"If there were a period of about a week where no symptoms arose, then the virus would become significantly more deadly."

This is precisely the problem with the new Ebola Zaire strain: the incubation period varies from ~3-21 days, during which the patient may show no symptoms yet can spread the virus. And since Ebola Zaire's mortality rate is 60-90% (early estimates were on the high end) this is an epidemiologist's nightmare.