TRUMP'S CLAIM: When asked how he would lead the country during the next phase of the pandemic, Trump said that "there was a spike in Florida, and it's now gone. There was a very big spike in Texas, it's now gone. There was a very big spike in Arizona, it's now gone. And there are some spikes and surges in other places. They will soon be gone."

FACT CHECK: Although cases did "spike" and reach record levels in Florida, Texas and Arizona earlier this summer, then steadily decreased for a few months, cases in all three states have been on the rise for the last several weeks.

Since Oct. 1, the seven-day average of new cases has doubled in Arizona, according to an ABC News analysis of COVID Tracking Project data, recording an average of 880 new cases a day.

In Texas, more than 6,000 cases were reported on Thursday, increasing by 37% in the last two weeks, and in Florida, the seven-day average is still hovering at 3,300 new coronavirus cases a day.

Additionally, nationally, cases are not in fact, going away.

New cases have been rising rapidly for the last five weeks.

Since Sept. 12, the seven-day average of new cases has surged by 77.5%. Just in the last 10 days, the U.S. has reported eight days with over 50,000 new cases reported, and on Thursday, the U.S. reported over 73,000 new coronavirus cases, the highest daily figure in nearly three months.

-ABC News' Arielle Mitropoulos

BIDEN CLAIM: "The idea that we're in a situation that is going to destroy Medicare, this is the guy that the actuary of Medicare said ... if, in fact, he continues to withhold -- his plan to withhold the tax on Social Security, Social Security will be bankrupt by 2023."

FACT CHECK: Biden’s claim is misleading on a number of fronts, but is rooted in an action Trump took and comments he made in August.

Trump signed an executive order in August that temporarily halted the collection of the payroll tax, a tax on wages split by workers and their employers. He subsequently asserted that he would like to permanently eliminate the tax.

In 2019, the tax financed 89% of Social Security. Workers and employers each contribute 6.2% of wages, while self-employed people pay the full 12.4%.

However, following Trump’s signing of the executive order, he has said publicly that he will draw from the government’s “general funds” to cover any lost funding for Social Security, a scenario the actuary accounted for in his response to the group of Democratic senators, telling them that the solvency of the program will be essentially unchanged if Trump follows through and actually proposes legislation akin to his public comments.

But since Trump issued his order, and despite Biden’s claims that Trump put forward a full-fledged “proposal,” Trump and the GOP have not unveiled more detailed legislation on how they would prevent the elimination of the payroll tax from impacting the financial security of Social Security.

In late August, Democratic Sens. Ron Wyden, Bernie Sanders, Chris Van Hollen and Chuck Schumer sent a letter to the chief actuary of the Social Security program asking what the effect of eliminating the payroll tax would be. In response, the chief actuary said he was not aware of any “hypothetical legislation” that had been proposed. In simply responding to the scenario posed by Senate Democrats, he said the Social Security benefit program would be depleted of funds by 2023 if there's no additional stream of funding identified to offset eliminating of the payroll tax.

What Trump has not said thus far is what programs could potentially be impacted by the redirection of funds from the government's general fund, only that he will protect Social Security benefits. The general fund finances the operations of the U.S. government, such as recording "funds received and distributed by the Department of the Treasury," and it "includes assets held by government-sponsored entities like Fannie Mae and the Internal Revenue Service."

-ABC News' John Verhovek

TRUMP'S CLAIM: "And I will tell you that I had something that they gave me, a therapeutic, I guess they would call it, some people could say it was a cure. But I was in for a short period of time and I got better very fast or I wouldn't be here tonight."

FACT CHECK: Trump also repeated something he has said before, praising the antibody treatment he received a "cure."

But as of yet, there is no known "cure" for the novel coronavirus.

The antibody cocktail given to the president -- made by biotech company Regeneron -- is thought to be promising, though still in its experimental phase.

Regeneron's experimental treatment is a cocktail of two synthetic, pharmaceutical versions of what occurs naturally in the body to fight off infection. Late last month, Regeneron published positive, yet preliminary data for its cocktail treatment showing it improved symptoms in patients without severe disease.

While the Food and Drug Administration has not yet authorized it, Trump was granted access to it under "compassionate use," enabling him to get it outside of a clinical trial.

A Regeneron spokesperson confirmed to ABC News that Trump's medical staff reached out to the company for permission to use its monoclonal cocktail, and that it was cleared with the FDA.

-ABC News' Sony Salzman and Sasha Pezenik

TRUMP'S CLAIM: "I want to open the schools. The transmittal rate to the teachers is very small."

FACT CHECK: The Centers for Disease Control and Prevention has updated its guidance to note a "body of evidence is growing" that kids "might play a role in transmission." Still, the role children play in community transmission is not yet fully understood. 

In one recent study, the CDC found transmission is unclear: "Recent evidence suggests that children likely have the same or higher viral loads in their nasopharynx compared with adults and that children can spread the virus effectively in households and camp settings."

Schools haven't been studied as closely because many remain closed and not every school is reporting outbreaks. One concern is that children might be transmitting the virus without exhibiting symptoms, and testing people without symptoms remains limited.

Overall, officials say the lower transmission levels in a community, the less likely schools will spread the virus.

-ABC News' Anne Flaherty