Epidemiology of Infectious Disease

Introduction to Infectious Disease Epidemiology

Infectious disease epidemiology sits at the interface of microbiology, population science, and public health practice. Understanding how pathogens spread through populations — and why some groups bear a disproportionate burden — is essential for both outbreak response and long-term disease control. This lecture covers the theoretical framework of transmission dynamics, practical outbreak investigation tools, and the critical dimensions of health inequity in New Zealand's experience with infectious disease.

Basic Reproduction Number (R₀)

The basic reproduction number (R₀, "R-naught") is defined as the average number of secondary cases generated by one infectious individual in a completely susceptible population with no control measures in place. It is the fundamental parameter of infectious disease dynamics.

Key interpretations:

• R₀ < 1: each case generates fewer than one new case → outbreak will die out
• R₀ = 1: each case replaces itself exactly → endemic equilibrium
• R₀ > 1: each case generates more than one new case → epidemic growth (exponential if R₀ >> 1)

R₀ depends on three factors: β (transmission probability per contact), κ (contact rate), and D (duration of infectiousness):

R₀ = β × κ × D

Interventions reduce R₀ by targeting each component: masks/hygiene reduce β; physical distancing reduces κ; early case detection and isolation reduce D.

The effective reproduction number (Rₑ or Rt) accounts for partial immunity and control measures:

Rₑ = R₀ × s (where s = proportion susceptible)

When Rₑ drops below 1, the epidemic declines. This is the goal of public health interventions.

Herd Immunity Threshold

If enough individuals are immune (through vaccination or natural infection), the effective reproduction number falls below 1 even though the pathogen continues to circulate. The herd immunity threshold (HIT) is:

HIT = 1 − (1/R₀)

Examples:

• Measles (R₀ ≈ 15): HIT = 1 − 1/15 = 93.3% — requires near-universal vaccination
• COVID-19 Delta (R₀ ≈ 5–8): HIT ≈ 80–87.5%
• Seasonal influenza (R₀ ≈ 2–3): HIT ≈ 50–67%

HIT is a population-level concept. In practice, vaccine hesitancy, clustering of unvaccinated individuals, and waning immunity mean the effective threshold may be higher than the theoretical HIT.

The SIR Model

The SIR compartmental model divides the population into three compartments:

• S (Susceptible): have not been infected; at risk
• I (Infectious): currently infected and can transmit
• R (Removed/Recovered): have recovered (immune) or died

Transition rates:

• S → I: rate = β × S × I (depends on contact between S and I)
• I → R: rate = γ × I (γ = 1/D, recovery rate)

At the epidemic peak, dI/dt = 0, which occurs when S = γ/β = 1/R₀. This is why herd immunity stops epidemic growth.

Limitations: assumes homogeneous mixing, no age structure, closed population, lifelong immunity. Extensions include SEIR (Exposed/latent period), SIRS (waning immunity), and age-structured models.

Outbreak Investigation: Case Definition

A structured outbreak investigation follows a standard protocol. The first step is establishing a case definition — precise criteria specifying who counts as a case. A good case definition includes:

1. Clinical criteria: signs and symptoms (e.g., acute gastroenteritis = ≥3 loose stools in 24 hours)
2. Laboratory criteria: confirmed pathogen (e.g., culture/PCR-positive)
3. Epidemiological criteria: time, place, and person (e.g., attended the event on a specific date)

Case classifications:

• Confirmed: meets clinical + laboratory criteria
• Probable: meets clinical + epidemiological criteria
• Possible/suspected: meets clinical criteria only

Sensitivity vs. specificity trade-off: a broad definition captures more cases (sensitive) but may include false positives; a narrow definition is specific but misses cases.

Attack Rate

The attack rate (AR) measures the proportion of exposed individuals who develop disease:

AR = (Number of cases / Number exposed) × 100%

In foodborne outbreaks, food-specific attack rates are calculated for each food item:

• Food-specific AR for those who ate the item vs. those who did not
• The food with the highest AR among exposed AND the greatest difference between exposed and unexposed is the most likely vehicle

The relative risk (RR) = AR(exposed) / AR(unexposed) — a value >>1 implicates the exposure.

Epidemic Curves

An epidemic curve (epi curve) plots the number of new cases over time. Its shape reveals the mode of transmission:

Point source (common source, single exposure): steep rise, bell-shaped curve, peak within one incubation period of the exposure. Example: food poisoning at a single event.

Continuous common source: cases arise over an extended period while the source persists. Example: contaminated water supply.

Propagated (person-to-person): successive waves of cases approximately one incubation period apart; the curve rises progressively. Example: measles spreading through a school.

Mixed outbreak: initial point source followed by secondary person-to-person spread — a combination pattern.

Māori and Pacific Health Inequities in Infectious Disease

Health inequities — systematic, avoidable differences in health status between population groups — are starkly apparent in infectious disease outcomes in Aotearoa New Zealand.

Rheumatic fever: group A streptococcal throat infection leading to rheumatic heart disease (RHD) is endemic in Māori and Pacific communities but virtually absent in NZ European communities. The determinants include overcrowded housing, poverty, and barriers to healthcare access. The incidence rate in Māori children is approximately 40 times higher than in NZ European children. RHD affects young adults in their most productive years and is a leading cause of preventable cardiac surgery in NZ.

COVID-19: during the Omicron wave (2022), Māori and Pacific people experienced higher rates of hospitalisation, ICU admission, and death despite younger median age. Contributing factors: higher rates of comorbidities (diabetes, obesity, respiratory disease), lower vaccine uptake due to systemic barriers and vaccine hesitancy rooted in historical mistrust, greater household overcrowding reducing isolation capacity, and occupational exposures (essential workers).

Tuberculosis: although rare in NZ overall, TB disproportionately affects Māori, Pacific, and overseas-born populations. Social determinants — poverty, overcrowding, nutritional deficiency, and immunocompromise — drive this disparity.

Respiratory syncytial virus (RSV) and pneumococcal disease: Māori and Pacific infants have higher rates of serious lower respiratory tract infections, reflecting intersecting biological (higher risk of early-onset RSV) and social (overcrowding, passive smoke exposure, formula feeding, healthcare access barriers) determinants.

The Te Tiriti o Waitangi (Treaty of Waitangi) obligates the Crown to actively protect Māori health. A genuine treaty partnership requires addressing the structural determinants — housing, poverty, racism within the health system — that underlie infectious disease inequities, not merely targeted vaccination campaigns.

Principles of Outbreak Response

A structured outbreak response follows the investigation of an outbreak: confirm existence → develop case definition → case-find → describe by person/place/time → develop hypotheses → test hypotheses (analytic epidemiology) → implement control measures → communicate. Control measures depend on the mode of transmission:

• Source control: remove contaminated food, close water supply, treat the source
• Transmission control: isolation of cases, quarantine of contacts, physical distancing
• Host protection: vaccination of susceptible contacts (ring vaccination), chemoprophylaxis

The index case is the first identified case; the primary case is the first person infected in the chain of transmission (may differ from index case if surveillance delay exists).