The state’s COVID-19 infection rate on Tuesday reached 3 percent — continuing a steady rise that one health expert considers “a little shocking.”

The jump to 3 percent Tuesday came after the state’s infection rate rose from 1.7 percent to 1.9 percent over the weekend.

“The fact that it’s happening so fast is a little shocking,” said Dr. Zane Saul, Bridgeport Hospital’s chief of infectious disease. “I think we all expected there would be an uptick in cases, but it seems to be going up pretty rapidly. I don’t know if we’re headed toward another lockdown or what it’s going to be.”

There were 434 new coronavirus cases reported on Tuesday, five deaths and 12 more hospitalizations, which have now reached 207. Just a few weeks ago, hospitalizations were down to 110 before rising to 195 on Monday.

“We’re very concerned,” said Dr. Gregory Buller, chairman of medicine and associate chief medical officer at Bridgeport Hospital. “A 3 percent infection rate right now translates into more hospitalization a few weeks from now. It’s just worrisome.”

The one bright spot seems to be that the patients coming to the hospital now are less sick than at the start of the pandemic. Buller said, of the 19 patients hospitalized at Bridgeport on Tuesday, only one was in the intensive care unit. Though the COVID patients at Bridgeport Hospital do need oxygen and other treatments, Saul said none of them are on ventilators.

Saul and Buller said the spike reinforces the need to wash hands, socially distance from others and wear a mask. Buller said he would also like to see greater penalties for not wearing a mask. He compared masks to seat belts in cars — both precautions meant to address a public health issue.

“You can’t drive a car without a seat belt — well, you can but you’ll be in big trouble if you get caught,” Buller said.

On Tuesday, Lamont also announced the creation of the Connecticut CARES Small Business Grant Program to help small businesses and nonprofits impacted by the economic downturn caused by the pandemic.

The program will provide businesses and nonprofits with fewer than 20 employees or a 2019 payroll of less than $1.5 million with a one-time $5,000 grant. Lamont will commit $50 million from the state’s Coronavirus Relief Fund, provided through federal CARES Act funding, to fund the program.

As the state’s infection rate continues to climb, universities and colleges in Connecticut are continuing to report virus cases and make changes as needed — though some schools are doing better than others.

Trinity College in Hartford, which switched to online classes last week, plans to resume in-person classes on Wednesday after it saw a drop in active cases from 32 last week to 18 — 17 students and one employee — on Monday. Of the 18 active cases, Trinity College said nine are students in isolation spaces on campus.

At the University of Connecticut, officials announced eight new cases — three on-campus cases where individuals were already in quarantine and five cases among employees/affiliates, one of whom had already been working remotely since March.

Sacred Heart University in Fairfield is reporting at least three additional COVID-19 cases since last week, the university announced Monday. The school has now reached a total of 36 infected students on campus and one infected employee, data shows.

Yale University reported 23 cases of the virus among students and four among faculty and staff last week. Five of the infected individuals are on-campus students, the data shows.

Fairfield University reported four new cases of the virus on Monday — all among students. Those additional cases put the university’s total number of active positive cases at 80, which includes four faculty and staff members. Eighteen of the student cases are on-campus individuals.

On Monday, the governor announced a change to the state’s travel advisory, which he further clarified Tuesday.

Connecticut previously required anyone traveling from states with at least 10 new COVID-19 cases per day per 100,000 residents or a 10 percent positivity rate to quarantine when coming to the state, or prove they were safe. Now, the state requires anyone to quarantine if they come from a state with both.

Lamont said Monday the change is meant to narrow the list of states impacted by the quarantine requirements, while also allowing officials to enforce mandates more effectively.

There are two exceptions to the travel advisory change so far — New York and New Jersey.

“Our states have worked together successfully in combating this pandemic since the beginning and we’ll continue to do so,” Lamont said Tuesday. “We’re urging all of our residents to avoid unnecessary or non-essential travel between states at this time, but will not subject residents of our states to a quarantine if coming from a neighboring state.”

Lamont said he is in the process of getting in touch with the governors of Massachusetts and Rhode Island to potentially expand the exception to include those states as well.