Bill Gates, left, and Paul G. Allen have committed funds to help fight the Ebola virus. (Nati Harnik/AP/Frazer Harrison/Getty Images/Eric Risberg/AP)

The U.S. emergency response team working on Ebola in Kemena, Sierra Leone, was stuck. The vehicle they had been using to transport patients, deliver oral rehydration packets and do other critical work had two flat tires. It was early October, a time when things seemed to be spiraling out of control in the epicenter of the crisis, and there wasn’t a moment to waste.

The stranded Centers for Disease Control and Prevention workers knew just where to call for help: a little-known nonprofit — the CDC Foundation — that received millions of dollars in donations in recent months from Facebook chief Mark Zuckerberg and his wife, Priscilla Chan, Microsoft founders Bill Gates and Paul Allen, and other philanthropists.

Within the hour, the organization authorized enough money for the staff to make the repairs. And within the week, it had begun ordering and shipping to the region about 200 additional pickup trucks and four-wheel-drive cars — $5 million worth.

The unpredictable nature of the Ebola virus has made the government’s partnerships with private donors critically important in the crisis response. Working outside the politically charged federal appropriations process and the sometimes sluggish bureaucracy, foundations and private individuals have been able to offer much-needed relief for those on the front lines.

“In an outbreak setting where you need flexibility and timeliness, this was critical for the gaps that were identified,” said Joseph Bresee, an epidemiologist who led the Centers for Disease Control’s mission in Sierra Leone until he returned to the United States a few days ago.

Bresee said these unexpected needs, big and small, came up nearly every day: motorcycles to deliver supplies through narrow roads; baby formula for a child whose parents had just died; data-entry staffers to help log the growing number of cases. “There would not have been an obvious second way to do what we did without foundation funds,” he said.

Unlike other major natural disasters — the 2011 tsunami in Japan or the 2010 earthquake in Haiti — the Ebola outbreak has been a bust when it has come to fundraising among members of the public. Instead, most of the donations have been from a handful of tech billionaires who have tried — with only limited success — to inspire others to give to the cause.

Private donors have pledged or provided $348 million in aid — $175 million from the Zuckerbergs, the Gateses and Allen. The U.S. government has contributed or committed about $378 million in aid and pledged an additional $45 million, according to a U.N. report.

President Obama last week asked Congress for an additional $6.18 billion in emergency aid to fight Ebola, but it could be weeks before any funds are approved and even longer before they will have an impact on the ground.

In contrast, the money from foundations often is available almost instantaneously. “Hours — literally hours,” said Dune Ives, who manages the day-to-day operations of the Paul G. Allen Family Foundation. One of the first organizations to donate money to the Ebola effort, it has committed more than $100 million. “In the case of this humanitarian crisis, we know how important it is to get the money out very quickly.”

Efforts to engage private donors and corporations in projects traditionally managed by the government have accelerated during the Obama administration. There are now at least four private foundations directly supporting the work of different parts of the government — the National Institutes of Health, the National Park Service, the military and the CDC — and there are at least 21 offices dedicated to nurturing strategic partnerships.

James M. Ferris, director of the Center on Philanthropy and Public Policy at the University of Southern California, said that past collaborations between government and donors have been informal and episodic. But in recent years, especially given budget concerns, there has been an effort to formalize them — leading to experimentation in new models of working together.

Much of the private money donated by the billionaires is being managed by the Atlanta-based CDC Foundation. It is the steward of the funds that the CDC’s Bresee and his colleagues said were critical to their work.

Created by Congress in 1995, the foundation is a private charity that exists to support the efforts of the CDC but is independent. It has received more than $43 million in donations for Ebola — the largest amount it has ever received in such a short time and significantly more than what the foundation usually receives in one year for the more than 250 other programs it manages around the world.

Ferris said the CDC Foundation and others are a mechanism for government agencies to receive private donations they could not otherwise accept. From the perspective of the philanthropists, the government-associated foundations are attractive because they can amplify their donations.

“They are looking to have a greater social impact, and even the larger philanthropic organizations can only go so far. That’s why they partner with government — to influence public policy,” Ferris said.

Charles Stokes, executive director of the CDC Foundation, said that after CDC Director Thomas Frieden came to them for help in the summer, his staff began contacting donors they had worked with in the past, such as the Bill & Melinda Gates Foundation, which gave $2 million, and the William and Flora Hewlett Foundation, which gave $1.5 million. As word got around, other donors began to approach the CDC Foundation.

The Allen foundation’s Ives said the group’s efforts in Ebola began in July when she received an e-mail from Allen. “He asked what the global response to this is, is anybody paying attention and how can we help,” she recalled. “As the number continued to escalate, he authorized the initial grants.”

As the crisis continued, Ives, Stokes and others from the Allen and CDC foundations worked together to try to figure out where they could make the greatest impact. They realized that in the chaos of the crisis, the emergency operations nerve centers , which facilitate communication between the responders, were lacking. So the organization earmarked $12.9 million to construct buildings and provide computers and staffers in affected countries.

“We saw that as a really critical backbone,” Ives said.

Stokes added that the Allen foundation was very forward-thinking in their grant. “They wanted to do this in a way that doesn’t just meet immediate needs, but prepares these countries for the next outbreak that could become a global disaster,” he said.

The call from the Zuckerbergs was a surprise.

“We had not previously worked with them, but they wanted to know how they could help,” said Stokes, a longtime public health official.

In a Facebook post on Oct. 14 announcing the couple’s $25 million grant, Zuckerberg wrote that “we need to get Ebola under control in the near term so that it doesn’t spread further and become a long term global health crisis that we end up fighting for decades at large scale.” They money has been used to purchase equipment such as medical supplies and the vehicles that were sent to West Africa. It also has gone toward the hiring of local workers, such as drivers and translators, to augment the efforts of the more than 165 CDC staffers in West Africa and the more than 500 staffers backing them up in the United States.