By CBS3 Staff

PHILADELPHIA (CBS) — Philadelphia officials are cautiously optimistic the city is past the worst of the coronavirus epidemic as the number of COVID-19 cases nears 13,000. More than 300 new cases were reported Monday, bringing the citywide total to 12,868. Twelve more deaths were also announced, raising Philadelphia’s death toll to 484.

“We are in a very critical point in this crisis. There may be early signs that we are past the worst of this but the epidemic could surge back at any point,” Mayor Jim Kenney said. “We are still very vulnerable to a rise in cases and the only way to prevent it is to continue staying at home unless it’s absolutely necessary.”

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During Monday’s press conference, Philadelphia Health Commissioner Dr. Thomas Farley says there “are signs of hope we are past the worst.”

“It’s looking like we are past the peak of this epidemic, that we are now on the downslope,” Farley said. “Now we’re not going down quickly, but the number of daily cases we’re getting seems to be going down on average.”

Farley explains that the falling case count shows that the reproductive rate is below 1.0, meaning people with the virus are spreading the infection on average to less than one person for every one who has COVID-19.

The reproductive rate number needs to stay below 1.0 for the epidemic to end.

“We’re showing that we can win but the game isn’t over yet, not by a long shot. There’s still much more we need to do in order to win,” Farley said.

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Kenney reiterated to Philadelphians to stay home and follow public health guidance after video showed residents ignoring social distancing guidelines on Saturday.

“The better we follow the public health guidance, the sooner we will get our lives back to normal. But I want to be very clear that the opposite is very true — ignoring the guidelines will only prolong our current circumstances,” Kenney said.

The commonwealth is preparing to reopen parts of Pennsylvania within the next two weeks, by easing restrictions on certain businesses. But a state with more than 43,000 positive COVID-19 cases can only expect a gradual return to some sense of normalcy.

In Philadelphia, experts say there’s no way to estimate a reopening time frame.

“There’s still many cases of this infection here in Philadelphia residents. Many people have the infection and don’t even have symptoms, they don’t even know it. You should assume that anyone you meet has the virus. Put it another way, you should assume you have the virus and may not know it,” Farley said. “So, you don’t want to spread this infection on to your family, or your friends, neighbors, or anybody you meet on the street, so that means following the recommendations we said before.

“I know it will be challenging in the southeast. The southeast will be able to go eventually from red to yellow, etc.,” Pennsylvania Health Secretary Dr. Rachel Levine said. “But it’s clearly not going to be at this time because that’s where we’re seeing most of the cases.”

Statewide, there are 43,255 COVID-19 cases and 1,807 deaths.

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CBS3’s Natasha Brown contributed to this report.