In Modeling the Human Trajectory, David Roodman introduces an internally consistent statistical model of world economic history. It casts a Gross World Product (GWP) series as a sample path whose specification is a stochastic calculus-based growth model.
Their univariate fit implies that, conditional on the 2019 GWP, explosion to infinity is essentially inevitable. It finds a median explosion date of 2047.
As of 2018, GWP was $82 trillion in 2010 US$.