Examining the Influence of Imbalanced Social Contact Matrices in Epidemic Models

Abstract

Transmissible infections such as those caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) spread according to who contacts whom. Therefore, many epidemic models incorporate contact patterns through contact matrices. Contact matrices can be generated from social contact survey data. However, the resulting matrices are often imbalanced, such that the total number of contacts reported by group A with group B do not match those reported by group B with group A. We examined the theoretical influence of imbalanced contact matrices on the estimated basic reproduction number (R0). We then explored how imbalanced matrices may bias model-based epidemic projections using an illustrative simulation model of SARS-CoV-2 with 2 age groups (<15 and ≥15 years). Models with imbalanced matrices underestimated the initial spread of SARS-CoV-2, had later time to peak incidence, and had smaller peak incidence. Imbalanced matrices also influenced cumulative infections observed per age group, as well as the estimated impact of an age-specific vaccination strategy. Stratified transmission models that do not consider contact balancing may generate biased projections of epidemic trajectory and the impact of targeted public health interventions. Therefore, modeling studies should implement and report methods used to balance contact matrices for stratified transmission models.

Keywords: SARS-CoV-2; contact balance; contact mixing; contact reciprocity; infectious disease modeling; vaccine policy.

Figure 1

Models with imbalanced (imbal) contact matrices underestimate R₀. Underestimation of R₀ in models with imbalanced contact matrices using data from Prem et al. (8, 9). bal, balanced; C, population contact rate; o, “old” (≥15 years); R₀, basic reproduction number; y, “young” (<15 years).

Figure 2

Imbalanced (imbal) contact matrices bias estimates of cumulative severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infections overall and among subgroups. Direction and magnitude of imbalance in synthetic contact matrices from Gambia (A), Luxembourg (B), and Singapore (C). Percent difference in cumulative infections overall and per age group from models parameterized with imbalanced versus balanced (bal) contact matrices in Gambia (D), Luxembourg (E), and Singapore (F). One infected individual was seeded per age group per model. Cumulative infections were compared 1 year after seeding in a completely susceptible and closed population in the absence of public health interventions. Contact matrices from Prem et al. (8, 9).

Figure 3

Imbalanced (imbal) contact matrices bias the impact of age-specific severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) vaccination strategies. Percent difference in cumulative infections averted in models parameterized with imbalanced versus balanced (bal) contact matrices when 50% of the population aged <15 years was vaccinated, using examples of different age-demographic settings: Gambia (A), Luxembourg (B), and Singapore (C). Percent difference in cumulative infections averted in models parameterized with imbalanced versus balanced contact matrices when 50% of the population ≥15 was vaccinated, using examples of different age-demographic settings: Gambia (D), Luxembourg (E), and Singapore (F). One infected individual was seeded per age group, per model. Cumulative infections averted were compared 1 year after seeding in a completely susceptible and closed population, in the absence of additional public health interventions other than vaccination. Contact matrices from Prem et al. (8, 9).