Hand-hygiene mitigation strategies against global disease spreading through the air transportation network

Christos Nicolaides; Demetris Avraam; Luis Cueto-Felgueroso; Marta C. González; Ruben Juanes

where od f i j is the number of passengers that traveled in September 2017 from origin i to destination j, and the origin-destination probability matrix O O OD D D p p p = [od p i j ] where od p i j is the probability that an agent travels from origin i to destination j. Each element of the O O OD D D p p p matrix is calculated by od p i j = od f i j / ∑ j od f i j where ∑ j od f i j is the total number of passengers that traveled from origin i. We then assign a 'home' population P i at each subpopulation i following the nonlinear empirical relation P i = α √ T i , where T i is the total traffic at airport i and α is a constant parameter that is identified to give a total population size of N = ∑ i P i individuals. In other words, each individual agent is initially assigned to its 'home' subpopulation i. Within the mobility route, the agent that was assigned to home i chooses to travel at a 'destination' airport j with probability extracted from the O O OD D D p p p matrix. If the two nodes i and j are connected by more than one path (i.e. direct when the two airports are connected with direct flights and indirect when the two airports are connected only with connecting flights), then the probability that the agent selects a given path is proportional to the relative number of passengers traveling in each direct or indirect flight from origin i to destination j. After each trip (from origin i to destination j), the agent returns back to its home airport. Thus, the stochastic mobility model generates the spatial trajectory for all agents. In addition, using realistic waiting times at the three distinct locations where an agent can be (i.e. home, connecting airport or destination) and actual flight times required to travel between the airports we express the spatio-temporal patterns of all the agents at the granularity of an hour. The waiting times at home airports, connecting airports and destinations are provided by the Bureau of Transportation Statistics 2010 34 , and follow right-skewed distributions with means 897.87 hours (∼37 days), 1.33 hours, and 127.36 hours (∼5 days) respectively. The average flight times between each airports i and j, are estimated as the ratio of the geographical distance of the two airports, d i j , calculated by the spherical law of cosines, over the average velocity of an airplane which is assumed to be constant and equal to 640 km/h considering the changes in takeoff, climb, cruise, descent and landing speeds.