The Last Emperor. The Remaining series, #5

A Japanese engineer in his fifties becomes Asia's sole survivor. He activates a service robot as his only companion, drives a bullet train alone, and walks the Great Wall in silence. When the robot dies, he sinks into grief - until he hears the UK woman's daily broadcasts. He hatches a plan to cross the Bering Strait on foot, only to realise the ice has betrayed him. He ends the book promising to build a ship and find her halfway.