Spreads Fast, or Hits Hard? From Virus Models to Digital Marketing傳得快，還是殺得狠？由病毒模型講到數碼營銷

Revisiting an old article

This article was first published on 27 February 2020 and has since been reworked. The “viruses” below belong to a deliberately simplified model for exploring exponential growth; they are not predictions about any real disease. Here, “transmission probability” means an assumed chance of infection per contact — not the epidemiological basic reproduction number, R₀. The model is crude, but the blind spot it exposes remains remarkably common.

The comparison sounds sensible. The trouble is that it stares at only one percentage.

Fatality tells us how likely an infected person is to die. The speed of transmission determines how many people enter that game of chance in the first place. The former is easier to notice. The latter tends to stay quiet—until it begins to compound.

So, let us run a simplified experiment.

First, make the world very simple

Imagine two viruses starting from exactly the same position and operating under exactly the same conditions:

1. Each scenario begins with 20 infected individuals.
2. Each newly infected person meets 10 entirely new contacts on the day after becoming infected and is isolated immediately afterwards, causing no further transmission.
3. The model runs for 10 days.

Now give the two viruses different characteristics:

• Virus A: an 80% chance of infection per contact and a 5% fatality rate.
• Virus B: a 20% chance of infection per contact and a 20% fatality rate.

In other words, A spreads faster; B is far more lethal.

Try not to vote by instinct just yet.

The real force at work is multiplication

On day one, Virus B causes four deaths. Virus A causes just one. If we look only at the immediate result, B is clearly more frightening.

On day two, the two viruses cause the same number of deaths that day. From day three onwards, A pulls ahead. Run this deliberately uncapped model to day ten and the cumulative totals are:

• Virus A: approximately 153 million deaths.
• Virus B: 4,092 deaths.

The difference is more than thirty thousandfold.

Obviously, 153 million is not a pandemic forecast. The model assumes that every infected person can always find ten new people to meet. There is no geography, social network, immunity, policy response or population ceiling. In its later stages, it even produces more infections than there are people on Earth.

This is not the real world. It merely magnifies something that is very easy to underestimate in the real world:

When one number is multiplied by another every day, it may look insignificant at first and become earth-shattering later.

Now weaken A

Reduce Virus A’s probability of infection per contact from 80% to 40%, and slash its fatality rate from 5% to 0.05%. Leave Virus B unchanged at 20% transmission and 20% fatality.

By day four, B has caused 60 cumulative deaths, while A has caused only about one. At that point, saying “See? The fatality rate is low. There is nothing to worry about” might feel entirely reasonable.

Wait another six days.

By day ten, A has caused approximately 3,495 deaths; B, whose fatality rate is four hundred times higher, has caused 4,092. Through faster transmission alone, A nearly catches B.

This does not make fatality unimportant—quite the opposite. It means that fatality cannot be pulled away from scale, time and the contact network, then judged on its own.

Reality fights back

The model’s “transmission” assumes that nobody takes precautions, contact patterns never change, and everyone encountered is new. Reality is less obedient.

Isolation, masks, ventilation, vaccination, border measures and even the simple decision to skip one gathering can all alter actual transmission. Nor is a fatality rate a constant handed down from the sky. Population age, underlying health, testing coverage, quality of care and pressure on hospital capacity all change the outcome.

Risk, in other words, is not a personality trait of the virus. It emerges from the virus, human behaviour and the surrounding system together.

That is what a simple model is for. It does not predict the future; it helps us step away from emotion and look calmly at which assumption deserves the most attention. What happens if contacts fall from ten to six? What if isolation begins a day earlier? The useful question is often not “Is this number exactly right?” but “Which lever changes the result most?”

So, which one is more frightening?

Numbers can be objective. Fear is somewhat more personal.

Ask one person who is already infected and fatality is naturally the number they care about most. Ask about society as a whole and we also need to consider how many people may ultimately be infected, die or live with long-term effects. Life and death are merely the two easiest boxes to count. Reality is inconveniently less binary.

At a minimum, any comparison of risk should ask:

• How many new infections can each case generate?
• How long can that pace continue?
• How many people could enter the chain of transmission?
• Beyond death, what irreversible harm might remain?
• Which human or institutional factors could change those numbers?

“The fatality rate is low” may be a fact. “Therefore, there is nothing to worry about” is already an inference. Between the two lies an entire chain of transmission.

When the virus becomes content

This kind of hasty judgement is not unique to public health. We see one seemingly straightforward rate and rush to draw conclusions about the whole outcome. In digital marketing, the same blind spot simply changes names: fatality and transmission rates become reach, share rate and conversion rate.

What a piece of content ultimately delivers cannot be understood by examining each rate in isolation. How many people it reaches, how many rounds it spreads through, how long it remains relevant and how many people eventually act are interconnected and must be analysed together.

A funny post or a cute animal clip may travel widely without making anyone remember the brand, let alone take action. Its “infection rate” is high; its conversion rate may be close to zero. At times, it attracts entirely the wrong audience and produces a negative effect instead.

The reverse is also true. A highly specific piece of content may be genuinely useful to a niche audience and convert extremely well, yet lack a network large enough to travel far. The content is not necessarily worse. It is simply operating under different conditions.

The awkward part is that audiences are not interchangeable. Communities differ in how densely they are connected, whom they trust and how they respond. Move the same creative idea into another group and its performance may change completely. What works today may stop working in a few weeks. Content does not go viral simply because someone types “viral” into the brief—if that were all it took, digital marketing would be the easiest job in the world.

Numbers do not tell the truth automatically either. Followers are not necessarily the target audience. Comments are not the same as agreement. Reach does not equal recall. A conversion may not have been caused by the post you credited for it. An untested number is still a wild guess—just one wearing a suit.

That is why, whether I am looking at disease, content or business growth, I have become increasingly reluctant to judge a beautiful percentage on its own. First ask how it is defined, what it correlates with, and under which conditions it holds. Then discuss the conclusion.

Many astonishing outcomes begin with a small, inconspicuous number hiding just beyond a multiplication sign.