Contact Rates and Mixing Patterns

Transmission requires contact between infectious and susceptible people, so the rate at which people make potentially infectious contacts, and the pattern of who mixes with whom, are central determinants of how a disease spreads. People do not mix at random: contacts are strongly structured by age, setting, and behaviour, and capturing this structure, often as a contact or mixing matrix, is essential for realistic transmission models.

Definition

Contact rate is the average number of potentially infectious contacts an individual makes per unit time, and mixing patterns describe how those contacts are distributed across groups (for example by age or setting), commonly summarised in a contact or mixing matrix.

Scope

This entry covers the concept of the contact rate, the difference between random and structured (assortative) mixing, the use of contact and 'who-acquires-infection-from-whom' matrices in transmission models, and how empirical contact surveys inform these patterns. It is a reference and methodological topic, not clinical guidance.

Core questions

• How often do individuals make contacts capable of transmitting an agent?
• Do people mix at random, or preferentially with others like themselves?
• How are mixing patterns encoded in transmission models?
• How do empirical contact surveys measure these patterns?

Key concepts

• Contact rate
• Homogeneous (random) mixing
• Assortative mixing
• Contact matrix
• Who-acquires-infection-from-whom (WAIFW) matrix
• Age-structured contact patterns
• Contact surveys (social contact data)

Key theories

Heterogeneous mixing and the next-generation matrix

When contact rates differ across groups, the reproduction number is obtained from a next-generation matrix that encodes the rate at which each group infects every other; this formalises how mixing structure, not just the average contact rate, governs spread.

Mechanisms

In the simplest models everyone mixes at random, so a single average contact rate suffices. In reality contacts are assortative, concentrated within age groups and settings such as households, schools, and workplaces, so transmission models represent mixing with a matrix giving the contact rate between each pair of groups. Combined with the per-contact transmission probability and the duration of infectiousness, this matrix yields a next-generation matrix whose dominant eigenvalue is the reproduction number. Large diary-based contact surveys provide the empirical inputs for these matrices, revealing strongly age-assortative patterns of close-contact mixing.

Clinical relevance

Contact and mixing structure underpins how analysts reason about which groups drive transmission and how changes in contact would alter population spread. This entry describes mixing as a reference determinant of transmission and is not a basis for individual clinical decisions.

Epidemiology

Empirical surveys show that contact patterns are highly age-structured and vary by setting and population, which is why mixing matrices are usually region- and age-specific. The realised mixing pattern strongly influences which groups bear the greatest force of infection.

History

Early transmission models assumed homogeneous mixing, but work in the late twentieth century introduced structured mixing matrices to capture heterogeneity by age and group. The 2008 multi-country POLYMOD contact survey then supplied large-scale empirical mixing data, which became a standard input for age-structured transmission models.

Key figures

• Joël Mossong
• Niel Hens
• Roy Anderson
• Robert May
• Odo Diekmann

Seminal works

• mossong-2008
• diekmann-1990
• anderson-may-1991

Frequently asked questions

What is a contact matrix?

It is a table giving the average number of contacts between members of different groups, usually age groups, used in transmission models to represent how a population mixes rather than assuming everyone contacts everyone equally.

Why does assortative mixing matter?

Because people tend to contact others similar to themselves (for example, of the same age), transmission can concentrate within groups, which affects who is most at risk and how interventions should be targeted.