Officials now report a 500% increase in the number of vaccines being administered when compared to the same time past year.
"We're just happy that we're prepared and that there is vaccine available".
The case is the seventh in Texas in recent days.
Meanwhile, Ukraine had the highest rate of measles cases in Europe, at 1,209 per one million population - 10 times the country's rate in 2017.
Statewide in Washington, orders for measles vaccine jumped about 30 percent in January compared with the same month previous year, climbing from 12,140 doses to 15,780 doses, figures showed. The government, with support from UNICEF and the World Health Organization, has initiated a series of vaccination campaigns to raise coverage closer to the more than 90 percent needed to protect the entire population against measles via herd immunity, where sufficiently high proportion of individuals limits the virus's spread.
"There's no reason we should be having this outbreak", says Melnick.
"I would rather it not take an outbreak for this to happen", he said.
Morning Rounds: Measles outbreak and vaccine safety
Washington State is under a measles state of emergency as measles cases grow and hot spots are flaring up across the country. This year, Washington state is averaging more than one new measles case a day as officials try to stop the disease's spread.
A case of measles was confirmed in Denton County on Wednesday, bringing the statewide total to seven. Denton County officials said they do not believe their case and the Houston ones are connected.
However, New York legislation opposes philosophical exemptions for vaccinations, meaning that children must be up-to-date on required vaccinations in order to attend school unless they have a religious or medical exemption.
Dr Zsuzsanna Jakab, WHO regional director for Europe, said: "The picture for 2018 makes it clear that the current pace of progress in raising immunisation rates will be insufficient to stop measles circulation".
Despite availability of safe and cost-effective vaccines since the 1960s, more than 100,000 people die globally from the illness each year - the majority of whom are children younger than five years old in developing countries. It can be prevented by the measles, mumps and rubella (MMR) vaccine...
Measles outbreaks have also sprung up in in more than a dozen U.S. states since the start of 2019.
Washington and Oregon Outbreaks: The Tell-Tale Signs Both Washington and Oregon permit religious and philosophical vaccine exemptions, according to the National Conference of State Legislatures.
Depending on the relevant state and territory health departments, in Australia, there are some governmen-funded catch up vaccination programs for refugees and migrants. Some anti-vaxxers cite a debunked study from the 1980's that vaccines to autism. Others object to the timing and combinations of vaccines and from compulsory vaccination of their children.