This is either misinformed or biased. Let me clarify a few things as a Chinese whose alma mater has been the very frontline against the virus in Wuhan.
Arrested doctors who warned others about a new disease.
I haven't heard of any doctor going to jail for that. Take the most notable one for a counterexample, our whistle-blower, Dr. Li Wenliang was summoned and admonished by local police on 3 Jan 2020, he signed "Yes, I understand." on the admonition letter and then returned.
While this is not something to be proud of, it's certainly not an arrest either. (the local police apologized to him days later and he is now officially recognized as a national hero).
Covered up the existence of this new disease for over two months.
The first known patient started experiencing symptoms on 1 Dec 2019. On 30 Dec 2019, The Wuhan Municipal Health Committee reported to the WHO that 27 people had been diagnosed with pneumonia of unknown cause.
So the cover-up was 1 month tops. You don't count from day 1 since very little was known at the time.
On 23 Jan 2020, lockdown on Wuhan is announced. If you still didn't know the *existence* of the coronavirus after that, it's your government's problem, or yours.
Punished anyone that talked about it until they could no longer deny it.
This is too broad. In my experience, everybody around me started talking about it since the middle of Jan, no one ever received any punishment, nor even felt the risk of going to be punished.
Did everything the same as the SARS epidemic and made everything worse up until it had reached the stage that infected people were traveling and infecting the rest of the world.
The virus has an asymptomatic incubation period of as long as 20+ days, while people are traveling across the planet every second. Plus, judging from how people reacted to the situation when China already had tens of thousands of cases, "just a flu", "a hoax", "only sick people wear face masks", I seriously doubt other country would do much better.
Of course, I'm not denying there should be people in the municipal authorities to be responsible for the initial cover-up.