Describe vaccines and herd immunity — Biology notes

1. Vaccines — WHAT, WHY, HOW

WHY do vaccines work? Because of the primary vs secondary immune response.

Formula How a vaccine builds protection (logical chain, not an equation)

$\text{Antigen in} \Rightarrow \text{primary response} \Rightarrow \text{memory cells} \Rightarrow \text{fast secondary response on real infection}$ Why each arrow?

Antigen in: the vaccine supplies the "shape" the immune system must recognise.
Primary response: naïve B/T cells that happen to match are selected and clonally expanded (clonal selection).
Memory cells: a fraction of these differentiate into long-lived memory cells instead of short-lived effector cells.
Fast secondary response: on real exposure these memory cells reactivate instantly.

Types of vaccine (WHY several exist)

Each type is a trade-off between safety and how strong/realistic the immune training is.

Type	What's in it	Why used
Live attenuated	Weakened live pathogen	Strong, long-lasting response (mimics real infection)
Inactivated ("killed")	Dead pathogen	Safer, but weaker → often needs boosters
Subunit / toxoid	Just antigen or inactivated toxin	Very safe, no risk of infection
mRNA / viral vector	Genetic code so your cells make the antigen	Fast to design, strong response

2. Herd Immunity — WHAT, WHY, HOW

The Herd Immunity Threshold (derive from first principles)

Formula Deriving the threshold

$H_c$ Let $R_0$ = the basic reproduction number = average number of new infections one case causes in a fully susceptible population.

Now suppose a fraction $p$ of the population is immune, and assume for now this immunity is 100% effective and lifelong. Then only a fraction $(1-p)$ of contacts can actually be infected. The effective reproduction number is: $R_e = R_0\,(1-p)$ Why? Each of the $R_0$ potential transmissions succeeds only if the contact is susceptible, which happens with probability $(1-p)$ .

An outbreak shrinks when each case produces fewer than one new case: $R_e < 1 \;\Rightarrow\; R_0(1-p) < 1 \;\Rightarrow\; 1-p < \tfrac{1}{R_0} \;\Rightarrow\; p > 1 - \tfrac{1}{R_0}$ So the minimum immune fraction — the herd immunity threshold — is: $\boxed{H_c = 1 - \frac{1}{R_0}}$ Why this shape? The more infectious the disease (larger $R_0$ ), the more people you must make immune before each case finally fails to replace itself.

Formula Real-world correction: imperfect vaccine (efficacy

$e$ ) No vaccine is 100% effective, and immunity can wane. If a fraction $p$ is vaccinated but each dose only makes a person immune with probability $e$ (the vaccine efficacy, $0<e\le1$ ), then the effectively immune fraction is $p\cdot e$ , not $p$ . So: $R_e = R_0\,(1 - p\,e)$ Setting $R_e < 1$ gives the required vaccination coverage: $p_c = \frac{1}{e}\left(1 - \frac{1}{R_0}\right) = \frac{H_c}{e}$ Why divide by $e$ ? If jabs only "take" a fraction $e$ of the time, you must vaccinate more people to reach the same immune fraction. Consequence: if $e < H_c$ (e.g. a 60%-effective vaccine against measles, $H_c=0.93$ ), no coverage — not even 100% — can reach herd immunity with that vaccine alone.

Figure — Describe vaccines and herd immunity

3. Why we care (80/20 core)

Individual protection for the vaccinated.
Community protection for those who can't be vaccinated (babies, immunocompromised, allergic).
Disease elimination/eradication (e.g. smallpox eradicated 1980). Eradication requires more than coverage above $H_c$ everywhere: it also needs no non-human reservoir of the pathogen (so it can't hide in animals/environment), effective sustained surveillance, and containment of any imported or residual cases. Smallpox was eradicable partly because it had no animal reservoir.

Recall Feynman: explain to a 12-year-old

Your body has a memory. The first time a bad germ attacks, your body is slow and you get sick, but it learns what the germ looks like. A vaccine is like showing your body a wanted poster of the germ — a harmless picture — so it already knows the face. If the real germ ever shows up, your body catches it instantly. And if almost everyone in your class has seen the poster, the germ has nobody left to jump to, so even the one kid who couldn't get the poster stays safe. That's herd immunity. But posters sometimes don't work perfectly and can fade over time, so you may need extra ones (boosters) — and if too many kids skip the poster, the germ finds a chain of new people and spreads again.

Flashcards

What is a vaccine?

A preparation of antigens (or instructions to make them) from a pathogen, given to trigger an immune response and memory without causing disease.

Why does a vaccine prevent illness on real infection?

It creates memory cells, so real exposure triggers a fast, strong secondary immune response before symptoms develop.

Difference between primary and secondary immune response?

Primary is slow, low antibody levels (first exposure); secondary is faster, higher and higher-affinity antibodies due to memory cells.

What is herd immunity?

When a large proportion of a population is immune, transmission is interrupted, indirectly protecting non-immune individuals.

Define

R_0

Basic reproduction number: average number of new infections caused by one case in a fully susceptible population.

Formula for herd immunity threshold and its meaning?

H_c = 1 - 1/R_0

; the minimum effectively immune fraction needed to push

R_e

below 1.

What assumptions does

H_c = 1-1/R_0

make?

Homogeneous mixing, 100% effective and lifelong immunity, and no births/deaths/migration or age/contact structure.

How do you adjust required coverage for imperfect vaccine efficacy

e

R_e = R_0(1-pe)

, so required coverage

p_c = H_c/e = (1-1/R_0)/e

; if

e<H_c

, herd immunity is unreachable with that vaccine alone.

Derive

R_e

when fraction

p

is (perfectly) immune.

R_e = R_0(1-p)

, because each transmission only succeeds if the contact is susceptible (probability

1-p

For measles (

R_0=15

), what herd immunity threshold?

1-1/15 \approx 0.93

, about 93% effectively immune.

Why does higher

R_0

need higher vaccine coverage?

More infectious diseases replace each case more times, so more people must be immune before

R_e<1

Besides coverage >

H_c

, what does eradication require?

No non-human reservoir for the pathogen, plus sustained surveillance and containment of imported/residual cases.

Steel-man: why "vaccines give you the disease" feels true, and the fix?

Post-jab mild symptoms feel like infection, but they are the immune response working; most vaccines contain no disease-causing living pathogen.

Connections

Immune System
Primary and secondary immune response
Antibodies and antigens
Memory B and T cells
Clonal selection
Basic reproduction number R0
Vaccine efficacy and waning immunity
Epidemiology and disease spread

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho, vaccine ka idea simple hai: tumhara immune system ek learner hai. Jab pehli baar koi germ attack karta hai to body slow hoti hai — isko primary response kehte hain, antibody dheere aur kam banti hai, isliye tum bimaar padte ho. Par body memory cells bana leti hai. Vaccine bas ek "safe practice fight" hai — germ ka antigen (poster/shakl) body ko dikha dete hain bina asli bimari diye. Ab jab asli germ aata hai, to secondary response hota hai — fast, strong, zyada antibody — aur germ symptoms se pehle hi khatam.

Ab herd immunity: agar population mein bahut saare log immune ho jaate hain, to germ ko aage jump karne ke liye susceptible log milte hi nahi. Isse jo log vaccine nahi le sakte (chhote bacche, immunocompromised) woh bhi safe rehte hain, kyunki germ un tak pahunch hi nahi pata.

Formula: $R_0$ matlab ek infected banda kitne naye logon ko infect karta hai fully susceptible population mein. Agar fraction $p$ log immune hain to $R_e = R_0(1-p)$ , aur outbreak tab rukta hai jab $R_e<1$ , jisse nikalta hai $H_c = 1 - 1/R_0$ . Par yaad rakho — yeh formula assumptions par tika hai: har koi randomly milta hai, immunity 100% aur lifelong hai, aur births/deaths/migration ignore. Real life mein vaccine efficacy $e$ 100% nahi hoti aur immunity waning hoti hai, isliye asli coverage $p_c = H_c/e$ — yaani zyada logon ko lagana padta hai. Measles ka $R_0 \approx 15$ , isliye ~93% effectively immune chahiye, aur efficacy adjust karke ~96% coverage.

Ek aur important baat: eradication (bimari puri tarah khatam karna, jaise smallpox 1980 mein) ke liye sirf coverage $> H_c$ kaafi nahi. Pathogen ka koi non-human reservoir (jaanwar/environment mein chhupne ki jagah) nahi hona chahiye, aur strong surveillance aur containment maintain karni padti hai. Smallpox isliye khatam ho paaya kyunki uska koi animal reservoir nahi tha.

Test yourself — Immune System