López Herrero, María JesúsMustaro, VerdianaTaipe Hidalgo, Diana Paulina2025-12-012025-12-012025-11-19Lopez-Herrero, M., Mustaro, V. and Taipe, D. (2025) “Incidence and Time Until Disease Detection in a Stochastic Model With Vaccination and General Transmission,” Mathematical Methods in the Applied Sciences [Preprint]. Available at: https://doi.org/10.1002/mma.70306.0170-421410.1002/mma.70306https://hdl.handle.net/20.500.14352/127382In 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.engjournal article1099-1476https://doi.org/10.1002/mma.70306https://onlinelibrary.wiley.com/doi/10.1002/mma.70306open access519.2:61616Detection of the diseaseImperfect vaccineMarkov chainStochastic epidemic modelMedicinaEstadística aplicada2404.01 Bioestadística6310.03 Enfermedad