The emergence and spread of the novel coronavirus in Washington and the world has exacted a steep toll in a very few weeks, carving a path of deaths, illnesses and tense uncertainty as a global outbreak unfolds.

The virus’ relentless spiderweb has spread in the weeks since the first cases were recognized in Wuhan, China, in December, shaking world leaders and emptying streets from Shanghai to Milan to Kirkland, Washington, where residents have found themselves at the unlikely U.S. epicenter of a worldwide health crisis.

Scientists tracking the spread of the virus in Washington expect the number of cases in the state to spike over the next several weeks — just as they did in China — and warn that, while the cost…