First of all, let's do a risk assessment:

Our immune system is built of processes of innate immunity and adaptive immunity.

Considering that people who have recovered from Covid-19 attested by 2 negative tests days apart are testing positive again, there is evidence that the virus is able to replicate itself inside the body of a healed person to a level large enough to be detected.
This means that despite that a recovered person may have antibodies, depending on the form and length of re-exposure, they may get reinfected.
So having anti-bodies does not mean that you can't get reinfected, and you can toss herd immunity out of the window for now.

Seeing how a lot of people are getting off with light to no symptoms despite infection, it suggests that innate immunity is effective at fighting a Covid19 infection and this is the primary defense mechanism for most of us.
People with weak innate immunity or too large an exposure are seeing worse outcomes.

Vaccines and anti-virals.
Vaccines may be years to decades away. During the SARS epidemic they were also floating vaccine lead times of 18 months, but to date, no effective vaccine has been brought to market.
Over a century after the influenza virusses have been isolated, flu vaccines are not very effective yet.
HIV has been isolated 40 years ago, and yet, no effective vaccine exists.

Effective anti-virals do exist, but it will be years until one which is mildly effective will be found.
Anti-virals will not be very effective when the infection has already progressed, but it can help in the early stages, to limit the progression and help the innate immune system to mount a stronger response.


So with all of this known, I think that there is only one strategy to combat this: eradication.
SARS, MERS and Ebola have been fought by isolating the virus. Of course, this was easier for those virusses as they were not as readily transmissible as Covid-19.
However, this is the only way to fight it IMO.
Social distancing strategies are only a delay mechanism and insufficient to achieve this.
We need to set up a full-sized curfew by geographical area for at least 4 weeks and start testing everyone within the area.
Once an entire geographical area has tested negative and the virus is eradicated from that area, allow it to reopen, and to merge with other such geo area's.
Maintain contact-tracing and local isolation strategies for eventual resurgence.

How air travel can resume.
Air travel can resume in many ways.
1. The least extreme first step would be to space passengers sufficiently and mandate mask-wearing aboard the flights, combined with a regime of paranoic disinfection between flights. Airports will have to adapt too, with security, immigration facilities and waiting area's adapted to the purpose. Airlines would have to ask higher fares to compensate for the lower density. Travel will be limited to essential travel, ie business class only.
2. The next step would be to modify aircraft so that people could sit in more dense arrangements without getting infected. It may involve mandating wearing plastic bubbles, which can be connected to the aircraft's ventilation inlet and outlet systems through quick-connect fittings, tubes and valves. But this poses a problem for long haul flights where people need to eat and drink often. Special isolated area's may need to be set-up in aircraft so that people can take turns eating. Families may be able to sit together in their own separate cabins.
3. Aircraft designs may see further changes to accommodate more passengers, including a more adapted use of the cargo compartments.