Incidence and Time Until Disease Detection in a Stochastic Model With Vaccination and General Transmission

In this study, we focus on the detection of a vaccine‐preventable communicable disease using a stochastic SIR compartmental model, which includes an additional compartment for individuals protected by vaccination. Although the 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 the time required for disease detection (i.e., full confirmation of the disease) and analyze the incidence rates before detection, both within the vaccinated group and throughout the population. To illustrate the usefulness of our theoretical derivations and algorithmic schemes, we will present a numerical study involving the above descriptors for outbreaks of foot‐and‐mouth disease (FMD) in cattle.