7 million scattered randomly worldwide wouldn’t be enough to ensure survival, they’d just be too thin on the ground and most of them would never even meet.
But real diseases don’t work like that. The people who survive are either genetically resistant or they are living in regions that make the disease less efficient. Since genetic resistance runs in families, we’d generally expect that the people who survive will be fairly well concentrated in a few small areas. With that in mind, survival of the species becomes much more likely even at 99.9% mortality.
So long as a few groups of a few dozen manage to form up, the species will almost certainly continue. Sure, a lot of technology will be lost and civilisation will cease to exist, but humans will continue.
I don’t think the lack of knowledge would be the killer that most people make it out to be. The modern world has huge amounts of resources available, and any disease that can’t be fought or survived through deliberate quarantine will need to work very fast, within 12 months at the most.
The survivors are going to find themselves in a world with huge herds of domestic animals, massive seed reserves, entire cities full of metal, glass, cigarette lighters, solar panels and so forth. Even if all the canned food is gone, the amount of readily available food will be massive for decades after the event, as will the amount of other technology. Things like houses, solar panels and cigarette lighters will last for 40 or 50 years with no maintenance. Even allowing for an increase in predator number’s, decaying infrastucture etc, basic survival won’t be a problem for decades for anyone with the ability to cook or fire a gun.
And basic survival skills aren’t so thin in the ground even in the US that over the course of decades people won’t be able to work things out. Hunting remains a popular sport such that any group of 20 people will almost certainly contain at least one person who knows how to shoot a cow. Gardening will provide the same basic ability to grow crops. And of course in many other parts of the world the proportions of people who were raised on farm is much higher and the capacity for subsistence agriculture much, much higher.
So I really don’t think that survival is much of an issue. We have produced such a human-ideal world that it will take decades before basic survival will become much of a struggle at all, and the point where farming and hunting become essential, rather than simply a means of obtaining variety and luxuries will creep up gradually, such that the first generation born after the event won’t even notice the transition.
But I think that XT’s point can’t be understated. For the first 200 years humanity will be fairly fragile. With a few thousand groups of a couple of dozen people on every continent, many of the groups will die through random chance: fire, famine, cyclone, other plagues etc. just as they have throughout history. Any worldwide catastrophe that even prevents population growth will leave humanity on the knife-edge. It’s only after the population has increased and societies stabilised enough to permit dispersal into thousands of truly self-sustaining groups and contact between the groups that we’d be out of the woods.
But for my money, humanity would survive even 99.9% mortality.