Modeling the impact of human mobility and travel restrictions on the potential spread of SARS-CoV-2 in Taiwan

Meng-Chun Chang; Rebecca Kahn; Yu-An Li; Cheng-Sheng Lee; Caroline O Buckee; Hsiao-Han Chang

We built a travel model to estimate the proportion of time people living in location i spend in location j (Pij) by fitting the model to the Facebook movement data. Xij represents the proportion of people living in location i currently in location j, and UV W represents the equilibrium state of Xij, and its value under the fitted model is used as our estimate of Pij. People living in location i travel with probability Fi, and the probability that a traveler from location i travels to location j is denoted by Tij. Travelers go back to their home location at probability # per unit of time. Mij,t,t+1 represents the number of people moving from location i to location j between time t and t+1. For simplicity, we assumed that the majority of travel is work-related travel and on average travelers spend eight hours in the travel destination ( # =1 given the unit of time is 8 hours) and that Tij is proportional to Mij, leaving Fi the only parameters to be fitted. We used a gradient descent algorithm to find the local optimum solution for Fi, where the cost function is defined by the sum of the squared difference between normalized mij and the normalized value of Mij from the model. We calculated UV W under fitted parameters to obtain estimates of Pij.