While I haven't found a reference discussing the libertarian approach to pandemics more generally, I did find one about vaccines, which should be relevant enough, because it's another, related "collective action problem":
Libertarianism and collective action: is there a libertarian case for mandatory vaccination?
In his paper ‘A libertarian case for mandatory vaccination’, Jason Brennan argues that even libertarians, who are very averse to coercive measures, should support mandatory vaccination to combat the harmful disease outbreaks that can be caused by non-vaccination. He argues that libertarians should accept the clean hands principle, which would justify mandatory vaccination. The principle states that there is a (sometimes enforceable) moral obligation not to participate in collectively harmful activities. Once libertarians accept the principle, they will be compelled to support mandatory vaccination. In my paper, I argue that the cases Brennan uses to justify this principle are disanalogous to the case of non-vaccination and that they are not compelling to libertarians. The cases Brennan offers can be explained by a libertarian using the individual sufficiency principle: which states that if an individual’s action is sufficient to cause harm, then there is a (sometimes enforceable) moral obligation not to carry out that action. I argue that this principle is more appropriate to Brennan’s examples, and more appealing to the libertarian, than the clean hands principle. In order to get libertarians to accept the clean hands principle, I present a modified version of one of Brennan’s cases that is analogous to the case of non-vaccination. Using this case, I argue that whether the clean hands principle will justify mandatory vaccination is dependent on whether the herd immunity rate in a given population is approaching a threshold after which a collective risk of harm will be imposed onto others.
So, one could say "libertarians disagree" [on the exact approach] to such matters based on that discussion. (And it would not be the only thing they disagree about.)
Actually, there is an article in the Telegraph that even says:
How can libertarians ever support mandatory quarantine and nationwide lockdowns?
Quite easily, as it happens. I can’t speak for all libertarians (who can?) but I see libertarianism as applied economics. The government should leave businesses alone unless there are demonstrable market failures and it should leave people alone unless they are doing direct harm to others.
In case it is not obvious, infecting somebody with a potentially fatal virus counts as direct harm to others....
I haven't read the rest, but I'm guessing he's going to argue from externalities viewpoint... which according to other libertarians (Ryan Bourne of Cato in this case) is rapid descent on the slippery slope:
The classic recommended government remedy for this problem is to try to calculate the marginal external costs or benefits associated with a given activity (beyond the private costs or benefits) and implement taxes or subsidies so these externalities are priced in when consumption or production decisions are made. Joseph Stiglitz’s Nobel lecture is a good description of this policy solution.
Given the pervasiveness of externalities, applying this logic consistently and universally would result in an extremely intrusive government. [...]
The logic of banning or adopting prohibitively high sin taxes, in contrast, is that the optimal consumption level of anything with external costs is zero. This is an absurd principle, albeit one that is regularly espoused. It is common, for example, to hear commentators and policymakers advocate for a zero-carbon economy. The UK government’s recent announcement that it plans to ban all gas and diesel vehicles by the year 2040 is an example of a policy that will almost certainly impose net social costs on society.
So yeah, from this latter "more" libertarian viewpoint, how do you account for the fact that infecting others is only a probability, not a certainty?
As an intermission, it would be interesting if the "father" of "paleolibertarianism" had something concrete to say on this ([the probability] of infection [of others]), but insofar I wasn't able to find out that, but only some imperfect analogies that he made:
Probably the most widely accepted doctrine within libertarianism is the “nonaggression” principle, which Rothbard uses as the central theme of his book. The “nonaggression” principle states that “no man or group of men may aggress against the person or
property of anyone else” (27). Thus, slavery was considered to be intrinsically evil because it
violated property rights, or the right of a person to be secure in themselves. Yelling “Fire!” in a
crowded theater, Rothbard argues, should not be restricted because free speech is only a relative
right; rather, it is criminal because it violates the private property rights of others in the theater
(52). Essentially, he ascribes to the belief that individuals have an absolute right to be secure in
their persons and goes on to apply it to numerous other aspects of life. Whether it be education,
roads, courts, foreign policy, or critiquing the ever-popular Keynesian theory of economics,
Rothbard consistently believes that the rights of the individual are incontrovertible. His beliefs
are best summed up as follows:
And, indeed, what is the State anyway but organized banditry? What is taxation but theft
on a gigantic, unchecked, scale? What is war but mass murder on a scale impossible by
private police forces? What is conscription but mass enslavement? Can anyone envision a private police force getting away with a tiny fraction of what States get away with, and
do habitually, year after year, century after century? (293-294)
This argument continues to be the bedrock of radical libertarianism and anarcho-capitalism, as it
provides a consistent philosophy that can be applied across all aspects of life. Moderate
libertarian thinkers tend to diverge from Rothbard, however, on the issue of how to implement
these ideals. Some, like Rothbard, want sweeping change and scoff at others who argue for
gradualism. Others, however, realize that government is needed in some limited capacity to
retain order and that the free market has limits.
Actually Lew Rockwell interprets Rothbard for us in the present context:
The fundamental rule for deciding whether anyone, including the government, is justified in using force to make us do something we don’t want to do is the nonaggression principle (NAP). As Murray put in in “War, Peace, and the State,” “No one may threaten or commit violence (‘aggress’) against another man’s person or property. Violence may be employed only against the man who commits such violence; that is, only defensively against the aggressive violence of another. In short, no violence may be employed against a nonaggressor.”
You might at first think that you can use the NAP to justify forced quarantines against the coronavirus. Suppose someone had a deadly disease that would always spread to others if he came in contact with them. Probably the person would want to isolate himself and not infect others, but if he refused, wouldn’t the people in danger be justified in isolating him? He is a threat to others, even if he doesn’t intend to harm them.
Thinking about this case can lead us astray, and here is where Murray can help us most. In his great book The Ethics of Liberty, he says, “It is important to insist, however, that the threat of aggression be palpable, immediate, and direct, in short, that it be embodied in the initiation of an overt act. Any remote or indirect criterion—any ‘risk’ or ‘threat’—is simply an excuse for invasive action by the supposed ‘defender’ against the alleged ‘threat.’” Murray hammers home the point later in the book. He says, “Once one can use force against someone because of his ‘risky’ activities, the sky is the limit, and there is virtually no limit to aggression against the rights of others. Once permit someone’s ‘fear’ of the ‘risky’ activities of others to lead to coercive action, then any tyranny becomes justified.”
When we apply what Murray says to the coronavirus situation, we can answer our question about forced quarantines. People are not threatening others with immediate death by contagion. Rather, if you have the disease, you might pass it on to others. Or you might not. What happens if someone gets the disease is also uncertain.
Bourne (whom one might peg in the less "paleo" camp) also comments on the Covid-19 issue as well (on Apr 6):
the longer lockdowns go on, the more the income losses for businesses and households turn into bankruptcies and defaults, risking a depression. So economists recognise that the costs and benefits of policy will change over time. They will look for ways of maintaining low health risks but at lower economic and social cost than crude shutdowns, recognising this balance changes as the pandemic evolves.
Indeed, once the transmission rate has been brought down and more people recover from the virus, the calculations could change drastically. If I were one of the last 50 people in the whole country to have not yet been infected, I would not expect a destructive national lockdown to protect me. So, clearly, there comes a point when it’s better to relax things from an economic welfare perspective. That could come much sooner than we think.
Interestingly, it still considers a/the notion of welfare to society as a whole as relevant... but in view of how much [herd] immunity there is... which actually is quite to the similar argument from the opening quote I gave in this answer.
And it's easy to get sucked into the myriad variation of responses to Covid-19 of US libertarian writers/personalities/politicians (thus make this answer way too long), but I'll mention here anyway that Ron Paul (who ran for president on a Libertarian Party ticket at one point), has called (April 10) for Fauci to be fired because (according to Paul) Fauci infringed on American liberties by overestimating the number of potential deaths from Covid-19.
"[...] they made these dire predictions so that they could go ahead and destroy peoples’ civil liberties and spend a lot of money and make up an excuse on why the stock market actually went down — all kinds of things by having this coronavirus event blown way out of proportion,” Mr. Paul said. “He should be fired,” Mr. Paul said about Dr. Fauci. [...]
Personality polemics aside, it seems that in most libertarian discourse the probability of infection (and death) needs to be considered, so it's not too different from how others approach the matter, but perhaps the probability is (subjectively?) "tuned down" at least in some US libertarian discourse. However, the most hardcore/paleo libertarians seem to reject that quantines could ever be justified.
