Adaptive immunity formulas

T and B cells, MHC, antigen presentation and immune regulation. 2 formulas for GATE BT General Biology, each with when to use it. Each is explained in the topic notes.

All 2 Adaptive immunity formulas

HLA MATCH BETWEEN TWO FULL SIBLINGS

P (HLA-identical) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}, P (exactly one shared) = \frac{1}{2}, P (none shared) = \frac{1}{4}

Applies when the two parents carry four different haplotypes between them and there is no recombination within the MHC. Each child receives one of two maternal and one of two paternal haplotypes, each with probability 1/2.

VACCINATION COVERAGE NEEDED FOR HERD IMMUNITY

p_{c} = \frac{1 - \frac{1}{R _{0}}}{E}

$R_{0}$ is the basic reproduction number and $E$ is vaccine efficacy (fraction, 0 to 1). $1 - 1/ R_{0}$ is the herd immunity threshold, the coverage needed when $E = 1$ . Assumes homogeneous mixing, and applies when $E$ is high enough that $p_{c}$ does not exceed 1.

Where this was asked: 2020 (1), 2023 (4), 2025 (2). See the 7 previous-year questions on Adaptive immunity. This shows what was asked, not what will be asked.

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Adaptive immunity: the notes and 7 solved previous-year questions