Impacts of Daily Travel by Distances on the Spread of COVID-19: An Artificial Neural Network Model

Abstract

The continued spread of COVID-19 poses significant threats to the safety of the community. Since it is still uncertain when the pandemic will end, it is vital to understand the factors contributing to new cases of COVID-19, especially from the transportation perspective. This paper examines the effect of the United States residents’ daily trips by distances on the spread of COVID-19 in the community. The artificial neural network method is used to construct and test the predictive model using data collected from two sources: Bureau of Transportation Statistics and the COVID-19 Tracking Project. The dataset uses ten daily travel variables by distances and new tests from March to September 2020, with a sample size of 10,914. The results indicate the importance of daily trips at different distances in predicting the spread of COVID-19. More specifically, trips shorter than 3 mi and trips between 250 and 500 mi contribute most to predicting daily new cases of COVID-19. Additionally, daily new tests and trips between 10 and 25 mi are among the variables with the lowest effects. This study’s findings can help governmental authorities evaluate the risk of COVID-19 infection based on residents’ daily travel behaviors and form necessary strategies to mitigate the risks. The developed neural network can be used to predict the infection rate and construct various scenarios for risk assessment and control.

The COVID-19 pandemic had a substantial impact on society. The spread of COVID-19 had been fluctuating over time in 2020, as shown in Figure 1. The infection rate increased exponentially in April 2020 and reached 30,000 new cases daily in mid-April. Then it decreased to the lowest of about 20,000 new cases in early June before it started to increase again at a higher rate in mid-June. The number of daily new cases reached a record high of more than 70,000 new cases in mid-July. Again, there was another decline in daily new cases to about 35,000 daily cases in mid-September. When it was thought that the infection rate would stabilize, there was another surge in early October ( 1 ).

Figure 1.

Daily COVID-19 cases in the United States (U.S.) from January to October 2020 ( 1 ).

The continued spread of COVID-19 is a major concern of society and the world since it affects not only the residents’ health but also the economy and society. Wearing masks and keeping distance has become the new norm. Several states issued stay-home orders, travel restrictions, mask mandates, and indoor dine-in for a period of time ( 2 ). With numerous states going into reopening, most businesses and schools were operating as normal. Daily transport has recovered quickly, with many residents going to work, grocery stores, schools, restaurants, and even beaches and theme parks. According to the Bureau of Transportation Statistics (BTS), U.S. residents made more than three billion trips per day as of September 30, 2020 (Figure 2) ( 3 ). While this number dropped about 30% from 2019, it was still a very large number. Research shows that the more people gathered nearby and in contained areas, the higher the risks of COVID-19 infection, and infected travelers can create a new exponential outbreak (4–7). The four states with the highest number of cases and deaths are California, Texas, Florida, and New York, which are the states with the largest populations and tourist attractions ( 1 ).

Figure 2.

Total number of daily trips in the United States (U.S.) in 2019 and 2020.

Several studies in the literature have studied the association between the spread of COVID-19 and residents’ mobility and travel. Beck and Hensher found that, while travel risk perception increased with age, it decreased with travel frequency ( 8 ). In other words, the more trips some people make, the lower risk of COVID-19 infection they perceive, resulting in more trips. Truong and Truong found that residents’ daily trips changed dynamically in responding to COVID-19 cases ( 9 ). The study indicated a possible two-way relationship between daily trips and COVID-19 infection, which could cause a close-loop scenario; that is, the more trips people make, the safer they feel, resulting in more trips, which could lead to more COVID-19 cases. Chang et al. indicated a strong association between the spread of COVID-19 and individuals’ mobility within short distances in the United States (U.S.) ( 10 ). Focusing on mobility patterns from the distancing perspective on the worldwide level, Nouvellet et al. found that reduction in mobility in most countries leads to a decrease in COVID-19 transmission ( 11 ). Similarly, using data in Italy, Cartenì et al. showed the impact of mobility habit (number of people making trips) and proximity on the spread of COVID-19 ( 12 ). Other studies focused on how COVID-19 affected public transport ridership and daily mobility, how physical distancing affected daily travel for work, and how COVID-19 affected air travel volumes (13–17).

Given the gravity of this pandemic and the rate of COVID-19 infection in society, many efforts have been put into developing models to predict the spread of COVID-19. The literature shows numerous COVID-19 forecast models that have been developed. There are two primary categories of COVID-19 forecast models ( 18 ). The first category includes models forecasting COVID-19 cases and deaths, assuming social distancing will change in the future. The models in the second category assume that existing social distancing measures will continue through the projected period (9, 18).

Two exemplar models are the ones by the Institute for Health Metrics and Evaluation (IHME) and the COVID-19 Simulator Consortium ( 19 ). The IHME model has been used by the government as the guideline to decide intervention and restriction strategies. This model combined a mechanistic disease transmission model and a curve-fitting approach to make the prediction. Using observed deaths as a starting point, the model approximates the progression of coronavirus by fitting a best fit growth curve based on how the virus progressed in people and regions that are farther along with their COVID-19 infections. It assumes that social distancing mandates will be lifted but will be re-imposed for 6 weeks if daily death rates reach 8 per million ( 20 ). The model produces predicted numbers for daily new deaths, infections, and hospitalizations for three different scenarios: current intervention, mandates easing, and universal masks.

The Covid19Sim model is developed by a team of experts from Massachusetts General Hospital, Harvard Medical School, Georgia Institute of Technology, and Boston University School of Medicine. The model uses the susceptible, exposed, infectious, and recovered compartments (SEIR) method with the continuous time progression to estimate the state-specific coronavirus spread dynamism. The goal of this model is to predict how coronavirus is transmitted, by moving the population through a set of connected compartments based on rates of incubation, infection, and recovery. It assumes current intervention will continue and, once the number of active COVID-19 cases in a given state is lower than ten active cases per 1,000,000 people, all cases can be isolated to stop the transmission of coronavirus in the community ( 19 ). This model produces predicted numbers of daily new cases, new deaths, and hospitalizations.

Those are great models providing very useful predictions of COVID-19 cases, deaths, and hospitalizations. They focus on estimating the progression of the coronavirus either by fitting a best fit growth curve to other geographies or estimating how the virus will be transmitted by modeling the complex variations in virus contact in various stages, including incubation, infection, and recovery.

This paper focuses on a different aspect of COVID-19 infection by exploring the effects of daily travel by distances, as novel variables, on the spread of COVID-19. Both the number of trips that residents make every day and the distances of those trips are looked at to determine how they are associated with daily new COVID-19 cases. This study does not intend to predict future COVID-19 infection nor find the causes of the infection. Its main purpose is to examine how residents’ daily trips at different distances contribute to the changes in COVID-19 cases in the U.S. It does not model the dynamic transmission and progression of the coronavirus, since such a study has been done extensively, as mentioned above. In addition, factors such as medical conditions, underlying conditions, and patients’ demographics are not considered, since identifying causes of the infection is not in the scope of the study, and such data are not available for public use. Finally, the paper examines the effects of daily trips by distances at the national level instead of state or county levels. Since states have different travel restrictions and safety policies issued at different times, the effects of those factors should be examined for each state separately. Regardless, the daily transport data does capture the residents’ daily travel behaviors in all counties in the U.S. over time, so it can be argued that the changes in their daily trips reflect their travel behaviors because of states’ restrictions and policies (9, 17). In other words, changes in daily trips could be proxies for changes in states’ policies, and the pattern of those trips does capture the variation in policies in various states during the studied period.

Because of the uncertainty of the COVID-19 spread pattern over time, this paper is exploratory and not grounded on traditional theories. The role of daily trips by distance is explored as novel variables to understand the spread of COVID-19 from the transportation perspective. Nonetheless, several studies are used as an important foundation to support the selection of these novel variables. First, Chang et al. modeled relationships between the spread of COVID-19 and individuals’ mobility from census block groups (CBGs)—locations with high population density—to points-of-interest (POIs), such as restaurants, grocery stores, or religious establishments ( 10 ). Mobility in short distances does play a role in increasing the COVID-19 infection, and social distancing is a key to reducing the spread. Secondly, Beck and Hensher indicated that travel risk perception decreased with travel frequency ( 8 ). Thus, the more trips residents make, the safer they would feel with traveling, and they will travel more. Third, Truong and Truong expanded this direction and forecasted the patterns of daily trips in comparison with the pattern of COVID-19 infection in the near future ( 9 ). They found that daily trips capture well residents’ dynamic travel behaviors responding to the pandemic. More specifically, short-distance trips changed promptly in response to the change in COVID-19 infection, while there is a time gap between the observations of COVID-19 development and changes in medium- and long-distance trips.

Based on that foundation, daily trips at different distances in the U.S. were selected as the predictors and daily new COVID-19 cases were selected as the target variable. While the spread of COVID-19 is reflected by new cases, new deaths, and new hospitalizations, the number of new deaths and hospitalizations are generally determined by the number of new cases. Therefore, the daily new cases were used as the target variable in the model. In addition, because of the close relationship between tests and cases, the number of daily tests was also used in the model as a control variable. The trip distances were selected based on the BTS’s recommendation with ten variables: shorter than 1 mi, 1–3 mi, 3–5 mi, 5–10 mi, 10–25 mi, 25–50 mi, 50–100 mi, 100–250 mi, 250–500 mi, and greater than 500 mi. To build a valid and precise predictive model with the number of predictors, the artificial neural network (ANN) method is selected.

The paper is organized as follows. The next section describes the ANN method, variables, and dataset. The Results section presents descriptive statistics of daily trips, the ANN model, and the prediction results. Finally, discussions of the findings and conclusions are presented.

Methods

Artificial Neural Network (ANN)

To construct a predictive model for new COVID-19 cases, in this paper, the ANN method was selected. This method has advantages over traditional statistical methods since it can capture possible non-linear relationships between predictors and the target variable and the inter-correlations among predictors. In addition, there are no strict statistical assumptions or limitations for scales of inputs (17, 21, 22). ANN is defined as a neural network method that uses multiple hidden layers. In essence, an ANN mimics the human brain’s biological neural network (21, 23). ANN is capable of detecting non-linear relationships in a complex network structure. It can also tolerate noisy data and complicated relationships. These advantages make ANN an appropriate analysis method for this study, since the aim is to explore new relationships between novel variables and new COVID-19 cases. On the other hand, ANN is usually considered a black box because it is hard to interpret the relationships between inputs and outputs. The mathematical relationships between inputs and outputs will be explained next. Additionally, it is a challenge to find the right network structure because of possible local optimum issues. Trial and error is needed to find a good network (21, 24).

Figure 3 presents the architecture of an ANN with one input layer, three hidden layers, and one output layer. In the network, artificial neurons are represented by nodes, including input nodes, output nodes, and node bias θ. Additionally, nodes are interconnected via synaptic weights (w), which are calibrated through a model training process (17, 23).

Figure 3.

Artificial neural network (ANN) architecture.

Formulas for calculating the value of each node in the network are presented in the following Equations 1 to 4 ( 17 ):

$$H_{1j}=f({\theta }_j+\sum _i{w}_i{T}_i)$$ (1)

$$H_{2k}=f({\theta }_k+\sum _j{w}_j{H}_{1j})$$ (2)

$$H_{3l}=f({\theta }_l+\sum _k{w}_k{H}_{2k})$$ (3)

$$C=f({\theta }_C+\sum _l{w}_l{H}_{3l})$$ (4)

where

T_i = input variables (i = 1–11 representing ten trip variables and the number of daily tests),

H_1j = hidden layer 1 (j = the number of nodes in this layer),

H_2k = hidden layer 2 (k = the number of nodes in this layer),

H_3l = hidden layer 3 (l = the number of nodes in this layer),

w = synaptic weight used in the functions for each node,

C = the output variable (the number of daily cases), and

θ = node bias.

In this paper, the multilayer perceptron (MLP) method, a feedforward ANN, was selected to construct the ANN. MLP is capable of stochastic modeling and producing approximate solutions for complex problems ( 17 ). In this network, the information is sent unidirectionally from the input layer to hidden layers to the output layer (21, 24). For each node, or artificial neuron, in the hidden layers, there is an activation function used to express the formulation of the hidden node by input nodes. Similarly, a particular activation function is used to formulate the output node by hidden nodes. In each function, weights are determined by the estimation algorithms. Equations 5 and 6 show common activation functions, including hyperbolic tangent and sigmoid (17, 23, 25). The range for hyperbolic tangent function is [−1; 1], while the range for sigmoid function is [0;1].

$$f\left(y\right)=\tanh \left(y\right)=\frac{e^y-e^{-y}}{e^y+e^{-y}}$$ (5)

$$f\left(y\right)=1+\frac{1}{1+e^{-2y}}$$ (6)

Before the neural network was constructed, input and output variables were standardized or normalized as needed. There are three methods for standardization or normalization. The first method is standardization using z-score (Equation 7). The second method is normalization using max and min values (Equation 8). The normalized values fall between 0 and 1, and this method is used if the output variable uses the sigmoid activation function. Finally, the third method is adjusted normalization using the adjusted value of the normalization (Equation 9). The adjusted normalized values also fall between −1 and 1, and this method is used if the output variable uses the hyperbolic tangent activation function (17, 23).

$$x\prime =\frac{x-\overline{x}}{s}$$ (7)

$$x\prime =\frac{x-\min (x)}{max\left(x\right)-\min (x)}$$ (8)

$$x\prime =\frac{2^{*}(x-min\left(x\right))}{max\left(x\right)-\min (x)}-1$$ (9)

where

x = an actual variable,

x^’ = the new variable,

$\overline{x}$ = the mean value, and

s = the standard deviation.

Since the output variable in this study is a continuous variable, the performance of the ANN model was evaluated by sum of squares error and relative error (Equations 10 and 11). The sum of squares error is calculated by summating the squares of variances between predicted and observed values. It captures the variance in the prediction. Additionally, the relative error is the ratio of the sum of squares error for the predictive model to the sum of squares error for the null model, which uses mean values as predicted values. It captures the ability to explain variances in the target variable by the predictors ( 17 ).

$$\mathrm{Sum}\mathrm{of}\mathrm{Squares}\mathrm{Error}=\sum (O_i-P_i{)}^2$$ (10)

$$RelativeError=\frac{\sum {(O_i-P_i)}^2}{\sum {(O_i-\overline{O})}^2}$$ (11)

where

O = the observed value,

$\overline{O}$ = the mean value, and

P = the predicted value.

An iterative process was used to construct the network. First, the data was partitioned into training and validation samples in the ratio of 50:50. In the modeling step, an ANN structure with one hidden layer was used as the initial model. Then, the ANN was configured iteratively one step at a time through trial and error. The number of hidden layers and the number of nodes in each hidden layer were determined by evaluating the network performance in one configuration and making improvements to the next configuration with necessary adjustments. The choice of activation functions for the output layer and hidden layers was also determined by examining which function would improve the performance of the ANN model.

Data Collection

In this paper, the target variable is daily new COVID-19 cases. As mentioned before, the spread of COVID-19 is normally measured by new cases, new deaths, and new hospitalizations (19, 20). However, daily new deaths and daily new hospitalizations are generally determined by daily new cases. Accordingly, it was chosen to measure the spread of COVID-19 in this prediction by daily new cases. The daily new cases and new tests at the state level were collected from the COVID Tracking Project ( 26 ). Because of the low and unreliable number of cases and tests at the beginning of the pandemic, only the data from March 1 to September 30, 2020, was used. This period captures well the first surge at the beginning of the pandemic and the second surge after the reopening in several states. It was also possible to notice the fluctuation of the daily trips during this period, representing the changes in residents’ daily travel behaviors. The data was collected for all counties in 50 states in the U.S. during that time frame.

The daily travel by distances data in the U.S. was collected from the database of daily travel during the COVID-19 pandemic, provided by the BTS. The data was collected by the Maryland Transportation Institute and Center for Advanced Transportation Technology (CATT) Laboratory at the University of Maryland (27, 28). The center used a mobile device data panel that collects and merges multiple data sources to capture people’s mobility. In this dataset, trips are defined as trips away from home that take longer than 10 min. The distance of each trip is measured by the distance from the origin to the destination. The quality of data is ensured by using “temporal frequency and spatial accuracy of anonymized location point observations, temporal coverage and representativeness at the device level, and spatial representativeness at the sample and county level.” CATT used the multi-level weighting method to extend the sample to the population ( 3 ). Accordingly, the dataset captures well the U.S. residents’ daily trips at different distances, with high reliability and generalizability.

The following are the variables and descriptions in the dataset ( 29 ). The dataset has ten primary variables, excluding the date, and covers all counties in 50 U.S. states for the selected timeframe from March 1 to September 30, 2020, which results in a sample size of 10,914 observations. All variables are numeric in the ratio scale.

1. Number of Trips < 1: Number of trips by residents shorter than 1 mi

2. Number of Trips 1–3: Number of trips by residents greater than 1 mi and shorter than 3 mi (1 ≤ trip distance < 3 mi)

3. Number of Trips 3–5: Number of trips by residents greater than 3 mi and shorter than 5 mi (3 ≤ trip distance < 5 mi)

4. Number of Trips 5–10: Number of trips by residents greater than 5 mi and shorter than 10 mi (5 ≤ trip distance < 10 mi)

5. Number of Trips 10–25: Number of trips by residents greater than 10 mi and shorter than 25 mi (10 ≤ trip distance < 25 mi)

6. Number of Trips 25–50: Number of trips by residents greater than 25 mi and shorter than 50 mi (25 ≤ trip distance < 50 mi)

7. Number of Trips 50–100: Number of trips by residents greater than 50 mi and shorter than 100 mi (50 ≤ trip distance < 100 mi)

8. Number of Trips 100–250: Number of trips by residents greater than 100 mi and shorter than 250 mi (100 ≤ trip distance < 250 mi)

9. Number of Trips 250–500: Number of trips by residents greater than 250 mi and shorter than 500 mi (250 ≤ trip distance < 500 mi)

10. Number of Trips ≥ 500: Number of trips by residents greater than 500 mi (trip distance ≥ 500 mi)

Results

Descriptive Statistics

Table 1 shows the descriptive statistics for new cases and the numbers of trips at the state level. Figure 4 presents the percentage of those trips from March to September 2020. The results show that short distance trips account for the majority of the daily trips. Trips shorter than 1 mi occur most often (about 26%), followed by trips between 1 and 3 mi (25%). The distance does not necessarily correlate with the number of trips, as there are fewer trips between 3 and 5 mi (12%) than trips between 5 and 10 mi (15%) and the trips between 10 and 25 mi (14%). Longer-distance trips occur much less often, with about 0.2% being trips between 250 and 500 mi and 0.12% being trips greater than 500 mi.

Table 1.

Descriptive Statistics

Variables	Minimum	Maximum	Mean	Standard deviation
Number of trips < 1	496,768	96,724,780	10,065,368.38	11,037,885.35
Number of trips 1–3	696,587	98,291,664	9,685,437.48	10,343,379.62
Number of trips 3–5	298,695	45,307,944	4,649,544.17	4,893,636.28
Number of trips 5–10	253,094	56,286,696	5,800,456.07	6,127,791.42
Number of trips 10–25	207,586	60,152,218	5,683,188.49	6,078,792.47
Number of trips 25–50	51,668	25,625,022	1,992,289.59	2,208,807.40
Number of trips 50–100	12,994	9,832,352	743,007.06	810,378.81
Number of trips 100–250	1,992	3,906,252	347,994.04	365,540.19
Number of trips 250–500	746	838,672	77,237.97	86,510.03
Number of trips > 500	470	1,177,114	45,384.87	74,339.47
New cases	0	17,820	655.54	1,309.27

Figure 4.

Daily trips by distance from March to September 2020.

Artificial Neural Network (ANN) Results

The neural network was constructed using the MLP method with a training sample of 5,455 cases and a validation sample of 5,459 cases. Through an iterative network constructing process with numerous trial and error procedures, a neural network with two hidden layers was selected. As shown in Table 2, this network has 11 nodes in the input layer, representing 11 predictors, and one node in the output layer, representing the target variable (new cases). Each hidden layer has 12 nodes or neurons. The input variables were standardized using the z-score method, and the output variable was normalized. The hyperbolic activation function was used for the hidden layers, and the sigmoid activation function was used for the output layer.

Table 2.

Artifical Neural Network Information

Layer	Description	Information
Input layer	Number of units a	11
	Rescaling method for covariates	Standardized
Hidden layer(s)	Number of hidden layers	2
	Number of units in hidden layer 1 a	12
	Number of units in hidden layer 2 a	12
	Activation function	Hyperbolic tangent
Output layer	Dependent variables	New cases
	Rescaling method for scale dependents	Normalized
	Activation function	Sigmoid
	Error function	Sum of squares

^aExcluding the bias unit.

The model performance evaluation shows the sum of squares error for this ANN model is 3.613, which is relatively low, given the mean and standard deviation of the target variable are 655 and 1,309, respectively. In addition, the relative error is 0.178; that is, the ANN model is able to explain about 82.2% of variances of the target variable based on the predictors, indicating a good predictive power of the model (21, 30). Figure 5 shows the predicted by observed chart, indicating the ANN model predicts well most cases with relatively high accuracy. Furthermore, as shown in Figure 6 (residual by predicted chart), there is no clear relationship between residuals and predicted values; that is, the residuals are random. Overall, the ANN model has a good model fit and prediction accuracy.

Figure 5.

Predicted by observed chart.

Figure 6.

Residual by predicted chart.

The full network structure is presented in Figure 7, with the input layer, two hidden layers, and the output layer. As explained before, a bias item is included in each layer. The synaptic weights in this figure represent the coefficient estimates indicating the relationship between nodes in a given layer to the nodes in the following layer. Blue lines indicate negative weights, and grey lines indicate positive weights. The detailed weight values are presented in the supplemental material. It is worth noting that these weights are generally not used to interpret the network results or the impact of predictors on the target variable because these nodes are correlated in a complex input-hidden-output layer structure with non-linear mathematical formulas between layers, as presented in the methodology section. In addition, the non-linear relationships between layers through using the activation functions also add complexity to the interpretation. The more hidden layers and nodes there are, the more complicated these correlations become.

Figure 7.

Neural network structure.

To evaluate the impact of predictors on the target variable, the variable importance is used. The importance values (between 0 and 1) and normalized importance (percentage) of all predictors are presented in Table 3. Additionally, Figure 8 shows the predictors in the order of their importance. The importance value indicates how changing a predictor would change the target variable, which is daily new cases. The importance values are normalized to percentages for comparison purposes. The higher the percentage, the higher the impact of a predictor on the spread of COVID-19. As shown in Table 3 and Figure 8, the importance is not linearly related to trip distances. It appears that the trips between 3 and 5 mi have the highest impact on the increase of daily cases (100%), followed closely by the trips shorter than 1 mi (95.4%). The results indicate that these particular short trips have significant contributions to the spread of COVID-19. Other short trips also have considerable contributions to the increased infection, including trips between 1 and 3 mi (46.3%) and between 5 and 10 mi (47.8%). However, the trips between 10 to 15 mi have almost the lowest impact (8%), which is a surprise. Another unexpected result is the significant impact of long distance trips, the trips between 250 and 500 mi (72.4%). While there is not a huge number of trips in this distance, it does represent the cross-state trips, which could be a reason for its impact on the coronavirus infection. As expected, the moderate-distance trips contribute to the increased number of new cases at a moderate rate. Specifically, there are trips between 25 and 50 mi (26.4%), 50 and 100 mi (20.3%), and 100 and 250 mi (22.9%). The longest distance trip (greater than 500 mi) has the least effect on the daily new cases (6%), which is not a surprise since there are so few of them, and people may choose to fly rather than drive for that kind of trip. Another unexpected result is that the number of new tests at the state level is not among the important contributing factors to the daily new cases. While new tests are clearly correlated with new cases, when this variable is included in a model with daily trips, the extent of its effect has reduced significantly. Figure 7 shows that new tests have a lower importance than most predictors (18.8%).

Table 3.

Independent Variable Importance

Variables	Importance	Normalized importance (%)
Number of trips < 1	.206	95.4
Number of trips 1–3	.100	46.3
Number of trips 3–5	.215	100.0
Number of trips 5–10	.103	47.8
Number of trips 10–25	.017	8.0
Number of trips 25–50	.057	26.4
Number of trips 50–100	.044	20.3
Number of trips 100–250	.049	22.9
Number of trips 250–500	.156	72.4
Number of trips > 500	.013	6.0
New tests	.040	18.8

Figure 8.

Normalized variable importance.

Discussion

The results of this study highlight some important findings about the association between residents’ daily travel behaviors and the spread of COVID-19 in society. The neural network outputs indicate that residents’ daily trips by distances have significant impacts on the infection of COVID-19 in relation to daily new cases. Short distance trips (shorter than 1 mi and between 3 and 5 mi) contribute most to predicting daily new cases in the U.S. states, followed by trips between 1 and 3 mi, and 5 and 10 mi. These trips present daily travel to nearby grocery stores, offices, schools, restaurants, or parks. Those are public places that are usually filled with people in close contact. These results are consistent with findings by Chang et al. and Cartenì et al., but add further insights into the effect of trip distances (10, 12). One interesting finding is that trips between 1 and 3 mi have a lower effect on new COVID-19 cases than trips between 3 and 5 mi, despite a larger number of trips in this distance. While this effect is still moderate, further exploration is needed to gain more understanding of the effect of trip distances. A possible underlying factor that could be added is the purpose of the trips, which could explain the changes in COVID-19 cases along with the number of trips. For example, short-distance trips that people make to pick up carryout at fast-food restaurants or curbside pickup items at nearby grocery stores may not contribute to the change in COVID-19 cases on the same level as the trips to shop in large supermarkets or eat in restaurants. Nonetheless, these trips capture the residents’ daily travel behaviors during the pandemic and how these trips affect the increased infection of COVID-19 ( 9 ). Once the stay-home orders were lifted, more residents decided to make short-distance trips for necessities or small get-togethers. As presented in Table 3 and Figure 8, changes in these trips will result in significant changes in daily COVID-19 cases. Thus, the more people go out to public places, the higher the population density in those places, which makes it harder to keep physical distance (10–12). Since masks are not a mandate in many places, the extent of daily trips contributes to creating an unsafe environment in which coronavirus can transfer from one to another. It is interesting to note that trips between 10 and 25 mi have a much lower effect on daily new cases. One possible explanation is that this distance typically presents trips to work. Since many companies and organizations had facilitated the work-from-home policies during the studied time, more employees work from home or commute to work less often. In addition, many small to medium organizations successfully established safety protocol and work schedule cycling, which could reduce the spread of coronavirus in the working environment.

The moderate-distance trips (between 25 and 250 mi) have moderate effects on the COVID-19 infection. These trips present the commute to work in larger corporations, business-related travels, or family visits within the state. These trips occur much less often and, given the limited events, there is a lower chance for social contact, which makes it harder for the coronavirus to transfer. Similarly, the work-from-home policies may reduce the number of face-to-face business meetings and conferences, which also helps reduce the effect on the COVID-19 infection.

One unexpected outcome is the high impact of trips between 250 and 500 mi, despite the low number of trips within this range. A possible explanation is that these trips are usually cross-state trips, either for business or personal purposes. Since states experience different patterns of daily new COVID-19 cases, people moving from one state to another could lead to changes in COVID-19 cases in the destination. As Truong and Truong indicated, there is a time lag between the change in long-distance trips and observation of COVID-19 cases ( 9 ). On the other hand, as expected, long-distance trips (greater than 500 mi) have the lowest impact on the spread of coronavirus. The reason for this could be that most organizations did not support long-distance trips for businesses during the studied time. In addition, such trips, even personal ones, usually involve more strict requirements in relation to COVID-19 testing or quarantine, which limit the number of trips and also reduce the risk of transferring coronavirus in the community.

Another unexpected finding is the lower impact of the number of new tests on new cases. While new tests are clearly correlated with new cases, it appears that when this variable is included in the predictive modeling with daily trip and distance variables, its effect decreases significantly. This finding sheds new light on the COVID-19 research by highlighting the important role of residents’ daily transport in the spread of coronavirus. The more people transport and contact in small, public places, the higher the risk of infection. Thus, the number of tests conducted should not be used as a primary factor to explain the changes in daily cases.

Conclusions

As the number of COVID-19 cases in the U.S. continues to increase statewide, it is vital to understand contributing factors to the infection rate. Because of the spread of the more contagious Delta variance, it is uncertain when the pandemic will end. Accordingly, understanding contributing factors from different perspectives is critical to establishing mitigation strategies to control the spread of COVID-19 and contain its infection. This paper focuses on the transportation perspective and examines the effects of residents’ daily transport at different distances. This research adds substantial contributions to the COVID-19 literature, in which most forecast models seem to focus primarily on fitting a best fit growth curve, or model various stages of the coronavirus contact. The effect of novel variables—daily trips by distances—on the spread of COVID-19 were explored. The ANN method was used to train and validate the predictive model. The model has good predictive power and produces useful findings. Daily trips by distance have been proven to have strong associations with the spread of COVID-19. An important finding is that the trip distances play a more important role in predicting new COVID-19 cases than the number of trips. The results indicate the importance of short-distance trips that people make every day, such as going to grocery stores, schools, offices, restaurants, or parks, in predicting the number of daily new cases of COVID-19. The more people go and contact in small places and near to each other, the higher the risk of infection. In addition, potential cross-state trips could also contribute to the spread of coronavirus in the community at the state level. Finally, daily new tests should not be used as a primary factor to explain the changes in COVID-19 new cases.

These findings help state authorities understand the severity of the pandemic and how residents’ daily transport and distances can contribute to the spread of coronavirus, especially after the stay-home orders were lifted. They can use the results to develop necessary strategies to mitigate the risk and set appropriate restrictions for residents and businesses to stop COVID-19 from spreading in the community. Trip distances play an important role in the spread of COVID-19, and the state authorities can focus their policies on the businesses and events that fall within distances with a higher impact on new COVID-19 cases. While the study is limited to 2020 data, the results still apply to the later phase of the pandemic, given the similar pattern of the daily new cases. However, the effect of vaccine rollout was not included in the analysis, since the vaccine data is only available in 2021. The neural network model can also be expanded to predict the infection rate by running various scenarios with different intervention options related to daily trips by distances to determine the best solutions. This option requires adding specific interventions and using data specific to the state. A simulation will be needed to evaluate how the intervention would work.

Future research can expand the data to 2021 to capture effects of the Delta variant and vaccine rollout efforts. The neural network model can be further trained with more data to improve its predictive power, given the dynamism of the pandemic and changes in daily new cases of COVID-19 in different states. In addition, simulations can be conducted using the validated neural network model to evaluate the efficiency of various decision alternatives in different states to determine the best decision given special circumstances of that state.