Professor Luke O'Neill says experts have calculated that around 20% of people in each country will initially need to be vaccinated against COVID-19.
The leading immunologist says healthcare workers and vulnerable people will be first in line when a vaccine is finalised.
Professor O'Neill was speaking in the context of the COVAX vaccine alliance, which is aiming to ensure countries have equitable access to a coronavirus vaccine once it's available.
The World Health Organisation (WHO) is overseeing the effort, with over 150 countries signed up.
Ireland is a member, although countries such as the US, Russia and China are not involved.
The alliance has already raised $1.4 billion of its $2 billion target - with countries, philanthropic organisations and even the drug companies themselves chipping in.
Speaking on today's Pat Kenny Show, Professor O'Neill said the alliance aims to buy up 2 billion doses of vaccines, and is getting ready to "vaccinate the world".
He said: "There are 10 vaccines now in phase three… which is fantastic news, because there’s so many shots on goal there.
"Optimism is growing, and [the idea is] when the vaccine arrives, get it out quickly.”
Professor O'Neill said calculations show there'll be a need to vaccinate around 20% of the people in each country initially.
He explained: "They’re the healthcare workers, first and foremost, and vulnerable people.
“If we keep our fingers firmly crossed, in November, December, January we’ll be getting results from [vaccine] trials with the signal saying it’s safe and [effective].
"Then you begin to roll this out - amazingly - in January, February, March, April next year. That’s if everything goes 100%."
The US and WHO
Professor O'Neill said it's a 'big mistake' that people like Donald Trump are trying to rush the coronavirus vaccine process.
The leading immunologist says it's a 'scandal of the highest order' that the US left the WHO, and that it's 'extremely important' that Democratic presidential candidate Joe Biden has pledged to rejoin the organisation if he wins next month's election.
He observed: “The Democrats were saying ‘we will rejoin the WHO’... that means they buy into this COVAX initiative, which is led by the WHO. If you’re a member, you’re obliged to pay your dues.
“Remember, most Americans want to help the world, and several of the vaccines are American companies.
“The scientists in America are telling the administration you need to vaccinate the world here, because it will keep coming back… unless we protect the whole world here, it will be pointless in the long-term. Trump isn’t saying that… [he's] saying ‘America first’."
He stressed that companies involved in developing a vaccine are all being very cautious and careful, as they understand any vaccine will effectively need to be 'the safest product ever'.