Inferring the structure of social contacts from demographic data in the analysis of infectious diseases spread

Abstract

Social contact patterns among individuals encode the transmission route of infectious diseases and are a key ingredient in the realistic characterization and modeling of epidemics. Unfortunately, the gathering of high quality experimental data on contact patterns in human populations is a very difficult task even at the coarse level of mixing patterns among age groups. Here we propose an alternative route to the estimation of mixing patterns that relies on the construction of virtual populations parametrized with highly detailed census and demographic data. We present the modeling of the population of 26 European countries and the generation of the corresponding synthetic contact matrices among the population age groups. The method is validated by a detailed comparison with the matrices obtained in six European countries by the most extensive survey study on mixing patterns. The methodology presented here allows a large scale comparison of mixing patterns in Europe, highlighting general common features as well as country-specific differences. We find clear relations between epidemiologically relevant quantities (reproduction number and attack rate) and socio-demographic characteristics of the populations, such as the average age of the population and the duration of primary school cycle. This study provides a numerical approach for the generation of human mixing patterns that can be used to improve the accuracy of mathematical models in the absence of specific experimental data.

Figure 1. Example of the computation of household contact matrix.

a Computation of contact frequencies for every member of a household composed by two adults aged 31 and two children of 5 and 6 years old. The sum of the four contributions gives contact frequencies within this household (in red). b Contact frequencies within a household composed of an adult aged 31 and a child aged 5. c Assuming that these two households constitute the whole population, the frequency of household contacts that individuals of age have with individuals aged is given by the sum of the contributions from each household, divided by the number of individuals aged having at least one household contact.

Figure 2. Mixing patterns by age in the UK.

Representations in logarithmic scale of contact matrices by one-year age brackets for the United Kingdom in the different social settings. Frequency of contacts (in arbitrary units) increases from blue to red. a Household. b School. c Workplace. d General community. e The total matrix obtained as a linear combination of the matrices represented in a–d; the coefficients used are the proportions of transmission in the four settings: 0.3 in households, 0.18 in schools, 0.19 in workplaces and 0.33 in the general community , , , –. f Proportions of contacts with individuals of the same age group, from the total matrix.

Figure 3. Characterization of synthetic contact matrices.

Clustering of countries on the basis of total matrices. a Dendrogram of cluster analysis based on the Canberra distance. b Map of Europe and grouping of countries made by the algorithm; countries having the same color belong to the same cluster. c Average age and household size for the 26 countries considered. Colors as in the map.

Figure 4. Comparison with Polymod contact matrices.

a Linear regression model with zero intercept for Polymod matrices against those from our model, (results shown in logarithmic scale). All countries are considered together and every matrix is normalized so that the sum of its elements is one. Yellow dots refer to the terms on the diagonal, light blue dots correspond to the other entries of the matrices. The value for the regression coefficient is 1.03 and the coefficient of determination results to be 0.71. b As in a but for each country singularly, without matrix normalization. In every plot the values for the regression coefficient and the coefficient of determination are reported. c Green bars represent the average seroprevalence of H1N1 influenza infections in England and Wales during the 2009 pandemic as estimated in a serosurvey (in that study a titre for haemagglutination inhibition has been considered for defining seroconversion in the population) and the black lines represent the 95%CI. Blue bars represent the seroprevalence as obtained by simulating a SIR model with using our contact matrix. Red bars represent the seroprevalence as obtained by simulating a SIR model with using the Polymod contact matrix. d Simulated seroprevalence profiles by age. using Polymod (red) and our matrices (blue), for an epidemic emerging in a completely susceptible population, assuming . In the plot for the Netherlands the profile obtained using the matrix from is also shown (dark green).

Figure 5. Country-specific matrices and European average.

a Final infection attack rate as a function of the basic reproduction number in the different countries (blue dots) by adopting country-specific matrices and by assuming the same probability of transmission in all countries – specifically, the value resulting in by adopting the average European matrix (green dot). The attack rate corresponding to the average European matrix is computed by assuming the average European age structure in the model. Red line represents the attack rate of the homogeneous mixing SIR model for values of in the range of variability of the basic reproduction number of country-specific matrices. Grey line represents the best fit of the linear model to data points related to the use of country-specific matrices. b Percentage variation of infection attack rate for increasing values of of models based on country-specific matrices with respect to models based on the average European matrix (with country-specific age structure). c As b but for the variation of the peak day. d–g Daily prevalence over time of models with based on either the country-specific matrix (solid lines) or the average European matrix (dashed lines, with country-specific age structure) in Germany, Italy, France and Slovakia respectively. In this figure we assume the generation time to be 3.1 days.

Figure 6. Socio-demography and disease epidemiology.

a Basic reproduction number as a function of the average age of the population in the different countries. Numbers inside the circles represent the duration (in years) of the primary school cycle; colors from red to yellow are proportional to those numbers. b Final attack rate as a function of the average age of the population in the different countries. c Basic reproduction number as a function of the fraction of individuals younger than 16 years of age in the different countries. d Final attack rate as a function of the fraction of individuals younger than 16 years of age in the different countries.