It is not in the interests of a virus to kill all of its hosts, so a virus is unlikely to wipe out the human race.
I think this reasoning is unsound.
Firstly, the argument is based on the supposition that a virus mutation that destroyed the human race would destroy itself as well. But this would be true only if the virus only affected humans. But we already know that many of the viruses most dangerous to humans have jumped from other species, such as birds. So exterminating the human race would not necessarily represent a failure for such a virus, because there may be lots of other species to infect. (And some of these other species may thrive better in the absence of humans, such as rats or insects.)
Secondly, the argument is based on the supposition that a virus mutation is not going to destroy itself. Of course, successful mutations don't do this - but surely one lesson of evolution is that successful mutations are hugely outnumbered by unsuccessful mutations. A mutation can generally be regarded as an evolutionary experiment: the survival of the fit equates to the non-survival of the unfit. A virus mutation that destroyed the human race might be regarded as a pretty unsuccessful virus, but that doesn't give us any less reason to fear such a virus.
Of course, a virus that killed its hosts too quickly (such as SARS) might fail to spread effectively through the population. A slow-acting virus (such as AIDS) may be more dangerous in the long run. It is perfectly possible that the human race could be exterminated by AIDS within a century or so.
Many diseases have become less dangerous over time, and this can be explained by evolution. For example, scarlet fever (a bacterial disease) was already diminishing in force before the advent of the modern antibiotics. (Source: Guardian 21 March 2016). But this observation doesn't justify the belief that all diseases will follow this evolutionary path.
Professor Zambon is offering what appears to be a teleological argument for the survival of the human race. The purpose of a virus is to infect humans - therefore there will always be a fresh supply of humans to infect.
On The Interests of a Virus
While it may be in the interests of a virus to take up residence in my lungs it would be stretching the notion of value to allege that the virus “values” that location. If the term “value” is to be useful, we must restrict its range to the category of such goals as may be pursued by conscious agents. (Thomas W Platt, Global Values: Actual, Unlikely and Necessary, doc). Paper given at the Fourth International Society for Value Inquiry Conference held in Florence Italy, Aug 2003.
It is not in the best interests of a virus to cause lethal tumors in its natural host. ... However, unexpected but important discoveries that HHV8 encodes a series of novel genes give credence to the tumorigenic properties of HHV8. (Gary Heywood, JNCI Cancer Spectrum, 1999).
Compare the following remark about the gambling industry.
It is far more profitable to have long-term customers who only spend what they can afford to lose, than to have a handful of customers overspending massively and burning out in a couple of months. (Raf Keustermans, Why studios need to think about the ethics of social gaming, The Guardian Feb 2012)
Threat of drug-resistant viruses (BBC News July 2005)
Hugh Pennington, Ebola in the UK? (LRB July 2014)
Florence Williams, How Animals May Cause the Next Big One (New York Review, April 2013)
Updated 21 March 2016