COVID-19 and the value of safe transport in the United States | Scientific Reports – Nature.com

The possibility of COVID-19 transmission introduces an additional margin when it comes to the choice of means of transport for commuters. Modeling from transportation economics can be used to highlight this choice. We will define the concept of value-of-avoiding-transmission (VAT), which captures the tradeoff between a higher dollar or time cost of transportation and a lower likelihood of disease transmission, perhaps as a result of exposure to a smaller number of travelers, resulting in a lower probability of infection. A central concept in transportation economics is the value-of-travel-time (VOT), which quantifies the well-known tradeoff between saved time and money. More precisely, VOT specifies the amount of money that if a commuter had a choice between paying this amount and enjoying a fixed amount of time-savings during his commute, or paying nothing and receiving no time savings, he would be exactly indifferent between the two options. The similar notion of the value of statistical life (VSL) is used in actuarial studies to quantify the tradeoff between reducing the probability of death and a corresponding reduction in income that makes the agent indifferent7,8. VOT is of central importance in transportation demand modeling, as well as in the costbenefit analysis of related public policies. For example, it was found that travel time and reliability account for 45% of the average social variable cost of travel in the US9.

In the age of COVID-19, there is an additional cost associated with public transportation, namely, an increased probability of exposure to the virus, leading to potential illness and the associated economic costs. When it comes to commuting, these costs can be modeled in a way that is parallel to the costs from potential traffic accidents. Exposure to the virus, just like a traffic accident, occur with some probability in every trip. In addition, just as the probability of an accident increases with congestion, so does the likelihood of infection increase with the number of people using the transportation mode under study. The VAT can be used to monetize the desire to reduce the probability of infection by appropriately adjusting the choice of transportation mode.

Transportation studies have explored the relationship between VOT and income, wealth, age, time constraints, etc. Travel demand modeling typically finds that travel time is an important explanatory economic variable, even more so than the direct economic cost of travel. The standard model is based on Lave10, while more involved theories of VOT build on the optimal time allocation framework11. People in this framework choose how much labor to supply given a constraint that total time devoted to work, leisure, and commuting equals the total time available to them. Since time can be transferred between work and leisure, any marginal savings in travel time can be used to increase labor income. Intuitively, optimization implies that travel time is valued at the after-tax wage rate. The commuters budget constraint can be expressed as

$$x + c le left( {1 - tau } right)w cdot h$$

(1)

while the commuters time constraint gives

where T is the total available time, t is the time spent commuting, h corresponds to hours spent at work under after-tax income, (Y = left( {1 - tau } right)w), and (l) denotes time spent on leisure. Finally, x is the expenditure in goods, and c is the direct cost of transportation. If the worker uses public transit, c would be the public transit fare; if the worker uses private transport, c would be the cost of fuel needed for travel; i.e., the price per gallon times miles travelled divided by miles per gallon (or ({{fuel;price times miles;driven} mathord{left/ {vphantom {{fuel;price times miles;driven} { , fuel;efficiency}}} right. kern-nulldelimiterspace} { , fuel;efficiency}})). Letting V denote the optimal value of the utility function, u, the first-order conditions for this problem yield

$$VOT = frac{{{raise0.7exhbox{${partial V}$} !mathord{left/ {vphantom {{partial V} {partial t}}}right.kern-nulldelimiterspace} !lower0.7exhbox{${partial t}$}}}}{{{raise0.7exhbox{${partial V}$} !mathord{left/ {vphantom {{partial V} {partial h}}}right.kern-nulldelimiterspace} !lower0.7exhbox{${partial h}$}}}} = left( {1 - tau } right)w + frac{{{raise0.7exhbox{${partial u}$} !mathord{left/ {vphantom {{partial u} {partial h}}}right.kern-nulldelimiterspace} !lower0.7exhbox{${partial h}$}} - {raise0.7exhbox{${partial u}$} !mathord{left/ {vphantom {{partial u} {partial t}}}right.kern-nulldelimiterspace} !lower0.7exhbox{${partial t}$}}}}{lambda }$$

(3)

where (lambda) is the marginal utility of money. The VOT increases with the after-tax wage rate and decreases with the marginal utility of money. This leads to a self-selection where commuters with a higher opportunity cost of time will tend to choose faster, generally more expensive modes of transport.

The recent events related to COVID-19 highlight additional constraints and concerns in connection to public transport. As noted in Figs.2, 3, 4 and 5 later in "Data visualization" section, there is evidence that the density of public transportation options is highly correlated with an increased probability of transmission of the virus3,4,5,6. This introduces an additional tradeoff. Increased use of public transport might lead to a higher probability of income loss due to infection and subsequent illness.

Consider a commuter during the COVID-19 era. Every time he uses public transportation, there is a probability, (Pleft( n right)), of contracting the virus. This probability is increasing in the number of passengers, n, since commuter contacteither direct or indirectwith other passengers increases the likelihood of contact with a COVID-19 carrier. Travel time, (tleft( n right)), also increases with n, since higher capacity utilization implies greater delays. The expected utility for a commuter is given by

$$U = Pleft( n right) cdot u^{V} left( {Y - F - L} right) + left[ {1 - Pleft( n right)} right] cdot u^{ - V} left( {Y - F} right) - Cleft( {tleft( n right)} right).$$

(4)

In the above expression, Y is the commuters income, while (u^{V}) and (u^{ - V}) stand for the resulting utilities if the commuter is infected and not infected, respectively, during commuting. Infection can lead to medical expenses and lost income from missed work due to mild or severe symptoms, or, in extreme cases, even to death. We denote the resulting expected income loss by L, and the commuting fare as F. Finally, (Cleft( {tleft( n right)} right)) denotes the opportunity costs of commuting travel-time, where ({{partial C} mathord{left/ {vphantom {{partial C} {partial t}}} right. kern-nulldelimiterspace} {partial t}} > 0). Thus, increased commuting time adds to commuting costs.

The probability of disease transmission will vary across different means of transport. For example, this probability should be close to zero if one drives their own car to work, especially if not carpooling. The probability will increase when using ride-sharing services or traditional taxis since, although the driver might be the only other person present in the vehicle, disease contagion from previous passengers is still possible. In a bus or train, the probability increases with the number of fellow travelers, n.

The model illustrates how infection risk and travel time are linked to commuting density as captured by the number of people, n, using this particular means of transport. The marginal change from an increase in the number of commuters can be decomposed into an increase in (a) the implied risk of infection, and (b) the commuting time. The expected marginal utility of income is defined as8:

$$lambda = P cdot frac{{partial u^{V} }}{partial Y} + left[ {1 - P} right] cdot frac{{partial u^{ - V} }}{partial Y}.$$

(5)

To avoid an exogenous increase in travel time, commuters would be willing to pay (frac{1}{lambda }frac{partial C}{{partial t}}). This is the standard expression for the VOT discussed earlier. The value of an exogenous increase in infection transmission risk is (- frac{1}{lambda }left( {u^{V} - u^{ - V} } right)). The value of choosing a transportation mode that implies a marginal reduction in the number of people commuting, thus resulting in a lower probability of infection, is given by

$$frac{1}{lambda }left[ {left( {u^{V} - u^{ - V} } right) cdot frac{partial P}{{partial n}} + frac{partial C}{{partial t}} cdot frac{partial t}{{partial n}}} right].$$

(6)

In this context, we will refer to (frac{1}{lambda }left( {u^{V} - u^{ - V} } right) cdot frac{partial P}{{partial n}}) as the value-of-avoiding-transmission (VAT). Equation(6) captures the combined value of the reduced risk and reduced travel time that would be afforded by a small reduction in the number of people commuting. This could be, for example, the result of using a different (or less crowded) mode for transport. Equation(6) can provide an interpretation for our empirical work related to the marginal rate of substitution between transportation modes associated with different likelihoods of infection.

Follow this link:

COVID-19 and the value of safe transport in the United States | Scientific Reports - Nature.com