By Amanda Jackson, CNN

(CNN) -- They are usually eligible for Covid-19 vaccinations, but homebound seniors can often struggle to find a way of making the appointment to get the shots

One city in Texas has found a solution that has brought relief to many family members -- and it's become a model across the state.

"The program came about as a need to vaccinate our most vulnerable population -- homebound seniors," Corpus Christi Mayor Paulette Guajardo told CNN. "We need to vaccinate as many people as we can and the fastest way."

For Jo Ann Garza, getting her 95-year-old mother vaccinated was a top priority -- but she struggled to get an appointment.

Garza said she called a doctor's office and tried applying online but wasn't able to secure a vaccine appointment. Then her phone rang.

"I don't normally answer the phone with numbers I don't know, but I picked it up," she told CNN on Wednesday. "The lady was like 'We would like to register your mother and we will send a firefighter to her house to vaccinate her.'"

Garza said she breathed a sigh of relief and then asked how soon they could get over there.

The program her mother, Alicia Perez, qualified for is called "Save our Seniors." It's a partnership between the city of Corpus Christi, the city's fire department and the local Meals on Wheels to vaccinate homebound citizens who can't travel.

Mayor Guajardo, only three weeks into her term, said she was inspired by her parents who are in their eighties. To date, more than 2,000 residents have been vaccinated.

"It's about finding those populations that are harder to reach for many reasons," she said. "I believe that every mayor in the state and country should take vaccinations directly to senior citizens and the homebound in their home."

At first, the program used the database for Meals on Wheels participants to reach out to residents and schedule appointments. That's how Garza said she received the call.

"Many say that our children are our most valuable commodity, I believe that it's our seniors," Corpus Christi Fire Chief Robert Rocha said during a press conference last week. "Those that make up the greatest generation of our country who deserve to have the vaccine delivered to their homes."

Now, since the list has been exhausted according to the mayor, each week a hotline is opened with a set number of appointments for residents who are homebound. It includes seniors and the disabled.

Firefighters then visit the citizen at their home and administer the vaccine, s well as the second shot a few weeks later that is required in the case of the Pfizer/BioNTech and Moderna vaccines.

"They are very nice and cordial," Garza said about when the firefighters visited her mom. "They sat with her the 15 minutes after to make sure there wasn't any side effects."

Garza said that the program helped ease her fear of what would happen if her mother contracted the virus.

As for her mother, the first thing she requested after being fully vaccinated was to go shopping and get her hair cut. "She's a handful and has a very strong will and mindset," said Garza. "She's set to live till she's 100. Now she can with the vaccine."

A model for the state

The program has been such a success that Texas Governor Greg Abbott announced last week that it will become a model for the state.

"A key part of our mission in the fight against COVID-19 is to vaccinate seniors and those who are most at risk — and senior vaccination programs like the one in Corpus Christi are crucial to accomplishing this mission," Abbott said in a press release.

"By implementing a similar model throughout the state, and with the support of the Texas National Guard, we will reach more homebound seniors in communities across Texas and provide them with these life-saving vaccines."

The state has deployed more than 1,100 National Guardsmen to assist in efforts and dedicated 8,000 vaccines for the program to distribute.

"The city of Corpus Christi is extremely proud to have a model that has been launched statewide and hopefully nationwide," said Mayor Guajardo. "We owe a debt of gratitude to Governor Abbott for making that happen. We are always open to assist other cities to help implement the program to their communities."

This week, Abbott announced that, partly due to the program, all seniors should be vaccinated by the end of March.

He also announced that he is rescinding executive orders requiring the use of face masks and is opening up businesses back to full capacity.