Age-Specific Incidence of Epidemic Spread

We explore the age-specific incidence of infection during the initial phase of an epidemic of an emerging infectious disease agent that spreads in a completely susceptible population. We focus on the generic features of epidemic spread along the transmission route that is specified by physical and nonphysical contacts as defined here. We partition the population into 5 y age bands, and we group all individuals aged 70 y and older together. This process results in 15 age classes. We denote the number of at-risk contacts of an individual in age class j with individuals in age class i by k_ij. We take k_ij as proportional to the observed number of contacts (both physical and nonphysical) that a respondent in age band j makes with other individuals in age band i. The matrix with elements k_ij is known in infectious disease epidemiology as the next generation matrix K [32 ]. The next generation matrix can be used to calculate the distribution of numbers of new cases in each generation of infection from any arbitrary initial number of introduced infections. For example, when infection is introduced by one single 65-y-old infected individual into a completely susceptible population, we can denote the number of initial cases in generation 0 by the vector x₀ = (0,0,0,0,0,0,0,0,0,0,0,0,0,1,0)^T. The expected numbers of new cases in the ith generation are denoted by the vector x_i, and this vector is calculated by applying the next generation matrix K i times to the initial numbers of individuals x₀, that is, x_i = Kⁱ x₀. For large i, the vector x_i will be proportional to the leading eigenvector of K. We find that, in practice, the distribution of new cases is stable after five generations; that is, the distribution no longer depends on the precise age of the initial case. The incidence of new infections per age band is obtained by dividing the expected number of new cases per age class by the number of individuals in each age class. To facilitate comparison among countries, we normalized the distribution of incidence over age classes such that for each country the age-specific incidences sum to one.