This is where the safety of society at large supersedes any individual rights.
Once a subject is found to be a carrier, I am for back-tracking the history of the individual's geo-location and proximity to others -- with the individual's colocation information collected and archived, encrypted, in the cloud.
This virus contagion is exponential (reasonable estimates are 1.25^n, where n is the number of days, effectively doubling the sick population every three days).  And until some mRDA inoculation is proven effective, maybe more than one year away, our society is at risk, and indirectly, all our freedoms are at risk as well.
["Full speed ahead!" with maximum effort, without reservations or delay, against this menace.]