where source city population and distance are normalized together. n and m are estimated parameters on source and destination population sizes, respectively. d ij represents the distance between cities with power parameter g to be estimated. w is an estimated parameter relating the infectivity of a city to its mortality rate. When w ¼ 1, the infectiousness of a city at time t i is proportional to the death rate in that city at time t i þ 1. We use one week as a lag from infection to death [24, [34] [35] [36] . A value of w ¼ 0 gives a flat infectiousness profile, independent of the death rate in the source city. Intermediate values of w give variation in infectiousness, which scales sub-linearly with weekly mortality. Estimating w allows us to assess whether mortality rate is a good proxy for infectiousness in an infected city. b is a time-invariant estimated infectivity term.