Measles cases in California reached triple digits for the first time this year, jumping by four since Wednesday to 103, state public health officials said Friday.

But the number of Bay Area cases remained steady at 13 and was contained to Alameda, Marin, San Mateo and Santa Clara counties.

The outbreak of the highly contagious viral infection dates to mid-December, when 39 people who visited or worked at Disneyland in Anaheim contracted the virus.

Health officials said an additional 28 cases include people who had close contact or were in a common room with one of the Disneyland visitors who contracted measles. But 36 cases — over one-third of the total — have no known route of exposure, officials said.

The latest numbers follow a high-profile proposal this week by two state legislators aimed at decreasing the chance of measles outbreaks in California schools.

Sen. Richard Pan, D-Sacramento, and Sen. Ben Allen, D-Santa Monica, on Wednesday said they will introduce a bill to eliminate a controversial “personal belief exemption” that allows California parents to refuse to vaccinate their children.

And California’s two Democratic U.S. senators, Dianne Feinstein and Barbara Boxer, asked state health officials to go further and consider eliminating the “religious exemption.”

The political momentum to reform California’s permissive “opt-out” vaccination policy comes at a time when the state is experiencing its worst measles outbreak in two decades — which some health care experts have attributed to the state’s growing anti-vaccine movement.

The groundswell continued Friday, when the University of California system announced that by 2017 all UC students must present proof of full immunization against the measles virus and eight other pathogens before they can register for classes. Students must also be screened for tuberculosis.

UC health and administration officials said they spent the past year drafting the requirements leading up to Friday’s announcement. “There are still documented cases of outbreaks of vaccine-preventable diseases in California and on the campuses each year amongst those who were not properly immunized,” Mary Knudtson, who chairs the UC Immunization Policy Committee, told the UC system’s news service.

The California Medical Association quickly lauded UC’s new vaccination requirements.

“We must keep these trends going in the right direction,” CMA president Luther Cobb said in a prepared statement Friday. “There is no need to be faced with dangerous and deadly diseases that are preventable thanks to some of the most monumental scientific discoveries in history.”

Currently, UC students must only present proof of vaccination for hepatitis B. Officials are now working out a verification system for immunization records and for students or their parents to seek an exemption from one or more vaccination requirements.

The new regulations will take effect fall 2016, but will not be enforced until fall 2017.

“We wanted to phase it in and build awareness before enforcing these new rules,” UC spokeswoman Shelly Meron said.

In addition to measles and hepatitis B, prospective UC students will have to show proof of vaccination against mumps, rubella, meningococcus, chicken pox, tetanus, diptheria and whooping cough. California recently experienced its largest outbreak of whooping cough since 2010, with more than 10,000 cases and two infant deaths.

At the national level, Sen. Boxer and Congresswoman Anna Eshoo, D-Palo Alto, on Friday announced they will introduce legislation next week requiring full vaccination for all children enrolled in Head Start and Early Head Start programs throughout the country.

“This bill is a ‘booster shot’ for our nation’s vaccine policies and will mitigate the spread of deadly disease,” Eshoo said.

Under their proposal, parents could still seek a medical exemption from a certified health professional. In fiscal year 2013, more than 900,000 students nationwide were enrolled in Head Start programs, with 99,000 in California.

State schools chief Tom Torlakson on Friday also released a statement urging California parents to have their children vaccinated.

Citing his background as a science teacher, Torlakson said, “Vaccines have been proven safe and effective for those students who are healthy enough to get the immunizations. They keep your child and your community protected.”

California public health officials recommend immunization with two doses of the MMR vaccine for anyone who has not been vaccinated against measles. If properly administered, health officials say the vaccine is more than 99 percent effective in preventing measles infection.

Contact James Urton at 408-278-3415. Follow him at Twitter.com/jamesurton.