EigoPro 準1級 読解 — The Mathematics of Epidemics

When a new disease begins to spread, the questions that matter most—how fast, how far, how many—are ultimately mathematical. Epidemiologists answer them with models, the best known of which divides a population into three compartments: those who are susceptible, those currently infected, and those who have recovered. By specifying the rate at which people move between these states, a handful of equations can sketch the entire arc of an outbreak, from its first cases to its eventual decline. The single most cited output of such models is the basic reproduction number, R₀, the average number of people an infected individual will infect in a population with no immunity. When R₀ exceeds one, the epidemic grows; when it falls below one, it fades. The seductive precision of these figures, however, conceals a more uncomfortable truth. A model is only as good as its assumptions, and those assumptions are invariably simplifications. Real populations are not uniform: people differ enormously in how many others they contact, and a model that treats everyone as identical will misjudge both the speed of spread and the impact of interventions. Crucially, human behaviour is not a fixed parameter but a moving target. The moment a frightening projection is published, people wash their hands, cancel gatherings, and avoid the sick—thereby falsifying the very forecast that prompted them. A prediction that changes the future it describes is, in a sense, designed to be wrong. This paradox does not render modelling useless; it reframes its purpose. The value of an epidemic model lies less in pinpointing a precise death toll than in comparing scenarios: what happens if schools close a week earlier, or if a vaccine arrives a month later. Treated as a crystal ball, a model will disappoint; treated as a laboratory for policy, it becomes indispensable. The mathematics cannot tell us exactly what will happen, but it can tell us, with rare clarity, which of our choices will matter most.

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この単元の問題を3問、解説つきで公開しています

準1級 · 読解 · 全5

1

What is the main idea of the passage?

  • The basic reproduction number R₀ is the only figure epidemiologists need to forecast an outbreak.
  • Mathematical models have proven incapable of describing how diseases spread through a population.
  • Public fear during an epidemic should be ignored because it distorts otherwise accurate forecasts.
  • Epidemic models are imperfect predictors but are valuable for comparing the likely effects of different policy choices.
Phrase

treated as a laboratory for policy, it becomes indispensable

準1級読解科学数学ジャーナリズム主旨把握
ひとことで

本文全体は「モデルは正確な予言装置ではないが、政策比較の道具として不可欠」という論旨。

選択肢の解説Choice Analysis

Epidemic models are imperfect predictors but are valuable for comparing the likely effects of different policy choices.

正解

本文は (1) モデルとは何か (S-I-R 区画と R₀)→ (2) その限界 (仮定の単純化・人間行動の可変性)→ (3) 真の用途 (death toll の特定ではなくシナリオ比較) という構成で進む。最終段の Treated as a crystal ball, a model will disappoint; treated as a laboratory for policy, it becomes indispensable がまさに主旨。よって「モデルは不完全な予測装置だが政策選択の効果比較に価値がある」が正解。

  • Mathematical models have proven quite incapable of describing how diseases spread through a population.

    = 数学モデルは記述不能だと証明された ━ 本文は This paradox does not render modelling useless と明言しており『記述不能』は逆。

  • The basic reproduction number R₀ is the only figure that epidemiologists need in order to forecast an outbreak.

    = R₀ だけあればよい ━ R₀ は most cited な指標として紹介されただけで『唯一必要な数値』とは述べていない。

  • Public fear during an epidemic ought to be ignored because it distorts otherwise accurate forecasts.

    = 公衆の恐怖は無視すべき ━ 本文は行動変化を予測が外れる原因として説明するだけで『無視せよ』とは主張していない。

Collocation
パターン意味
the arc of an outbreak流行の推移・全容sketch the entire arc of an outbreak
move between states状態間を移動するthe rate at which people move between these states
be only as good as ~~次第でしかないA model is only as good as its assumptions.
render ~ useless~を無用にするThis does not render modelling useless.
treated as ~~として扱われるとTreated as a crystal ball, it will disappoint.
例文
  • A model can sketch the entire arc of an outbreak.

    モデルは流行の全容を描き出せる。

  • The forecast is only as good as its assumptions.

    予測はその前提次第でしかない。

  • Treated as a laboratory for policy, the model is indispensable.

    政策の実験室として扱えば、そのモデルは不可欠だ。

💡Tip · 覚えるコツ

主旨設問は最終段の対比文 (Treated as A, ... ; treated as B, ...) に答えが凝縮されやすい。本文も crystal ball (失望) vs laboratory (不可欠) の対比が核。

2

According to the passage, what does the basic reproduction number R₀ measure?

  • The proportion of a population that must be vaccinated to end an epidemic.
  • The speed at which a recovered person loses their immunity over time.
  • The average number of people that one infected person will infect in a population with no immunity.
  • The total number of people who will eventually die during an outbreak.
Phrase

the average number of people an infected individual will infect in a population with no immunity

準1級読解科学数学ジャーナリズム詳細把握
ひとことで

R₀ = 免疫のない集団で感染者1人が感染させる平均人数。

選択肢の解説Choice Analysis

The average number of people that one infected person will infect in a population with no immunity.

正解

第1段で R₀ を the basic reproduction number, R₀, the average number of people an infected individual will infect in a population with no immunity と定義している。これをほぼ言い換えた「免疫のない集団で1人の感染者が感染させる平均人数」が正解。

  • total number of people who will eventually die

    = 最終的に死ぬ人数の総数 ━ R₀ は死者数ではなく感染させる平均人数。death toll は最終段で『特定すべきでない』とされる別概念。

  • The speed at which a recovered person gradually loses all of their immunity over time.

    = 回復者が免疫を失う速度 ━ 本文に免疫喪失の速度の記述はない。

  • The proportion of any population that must be vaccinated in order to end an epidemic.

    = ワクチン接種が必要な割合 ━ それは集団免疫閾値の話で R₀ の定義そのものではない。

Collocation
パターン意味
the basic reproduction number基本再生産数the basic reproduction number, R₀
with no immunity免疫のないa population with no immunity
exceed one1を超えるWhen R₀ exceeds one, the epidemic grows.
fall below one1を下回るwhen it falls below one, it fades
the most cited output最も引用される出力the single most cited output of such models
例文
  • R₀ measures how many others one case will infect.

    R₀ は1症例が何人に感染させるかを測る。

  • When R₀ exceeds one, the epidemic grows.

    R₀ が1を超えると流行は拡大する。

  • In a population with no immunity, spread is fastest.

    免疫のない集団では拡散が最も速い。

💡Tip · 覚えるコツ

定義を問う detail 設問は本文の定義文を一語ずつ照合する。death toll や vaccination はもっともらしいが本文の定義語 (average number ... will infect) と一致しない。

3

Why does the passage say that a published projection can end up being wrong?

  • People who hear a frightening forecast change their behaviour in ways that prevent the predicted outcome.
  • Epidemiologists deliberately publish exaggerated figures to alarm the public.
  • Governments censor accurate projections before they can reach the population.
  • The equations used in the models contain mathematical errors that accumulate over time.
Phrase

thereby falsifying the very forecast that prompted them

準1級読解科学数学ジャーナリズム詳細把握
ひとことで

怖い予測を見た人が行動を変え→予測自体を外れさせる (自己否定的予言)。

選択肢の解説Choice Analysis

People who hear a frightening forecast change their behaviour in ways that prevent the predicted outcome.

正解

第2段で The moment a frightening projection is published, people wash their hands, cancel gatherings, and avoid the sick—thereby falsifying the very forecast that prompted them と述べ、A prediction that changes the future it describes is, in a sense, designed to be wrong と結ぶ。よって「怖い予測を聞いた人が行動を変え、予測された結果を防ぐ」が正解。

  • deliberately publish exaggerated figures

    = 意図的に誇張した数字を公表する ━ 本文は予測者の誇張ではなく受け手の行動変化を原因としている。

  • The equations used in these models contain mathematical errors which accumulate over time.

    = 方程式に数学的誤りが含まれる ━ 外れる理由は計算ミスではなく行動という可変要因。本文に計算誤りの記述はない。

  • Governments censor all accurate projections before they can ever reach the wider population.

    = 政府が正確な予測を検閲する ━ 検閲の記述はなく、むしろ公表 (published) されている。

Collocation
パターン意味
a moving target動く標的・絶えず変わるものhuman behaviour is a moving target
the moment ~~した瞬間にThe moment a projection is published, people react.
falsify a forecast予測を覆す・反証するbehaviour falsifies the forecast
the very ~ that ...まさに~したその…the very forecast that prompted them
be designed to V~するようにできているdesigned to be wrong
例文
  • Human behaviour is a moving target, not a fixed parameter.

    人間の行動は固定された変数ではなく動く標的だ。

  • People react the moment a projection is published.

    予測が公表された瞬間に人々は反応する。

  • Their precautions falsified the very forecast that warned them.

    彼らの用心がまさに警告した予測を覆した。

💡Tip · 覚えるコツ

因果を問う detail 設問は『—thereby V-ing』のような結果を示す分詞句が決め手。self-defeating prophecy (自己否定的予言) のキーは受け手の行動変化にある。

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