Age-Dependent Branching Processes for Surveillance of Vaccine-Preventable Diseases with Incubation Period

The purpose of this paper is to review the recent results of the authors in the area of infectious disease modeling by means of branching stochastic processes. This is a new approach involving age-dependent branching models, which turned out to be more appropriate and flexible for describing the spread of an infection in a given population, than discrete time ones. Concretely, Bellman-Harris and Sevast'yanov's branching processes are investigated. It is justified that the proposed models are proper candidates as models of infectious diseases with incubation period like measles, mumps, avian flu, etc. It is worth to notice that in general the developed methodology is applicable to the diseases that follow the so-called SIR (susceptible-infected-removed) scheme in terms of epidemiological models. Two policies of extra-vaccination level are proposed and compared on the ground of simulation examples.