Failure to balance social contact matrices can bias models of infectious disease transmission
Authors: Hamilton Mackenzie A. , Knight Jesse , Mishra Sharmistha 
Published: July 2022

Spread of transmissible diseases is dependent on contact patterns in a population (i.e. who contacts whom). Therefore, many epidemic models incorporate contact patterns within a population through contact matrices. Social contact survey data are commonly used to generate contact matrices; 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. While the importance of balancing contact matrices has been acknowledged, how these imbalances affect modelled projections (e.g., peak infection incidence, impact of public health measures) has yet to be quantified. Here, we explored how imbalanced contact matrices from age-stratified populations (<15, 15+) may bias transmission dynamics of infectious diseases. First, we compared the basic reproduction number of an infectious disease when using imbalanced versus balanced contact matrices from 177 demographic settings. Then, we constructed a susceptible exposed infected recovered transmission model of SARS-CoV-2 and compared the influence of imbalanced matrices on infection dynamics in three demographic settings. Finally, we compared the impact of age-specific vaccination strategies when modelled with imbalanced versus balanced matrices. Models with imbalanced matrices consistently underestimated the basic reproduction number, had delayed timing of peak infection incidence, and underestimated the magnitude of peak infection incidence. Imbalanced matrices also influenced cumulative infections observed per age group, and the projected impact of age-specific vaccination strategies. For example, when vaccine was prioritized to individuals <15 in a context where individuals 15+ underestimated their contacts with <15, imbalanced models underestimated cumulative infections averted among 15+ by 24.4%. We conclude stratified transmission models that do not consider reciprocity of contacts can generate biased projections of epidemic trajectory and impact of targeted public health interventions. Therefore, modellers should ensure and report on balancing of their contact matrices for stratified transmission models.

AUTHOR SUMMARY

Transmissible diseases such as COVID-19 spread according to who contacts whom. Therefore, mathematical transmission models – used to project epidemics of infectious diseases and assess the impact of public health interventions – require estimates of who contacts whom (also referred to as a contact matrix). Contact matrices are commonly generated using contact surveys, but this data is often imbalanced, where the total number of contacts reported by group A with group B does not match those reported by group B with group A. Although these imbalances have been acknowledged as an issue, the influence of imbalanced matrices on modelled projections (e.g. peak incidence, impact of public health interventions) has not been explored. Using a theoretical model of COVID-19 with two age groups (<15 and 15+), we show models with imbalanced matrices had biased epidemic projections. Models with imbalanced matrices underestimated the initial spread of COVID-19 (i.e. the basic reproduction number), had later time to peak COVID-19 incidence and smaller peak COVID-19 incidence. Imbalanced matrices also influenced cumulative infections observed per age group, and the estimated impact of an age-specific vaccination strategy. Given imbalanced contact matrices can reshape transmission dynamics and model projections, modellers should ensure and report on balancing of contact matrices.