-19 was identified in Wuhan, China, in December 2019 and the virus has rapidly grown across the world since then. Studies have shown that the virus is dominantly transmitted through close contact with infected people and contaminated surfaces as well as respiratory droplets [1], [2]. Recent studies support that the incubation period of the disease is within 14 days [3], [4]. However, there is uncertainty about the median incubation period of the virus as researchers have reported median incubation periods of 4 days [4], 5.1 days [5], and 6.4 days [6]. Metapopulation Dynamics [7]–[9], Mean-Field Theory [10]–[13], the SIR method [14], [15], and SEIR dynamics [16]–[18] are existing models used to estimate the dynamics of infectious disease. Atkeson applies the SIR model to estimate and evaluate the negative impacts of the growth of COVID 19 in the United States. Metapopulation Dynamics is used in [19] to evaluate the impact of domestic and international travel on the spread of COVID-19. The SEIR model was used to analyze the epidemic of COVID-19 in mainland China [20] and the Diamond Princess cruise ship [21]. Fanelli and Piazza [12] applies mean-field theory to analyze and predict the spread of COVID-19 in China, Italy, and France. Also, van Doremalen et al. [2] applies a Bayesian regression model to analyze the aerosol stability of COVID-19.
Several researchers have studied the negative impacts of COVID-19 on daily life. Negative psychological outcomes of COVID-19 were studied [22]–[24]. Zhang and Ma [28] and Liang et al. [29] investigated the influences of the COVID-19 outbreak on mental health and family support in China. Researchers have also investigated the negative impacts of COVID-19 on the economy [27]–[30], environment [31], gender equality, education [32], healthcare system [33], tourism [34], [35], agriculture, food security, and supply chain management [36].
The COVID 19 global pandemic has had a devastating impact throughout the United States and the world. To date, more than 46 900 000 confirmed cases have been identified and there have been 1 210 000 deaths worldwide. The numbers are still increasing and being updated daily by the World Health Organization [37], Centers for Disease Control and Prevention [1], and European Centre for Disease Prevention and Control [38]. The delay in responding effectively to the pandemic spread has exacerbated its negative impacts on public health, economy, education, and other sectors across the World, and revealed an urgent need for a plan. The ever-evolving consequences of COVID-19 and inevitable future pandemics will be better controlled if knowledge is gained from this outbreak to support construction and validation of a more informed pandemic model and intervention plan.
The primary objective of this article is to develop a data-driven model for finite-time estimation of the growth of a pandemic across the human population to effectively predict the spread of disease. This model can facilitate taking required preventive nonpharmaceutical interventions when there is no vaccine available. To this end, we first apply the mass conservation law to model evolution of the total number of cases, deaths, and recoveries across the human population. We then develop a constrained optimization problem to obtain parameters of the proposed dynamics based on statistics of the number of infected cases, deaths, and recoveries recorded in a time-sliding window. By learning the parameters of the proposed model, we develop a finite-time dynamics model to continuously predict the number of infection cases, deaths, and recoveries within a finite number of future days. The proposed prediction dynamics is validated by finite time estimation of COVID-19 infection cases, deaths, and recoveries in the United States from March 12, 2020 to December 9, 2020. Compared to the existing Mean-Field Theoretic, SIR, and SEIR models, our proposed method can estimate the growth of a pandemic for a shorter future time horizon but with better accuracy. This is because the proposed method consistently learns and incorporates real-time data into growth modeling of the outbreak disease. As the result partial information about incubation period and exposure to the virus has minimal impact on predicting the spread of the pandemic disease.
The secondary objective of this article is provide a criterion for stability of a pandemic. In particular, the proposed stability criterion is applied to analyze the stability of the growth of COVID-19 in the United States where the publicly available data provided in [39] is used to incorporate day-to-day information about the number of confirmed cases, deaths, and recoveries into modeling of spread dynamics.
This article is organized as follows. A problem statement presented in SectionII is followed by stability analysis and parameter estimation approaches developed in SectionIII. A novel finite-state prediction dynamics are obtained in SectionIII-B. Results are presented in SectionV followed by concluding remarks in SectionVI.
II. Problem Statement
Let
be the total number of cases with confirmed disease,
be the total number of deaths,
be the total number of recovered cases,
be the total number of new infected cases,
be the number of new deaths, and
be the number of new recovered cases. Using the mass conversation law, the spread dynamics of COVID-19 is given by
 |
where
denotes a calendar day,
is the state vector, and
is the input vector. This article assumes that the existing data of COVID-19 is valid, thus,
is observable at every day
from the establishment of the pandemic. Given the total number of confirmed cases, deaths, and recoveries, the number of active cases becomes
 |
The underlying mass-conservation model is also used to estimate the growth of COVID-19. We define
and
as the estimations of the actual state vector
and the actual input vector
at day
, where the estimation of the growth of the pandemic is modeled by dynamics
 |
Estimations of new total cases, denoted by
, new deaths, denoted by
, and new recoveries, denoted by
, are defined as follows:
 |
where
,
, and
.
Given the above problem specification, the main objective of this article is to study the following two problems.
-
1)
Problem 1—Estimation and Stability Analysis of Pandemic Growth Dynamics: We use the underlying mass conservation law to obtain
,
,
, and
for
at day
such that estimation vector
converges to actual state vector
. We also analyze the stability of the growth of COVID-19 by analyzing the stability of estimation dynamics (3). -
2)
Problem 2—Growth Prediction: Assuming the total number of infected cases, deaths, and recoveries are known in a time sliding window of length
at days
,
, and
, we propose a model based on mass conservation to predict the infected cases, deaths, and recoveries within the next
days, at days
,
, and
.
III. Estimation of COVID-19 Spread
We first use the mass conservation law to obtain a data-driven time-varying dynamics in Section III-A to model the spread of COVID-19. We then propose an optimization problem in SectionIII-B to determine parameters of the proposed model by relying on the existing data of COVID-19.
A. Estimation Dynamics
Let active cases given by (2) be expressed as follows:
 |
where
 |
By knowing
, we can use (4) and express
,
, and
as follows:
 |
where
 |
Substituting
and (8b), matrix
is obtained as follows:
 |
for
at discrete time
. Replacing
by (7), the estimation dynamics (3) is converted to
 |
for
and
, where
is the identity matrix. Fig. 1 shows a block diagram of estimation dynamics (10).
Fig. 1.
Block diagram of the proposed mass-conservation model for the spread of a pandemic disease.
1). Finite-Time Estimation Dynamics:
Define vector
 |
providing estimated number of infected cases, deaths, and recoveries in the past
days for day
. If
is updated by (10),
is updated by finite-time estimation dynamics
 |
where
 |
It is noted that
is the identity matrix and
is a zero-entry matrix.
2). Dynamics of Spread of Active Cases:
By considering (2), (6), and (8a), the estimation dynamics (10) can be expressed as follows:
 |
Premultiplying both sides of (14) by
, (14) is converted to
 |
Now, define
 |
at day
for
. We can replace
,
, and
by
,
, and
, respectively, in (15). Then, dynamics of spread of active cases is given by
 |
Theorem 1:
The growth of active cases, governed by dynamics (17), reaches the stability if there exists a day
such that eigenvalues of matrix
are all inside the unit disk centered at the origin at every day
.
Proof:
Given the spread dynamics (3) with control input
defined by (4), the dynamics of the growth of active cases becomes
where
Eigenvalues
,
,
are the roots of the following characteristic polynomial:
The growth of active cases achieves stability at day
if the eigenvalues of matrix
all occur inside the unit disk centered at the origin at every
. If
achieves stability at time
, then
,
,
, defined by (4), reach stability at time
.
B. Parameter Estimation
Let set
 |
define possible incubation periods of COVID-19 ranging from one day to
days. We define
 |
as the cost function for determining
,
,
,
, where
is positive-definite and diagonal, and the gain vectors
,
,
are candidates for
,
,
per (8b). This articleuses
to obtain presented results.
1). Matrix
:
Weight matrix
is a positive-definite and diagonal matrix defined based on the likelihood of the incubation period of COVID-19. We use the longnormal distribution to estimate the incubation period of COVID-19 by
 |
where
and
are the median and standard deviation of the distribution where
. Per the results reported in [40],
and
are chosen to determine matrix
.
2). Assignment of
and Gains K1,
,
The cost function Ch depends on real-valued vectors
,
,
and discrete-valued variable
. We determine
,
,
, and
by solving the following optimization problem:
 |
subject to inequality constraints
 |
and equality constraint
 |
where
. By solving the above optimization problem,
,
,
, and
are used to assign matrix
, defined in (13).
Remark 1:
For
,
,
,
denote the optimal gain vectors obtained by solving the following quadratic programming optimization problem with linear equality and inequality constraints:
subject to constraints (26) and (27). Then, we can write
where
and
,
,
are assigned by solving (28) subject to constraints (26) and (27). Hence
and
. The flowchart on the left-hand side of Fig. 1 and the algorithm presented in Table I provides a method for solving the above optimization problem.
Define
 |
and
 |
for
where “vec” is the matrix vectorization operator. The inner-loop constrained quadratic optimization problem (28), presented in Remark (1), can be defined as follows:
 |
for
subject to
 |
where
is a zero-entry matrix and
is the Kronecker product symbol. We use the MATLAB command “quadprog” to obtain gain vectors
,
,
for
. More specifically,
 |
for
where
is the solution of the above quadratic programming problem, minimizing cost function (30) and satisfying constraints (31a) and (31b), and
is the Kronecker delta defined as follows:
 |
By knowing matrix
at day
, a prediction dynamics is developed in Section IV to estimate the number of infected cases, deaths, and recoveries within the next
days.
IV. Finite-Step Prediction Dynamics
Let
,
,
be known at day
. Prediction of the state
at day
is denoted by
where
,
, and
are the predictions for the total numbers of infected cases, deaths, and recoveries at day
. Note that subscript “p” denote “prediction” and
predicts total infected cases, deaths, and recoveries at day
where
. We define the prediction state vector
where
 |
It is noted that
if
.
is updated by the following prediction dynamics:
 |
subject to initial condition
 |
where
,
is the identity matrix, and
is the output vector of prediction dynamics (34).
Algorithm 1.
Assignment of
and Gain Vectors
at Day
V. Results
We consider the spread of COVID-19 in the United States over 272 days from March 12, 2020 to December 9, 2020 where the number of infected cases (
), deaths (
), and recoveries (
) are incorporated from [39] for
. We chose
to obtain parameters of the proposed model. Therefore, the statistics of the first 14 days, from March 12 to March 25, are only used to learn parameters of the proposed model for
, and we predict the growth of the total infected cases, deaths, and recoveries after March 26, 2020. As a result, the plots provided in this section do not provide information for
.
We obtain gains
,
,
and
by solving optimization problem (25) subject to constraints (26) and (27). In Fig. 2,
is plotted versus
for days 15 through 272. It is seen that
for
. Therefore,
,
,
, and matrix
are computed for every
. Eigenvalues of matrix
are plotted versus
in Fig. 3. One of the eigenvalues of matrix
that has the largest magnitude at day
is considered as the first eigenvalue of matrix
. It is seen that the magnitude of the first eigenvalue of matrix
fluctuates near 1 while the magnitudes of the remaining eigenvalues of matrix
are all between 0 and 1 for
. Additionally, we observe that the magnitude of the first eigenvalue of matrix
is greater than 1 every day after October 12, 2020 (
).
Fig. 2.
versus day
.
Fig. 3.
Eigenvalues of matrix
.
Therefore, the growth of the total infected cases, deaths, and recoveries have not reached stability although the magnitudes of eigenvalues of matrix
are all less than 1 some days after March 12, 2020.
In Figs. 4–6 actual and predicted numbers of infected cases, deaths, and recoveries are plotted for
through
. To quantify the error of the proposed prediction model, we define
 |
as the relative error formulas in predicting the numbers of infected cases, deaths, and recoveries at day
. In Figs. 7–9, relative errors in predicting the total infected cases, deaths, and recoveries are plotted for
at day
. It is seen that the relative errors are significantly decreased after
.
Fig. 4.
Total number of infected cases for
. (a) Total number of infected cases reported in [39]. The predicted numbers of infected cases are shown by red, green, black, cyan, and orange for (b)
, (c)
, (d)
, (e)
, and (f)
, respectively.
Fig. 5.
Total number of deaths for
: (a) Total number of deaths reported in [39]. The predicted numbers of deaths are shown by red, green, black, cyan, and orange for (b)
, (c)
, (d)
, (e)
, and (f)
, respectively. (a) Actual number of deaths. (b) Predicted deaths for
. (c) Predicted deaths for
. (d) Predicted deaths for
. (e) Predicted deaths for
. (f) Predicted deaths for
.
Fig. 6.
Total number of recoveries for
: (a) Total number of recoveries reported in [39]. The predicted numbers of recoveries are shown by red, green, black, cyan, and orange for (b)
, (c)
, (d)
, (e)
, and (f)
, respectively.
Fig. 7.
Relative error of finite-time prediction of infected cases for
at day
.
Fig. 8.
Relative error of finite-time prediction of deaths for
at day
.
Fig. 9.
Relative error of finite-time prediction of recoveries for
at day
.
VI. Conclusion and Future Work
This article described a new data-driven approach, inspired by the law of mass conservation, to model and analyze the stability of COVID-19 spread dynamics. We developed an algorithm to learn the parameters of the proposed mass conservation-based model based on the history of infected cases, deaths, and recoveries recorded in time sliding windows. We used the history of total infected cases, deaths, and recoveries to develop a prediction model for estimating the numbers of infected cases, deaths, and recoveries within a receding finite time horizon. We evaluated the accuracy of the proposed prediction model by estimating the statistics of COVID-19 in the United States from March 12, 2020 to December 9, 2020. Results show that the relative estimation errors of the total number of infected cases, deaths, and recoveries are less than 3% after June 1.
The results of our model show that COVID-19 growth is unstable for all days after October 12, 2020 per Fig. 3. This result is consistent with the status of pandemic growth in the United States after mid-October. As shown in Fig. 10, the total number of new COVID-19 cases has significantly increased in the United States after October 12, 2020.
Fig. 10.
New infected cases at day
.
In future work, we plan to determine the underlying relation between control gains
,
,
,
,
,
,
,
,
and state-wide and nationwide executive order release in the United States. To this end, we will use the existing SIR model to obtain the projection of disease spread and model the pandemic by an autonomous dynamics. By comparing the projected SIR dynamics and the nonautonomous conservation-based dynamics proposed in this article, control gains can be quantified and related to executive orders for every US state/district.
Furthermore, we plan to develop a novel decision-making model for optimal planning of infection control actions in the presence of uncertainty and ambiguity. More specifically, we will apply the finite-estimation model, proposed in this article, to model the spread of a pandemic disease as a Markov process with a Markov decision process (MDPs) applied to optimize nonpharmaceutical actions under a full-state observability assumption. The proposed decision-making model can also be applied to evaluate the effectiveness of statewide and nationwide orders and recommendations aimed at avoiding or mitigating rapid case growth.
Funding Statement
This work was supported by the National Science Foundation under Award 1914581 and Award 1739525.
Contributor Information
Hossein Rastgoftar, Email: hossein.rastgoftar@villanova,edu.
Ella Atkins, Email: ematkins@umich.edu.
References
- [1].C for Disease Control and Prevention. (2020). Coronavirus (COVID-19). [Online]. Available: https://www.cdc.gov/coronavirus/2019-ncov/index.html
- [2].van Doremalen N.et al. , “Aerosol and surface stability of SARS-CoV-2 as compared with SARS-CoV-1,” New England J. Med., vol. 382, pp. 1564–1567, Apr. 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [3].Li Q.et al. , “Early transmission dynamics in Wuhan, China, of novel coronavirus–infected pneumonia,” New England J. Med., pp. 1200–1207, Jan. 2020. [DOI] [PMC free article] [PubMed]
- [4].Eastin C. and Eastin T., “Clinical characteristics of coronavirus disease 2019 in China,” J. Emergency Med., vol. 58, no. 4, pp. 711–712, Apr. 2020. [Google Scholar]
- [5].Lauer S. A.et al. , “The incubation period of coronavirus disease 2019 (COVID-19) from publicly reported confirmed cases: Estimation and application,” Ann. Internal Med., vol. 172, no. 9, pp. 577–582, May 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [6].Lai C.-C., Shih T.-P., Ko W.-C., Tang H.-J., and Hsueh P.-R., “Severe acute respiratory syndrome coronavirus 2 (sars-cov-2) and corona virus disease-2019 (COVID-19): The epidemic and the challenges,” Int. J. Antimicrobial Agents, vol. 17, Feb. 2020, Art. no. 105924. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [7].Grenfell B., “(Meta)population dynamics of infectious diseases,” Trends Ecology Evol., vol. 12, no. 10, pp. 395–399, Oct. 1997. [DOI] [PubMed] [Google Scholar]
- [8].Hanski I., “Metapopulation dynamics,” Nature, vol. 396, no. 6706, pp. 41–49, 1998. [Google Scholar]
- [9].Keeling M. J., Bjørnstad O. N., and Grenfell B. T., “Metapopulation dynamics of infectious diseases,” in Ecology, Genetics and Evolution of Metapopulations. Amsterdam, The Netherlands: Elsevier, 2004, pp. 415–445. [Google Scholar]
- [10].Wu Q. and Chen S., “Mean field theory of epidemic spreading with effective contacts on networks,” Chaos, Solitons Fractals, vol. 81, pp. 359–364, Dec. 2015. [Google Scholar]
- [11].Nagy V., “Mean-field theory of a recurrent epidemiological model,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 79, no. 6, Jun. 2009, Art. no. 066105. [DOI] [PubMed] [Google Scholar]
- [12].Fanelli D. and Piazza F., “Analysis and forecast of COVID-19 spreading in China, Italy and France,” Chaos, Solitons Fractals, vol. 134, May 2020, Art. no. 109761. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [13].Kleczkowski A. and Grenfell B. T., “Mean-field-type equations for spread of epidemics: The small world’ model,” Phys. A, Stat. Mech. Appl., vol. 274, nos. 1–2, pp. 355–360, Dec. 1999. [Google Scholar]
- [14].Biswas K. and Sen P., “Space-time dependence of corona virus (COVID-19) outbreak,” 2020, arXiv:2003.03149. [Online]. Available: http://arxiv.org/abs/2003.03149 [Google Scholar]
- [15].Maier B. F. and Brockmann D., “Effective containment explains sub-exponential growth in confirmed cases of recent COVID-19 outbreak in mainland China,” 2020, arXiv:2002.07572. [Online]. Available: http://arxiv.org/abs/2002.07572 [Google Scholar]
- [16].Li M. Y., Graef J. R., Wang L., and Karsai J., “Global dynamics of a SEIR model with varying total population size,” Math. Biosci., vol. 160, no. 2, pp. 191–213, Aug. 1999. [DOI] [PubMed] [Google Scholar]
- [17].Dukic V., Lopes H. F., and Polson N. G., “Tracking epidemics with Google flu trends data and a state-space SEIR model,” J. Amer. Stat. Assoc., vol. 107, no. 500, pp. 1410–1426, Dec. 2012. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [18].Liu Y., Gayle A. A., Wilder-Smith A., and Rocklöv J., “The reproductive number of COVID-19 is higher compared to SARS coronavirus,” J. Travel Med., vol. 27, no. 2, Mar. 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [19].Chinazzi M.et al. , “The effect of travel restrictions on the spread of the 2019 novel coronavirus (COVID-19) outbreak,” Science, vol. 368, no. 6489, pp. 395–400, Apr. 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [20].Peng L., Yang W., Zhang D., Zhuge C., and Hong L., “Epidemic analysis of COVID-19 in China by dynamical modeling,” 2020, arXiv:2002.06563. [Online]. Available: http://arxiv.org/abs/2002.06563 [Google Scholar]
- [21].Rocklöv J., Sjödin H., and Wilder-Smith A., “COVID-19 outbreak on the diamond princess cruise ship: Estimating the epidemic potential and effectiveness of public health countermeasures,” J. Travel Med., vol. 27, no. 3, May 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [22].Cao W.et al. , “The psychological impact of the COVID-19 epidemic on college students in China,” Psychiatry Res., vol. 287, May 2020, Art. no. 112934. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [23].Li S., Wang Y., Xue J., Zhao N., and Zhu T., “The impact of COVID-19 epidemic declaration on psychological consequences: A study on active Weibo users,” Int. J. Environ. Res. Public Health, vol. 17, no. 6, p. 2032, Mar. 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [24].Tull M. T., Edmonds K. A., Scamaldo K. M., Richmond J. R., Rose J. P., and Gratz K. L., “Psychological outcomes associated with Stay-at-Home orders and the perceived impact of COVID-19 on daily life,” Psychiatry Res., vol. 289, Jul. 2020, Art. no. 113098. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [25].Zhang Y. and Ma Z. F., “Impact of the COVID-19 pandemic on mental health and quality of life among local residents in liaoning province, China: A cross-sectional study,” Int. J. Environ. Res. Public Health, vol. 17, no. 7, p. 2381, Mar. 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [26].Liang L.et al. , “The effect of COVID-19 on youth mental health,” Psychiatric Quart., vol. 4, pp. 1–12, Apr. 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [27].Gupta M., Abdelmaksoud A., Jafferany M., Lotti T., Sadoughifar R., and Goldust M., “COVID-19 and economy,” Dermatologic Therapy, pp. 1435–1443, Mar. 2020. [DOI] [PMC free article] [PubMed]
- [28].McKibbin W. and Fernando R., “The economic impact of COVID-19,” Econ. Time, vol. 45, pp. 1–13, Oct. 2020. [Google Scholar]
- [29].Baldwin R. and Tomiura E., “Thinking ahead about the trade impact of COVID-19,” Econ. Time, vol. 59, pp. 59–71, Oct. 2020. [Google Scholar]
- [30].McKibbin W. J. and Fernando R., “The global macroeconomic impacts of COVID-19: Seven scenarios,” Austral. Nat. Univ., Canberra, ACT, Australia, Tech. Rep., 2020. [Google Scholar]
- [31].Zambrano-Monserrate M. A., Ruano M. A., and Sanchez-Alcalde L., “Indirect effects of COVID-19 on the environment,” Sci. Total Environ., vol. 728, Aug. 2020, Art. no. 138813. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [32].Sahu P., “Closure of universities due to coronavirus disease 2019 (COVID-19): Impact on education and mental health of students and academic staff,” Cureus, vol. 12, p. e7541, Apr. 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [33].Sarasohn-Kahn J.. (2020). The Median Hospital Charge In U.S. for COVID-19 Care Ranges From 34-45K. [Online]. Available: https://www.healthpopuli.com/2020/07/17/the-median-hospital-charge-in-t%he-u-s-for-covid-19-care-ranges-from-34-45k/ [Google Scholar]
- [34].Niewiadomski P., “COVID-19: From temporary de-globalisation to a re-discovery of tourism?” Tourism Geographies, vol. 23, pp. 1–26, Apr. 2020. [Google Scholar]
- [35].Qiu R. T. R., Park J., Li S., and Song H., “Social costs of tourism during the COVID-19 pandemic,” Ann. Tourism Res., vol. 84, Sep. 2020, Art. no. 102994. [DOI] [PMC free article] [PubMed] [Google Scholar]
- [36].Siche R., “What is the impact of COVID-19 disease on agriculture?” Scientia Agropecuaria, vol. 11, no. 1, pp. 3–6, Mar. 2020. [Google Scholar]
- [37].World Health Organization. (2020). Novel Coronavirus-2019 Situation Reports. [Online]. Available: https://gisanddata.maps.arcgis.com/apps/opsdashboard/index.html?fbclid=IwAR1smzyZx1mLzj3zOpv9cmWXUudS72comshBltYE2gw9QBk47BgRB3TNQKI#/bda7594740fd40299423467b48e9ecf6
- [38].E. C. for Disease Prevention and Control. (2020). Covid-19. [Online]. Available: https://www.ecdc.europa.eu/en/covid-19-pandemic
- [39].(2020). Worldometer. [Online]. Available: https://www.worldometers.info/coronavirus/country/us/
- [40].Backer J. A., Klinkenberg D., and Wallinga J., “Incubation period of 2019 novel coronavirus (2019-nCoV) infections among travellers from Wuhan, China, 20–28 January 2020,” Eurosurveillance, vol. 25, no. 5, Feb. 2020, Art. no. 2000062. [DOI] [PMC free article] [PubMed] [Google Scholar]