Epidemics in heterogeneous populations: II. Nonexponential incubation periods and variable infectiousness

Two stochastic models for the spread of an infection through a heterogeneous population are considered. First, we consider a model where the incubation period has an increasing hazard rate but constant infectiousness; in the second model, the incubation period is the sum of p exponentially distributed stages, each with its own mean and level of infectiousness. By using multitype birth-death and branching processes as approximations to each epidemic model, it is shown that the epidemics initially have underlying exponential growth. Furthermore, the growth rate theta is an increasing function of the Frobenius root of the matrix of reproductive ratios R0. The results have applications in long-term sensitivity analyses, model fitting, and the determination of optimal vaccination strategies.