TY - JOUR

T1 - Epidemics in heterogeneous populations

T2 - II. Nonexponential incubation periods and variable infectiousness.

AU - Cairns, A. J.

PY - 1990

Y1 - 1990

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0025619794&partnerID=8YFLogxK

M3 - Article

VL - 7

SP - 219

EP - 230

JO - IMA Journal of Mathematics Applied in Medicine and Biology

JF - IMA Journal of Mathematics Applied in Medicine and Biology

SN - 0265-0746

IS - 4

ER -