Age-stratified epidemic model using a latent marked Hawkes process

We extend the unstructured homogeneously mixing epidemic model introduced by Lamprinakou et al. [arXiv:2208.07340] considering a finite population stratified by age bands. We model the actual unobserved infections using a latent marked Hawkes process and the reported aggregated infections as random quantities driven by the underlying Hawkes process. We apply a Kernel Density Particle Filter (KDPF) to infer the marked counting process, the instantaneous reproduction number for each age group and forecast the epidemic's future trajectory in the near future; considering the age bands and the population size does not increase the computational effort. We demonstrate the performance of the proposed inference algorithm on synthetic data sets and COVID-19 reported cases in various local authorities in the UK. We illustrate that taking into account the individual heterogeneity in age decreases the uncertainty of estimates and provides a real-time measurement of interventions and behavioural changes.