Dr Anthony Fauci said spikes in cases usually take "a couple weeks" after the event.
https://www.nbcnews.com/meet-the-press/video/full-dr-fauci-it-likely-will-get-worse-in-the-next-couple-of-weeks-98718789839
I suspect he's trying to save lives, in which case he's right that people need to be careful for 2 weeks after an event (14 day incubation period). Otherwise I don't understand why he's say a spike is not evidence for 2 weeks... maybe up to 2 weeks? I should check what other epidemiologists or virologists say about it.
In the meantime, the data is starting to show faster growth in cases. Here's the past 4 days of growth, measured against 7 days prior:
Dec 30 .. Jan 2 : 6.90% .. 6.98% .. 7.26% .. 7.56%
I initially (mistakenly) expected simple exponential growth, such as what happens if each carrier infects on average two more people (r=2) typically 3-5 days after infection: 2, 4, 8, 16, 32, 64, 128, 256... What has actually happened seems to be that the virus hits a few limiting factors as it spreads, and so the growth rate does not continue increasing forever:
1) The virus invades new territories, quickly infects the most risk-exposed, including, but not limited to, the reckless, and then spreads at a rapid rate to the next generation, a slower rate to the next generation, and a steady rate to the next - essentially moving down the tiers of risk-exposure. This all happens within a geographical area (e.g. NYC, the Dakotas). Exponential growth in any given area eventually slows as the population of highly-risk-exposed people is depleted and the virus must spread among the more careful, with a lower "r".
2) The virus spreads by penetrating "bubbles" or social/work networks and rapidly infecting people in those networks before growth slows. Fast growth only occurs when the virus infects a new set of bubbles/networks, which goes hand in hand with its movement to new geographic areas. As networks are infected, people in them reduce contact as they observe multiple cases among other people they know, thus slowing the spread. As people get more careful, the "r" lowers and there are fewer bridges between networks.
3) The virus spreads in waves as restrictions are enacted or relaxed, or as cultural behaviors such as restarting school after summer break, gathering for holidays, or the Sturgis rally occurs. Note that each wave has a behavioral/historical explanation or cause, that occurred a few weeks before cases really began to jump. Collective behavior drives the "r" value.
So the virus may face natural limiting factors including (1) the supply of risk-exposed people within any given geographic area, and (2) the informal lockdown of social/work networks after people become aware of multiple infections around them. Note that it would likely take several weeks to exhaust the supply of risk-exposed people in a given area, even if the average time to transmit the infection one generation was only 3-5 days. Also note that it would take a couple of weeks for people to realize others in their network are getting sick, and for them to reduce contact in time so that their own infection is the end of the line (r=0). Contact tracing attempts to speed information transfer so that factor #2 is increased, but most people aren't answering the phone.
So we're left with limiting factor #3. As Republican governors in Florida, the Dakotas, and the South have demonstrated, the pandemic will never get bad enough for them to close restaurants, ban superspreader religious events, or even mandate masks. Mayors have been more bold, despite the pushback, but apparently not bold enough. So January-February will see hundreds of thousands of deaths, but starting in late Feb. I would not be surprised to see a nationwide mask mandate and some herd immunity start to lower the "r". The herd immunity might be due to equal parts infection and vaccination though!
