of course if the plague continues and lasts a long time it will greatly impact the economy, even now there is news that says 80% of patients have recovered in China and have started their activities as usual.
then in other countries this is still the beginning, where prices for staples or things related to this virus go up very high like masks.
So the rumor that the virus will be completely solved in June might be true and maybe a little longer.
The economic impact of this pandemic is already huge, but the banking system is intact, fortunately. Few people, if any, would profit from its collapse.
As for when things will start to improve, I think it can take a month or two, but hardly more than that. These days it's very important to stay out of panic, keep calm, and keep the quarantine, of course.
The banking system is not completely intact, it has received some relatively large influence during this period although it is still operating, the most visible thing is that people are constantly withdrawing the money they have saved to spend during the time they are off work, the capitalization that can be transferred in banks is probably not too much, some loans and investments may be delayed, causing considerable losses. A few months of improvement may not be enough, the bank will take more time but now, as you say, what we should be concerned about is stabilizing health.