How population heterogeneity in susceptibility and infectivity influences epidemic dynamics

An important concern in public health is what population group should be prioritised for vaccination. To this end, we present an epidemic model with arbitrary initial distributions for population susceptibility, and corresponding infectivity distributions. We consider four scenarios: first, a population with heterogeneous susceptibility with a uniform distribution, but homogeneous infectivity; second, a heterogeneously susceptible population with linear heterogeneous infectivity functions, where the most susceptible are either the most or least infectious; third, a bimodal distribution for susceptibility, with all combinations of infectivity functions; finally, we consider the effects of additional pre-epidemic immunity, ostensibly through vaccination, on the epidemic dynamics. For a seasonal influenza-like infectious disease, we find the smallest final size and overall number of deaths due to the epidemic to occur if the most susceptible are vaccinated, corresponding to targeting children.