Incidence and time until disease detection in a stochastic model with vaccination and general transmission

Abstract

In this study, we focus on the detection of a vaccine-preventable communicable disease using a stochastic SIR com-partmental model, which includes an additional compartment for individuals protected by vaccination. Althoughthe vaccine is administered as a preventive measure before the onset of the disease, its efficacy diminishes with time,which requires booster doses for susceptible individuals. Using a continuous-time Markov chain, we examine thetime required for disease detection (i.e., full confirmation of the disease) and analyze the incidence rates before detec-tion, both within the vaccinated group and throughout the population. To illustrate the usefulness of our theoreticalderivations and algorithmic schemes, we will present a numerical study involving the above descriptors for outbreaksof foot-and-mouth disease (FMD) in cattle.