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You can use the "dateFrom" and "dateTo" to keep track of the logs (within the specified date/time period) you have downloaded.

now = time.time()
less15Mins = now - (60 * 15)

dateFrom = datetime.utcfromtimestamp(less15Mins).strftime('%Y-%m-%dT%H:%M:%S.000Z'
params = {
    'dateFrom': dateFrom,
    'perPage': 1000
}

Every time you read 15 mins backward from the current time.