If you are eligible for funding (US citizen/PR) and you are seeking funding then it is best to wait for the next cycle.
But if you are not a US student and/or not seeking funding then I would suggest you take a chance and apply based on where your profile may have a chance at regardless of the fact that it is too late into the cycle.
There are schools with late deadlines/rolling admissions for some MPH programs. Here are some schools that I had looked into and applications can still be sent to. There may be more programs out there with open admissions that I haven't listed below. So do check SOPHAS.
Tufts - 15/4
Cincinatti - 1/4 to 1/8 depending on concentration
Texas A&M - 1/5
WU - Rolling
Boston - Rolling
Brown uni - Rolling
Buffalo - 15/7 (US) 1/4 (Intl)
LLU - 1/4 to 1/8 depending on concentration
Tulane - Rolling
Icahn - 1/6
Rutgers - 1/5
Minnesota - 1/5 to 1/8 depending on concentration
ETSU - 1/6 (US) 1/5 (Intl)
Thomas Jefferson - Rolling
Emory - 15/7