A counterexample: HIV is pretty deadly, but slow to progress, so it infected a lot of people. In countries with insufficient healthcare infrastructure (Subsaharan Africa), it actually killed a significant percentage of the population, precisely because it was so successful in spreading. Without modern medicine, it could have wiped out entire cultures, especially those that were more sex-positive.

(An interesting question to chew on is: what was the impact of religious sex taboos in pre-modern and early modern era? If monogamous couples were more likely to have healthy offspring and nurse their kids into adulthood, it might explain some of the societal swings towards puritanism in the 16th-19th century, which was a period of endemic syphilis.)

Indeed as you and another commenter pointed out correctly, it is not the whole picture, and given an intelligent, evil design one could possibly create a disease that spreads fast and kills only much later (by let’s say, causing cancer). But fortunately we are not inside Plague Inc.

But if I am not mistaken, from a strictly evolutionary perspective there is no pressure towards such a disease — a genetic variation that is more deadly won’t dominate over its less deadly variant and thus deadliness could be a variable that only changes randomly from the initial level (and decreasing if it is actively detrimental to spreading, where I would say that in case of a human population deadliness does correspond with fear).

But IANAE, nor a mathematician.

> The more deadlier a virus, the rest likely it is to spread.

Not really. The two primary factors controlling how fast a disease spreads is the infectiousness (R0 or other similar measures), and how long victims are infectious before they display symptoms.

The deadliness, the victim living or dying, happens significantly after they've finished their role as spreader of disease and thus does not significantly affect the spread.

Ebola fails to spread, not because it's deadly, but because the symptoms are almost immediate and dramatic.

(I took graduate level course in the mathematics of epidemiology and got an A, which makes me no expert at all, but this is fairly fundamental.)

I gave the OP another example of a deadly and yet widespread virus, HIV.

He is not completely off the ball, though. Our immune systems are rather good, so (with significant exceptions like HIV) if some virus doesn't kill us quickly, we tend to clear it out of the organism or at least get it under control, so it won't kill us at all.

Viruses that are very deadly but take a long time to kill you (thus enhancing the risk of transmission), like HIV, aren't very typical.