How many Malaysian should be vaccinated to get herd immunity from COVID-19?

Recently I have read an article that the Malaysian government have made a deal with Pfizer for 6.4 million Malaysian to be vaccinated. So, I am wondering what is the minimal number of people should be vaccinated.

I have also come across this interesting article, which explains how we can calculate a minimal number of people to be vaccinated to achieves herd immunity based on R naught (R₀).

R naught (R₀)

The basic idea of R₀ or basic reproduction number is quite simple. It describes how many secondary infections will derive from the first case. I think Figure 1 below describes this idea very well.

Figure 1: Basic idea of R₀(image from https://www.atrainceu.com/content/3-basic-reproduction-number-r-naught)

So, R₀ can be affected by a few factors, such as:

• proportion of susceptible people at the initial outbreak
• infectiousness of the virus or the disease
• rate of recovery or death
• and a few other factors

As R₀ increases more than 1, the spread of the disease will increases, while R₀ below 1 indicates the spread of the disease will decrease and eventually dies out.

However, I noticed that quite a few including KKM (Ministry of Health, Malaysia) have used the term R₀ in their reports instead of R_e or R_t which is the effective reproduction number or time-varying reproduction number. R₀ refers to the initial reproduction number at the beginning of the outbreak. The “naught” or “zero” in R naught (R₀) is referring to population condition that has zero immunity to the disease.

Herd immunity

Herd immunity is said to occur when a significant proportion of the population is immunized. Subsequently, those whose susceptible (not immunized) will be protected.

How many should be vaccinated

So, back to the initial topic. We can use the formula below to answer this question.

\[P_i > 1 - \frac{1}{R_0}\]

P_i refers to the number of proportion that should be immunized or in this case, vaccinated.

So, after googling, I found one calculation by my lecturer in Biostat Unit, USM, Dr Wan Arifin and his colleague. The R₀ based on his calculation is 2.673. Also, I found another article reported that the R₀ is 3.55 in March, according to KKM.

Malaysian’s population is estimated at 32.7 million by the Department of Statistics, Malaysia (DOSM). So, using the formula above, about 63% to 72% of Malaysian population should vaccinated, and this translates to about 20.6 to 23.5 million people.

The deal that the Malaysian government made with Pfizer is far from enough, but of course, this is a very good and quick decision. We also have other vaccines like Moderna’s vaccine coming up.

Disclaimer: This is just my opinion. Please take it with a massive grain of salt.