Speaker
Description
This contribution studies the dynamics of an infectious disease outbreak in a closed homogeneously mixed population using a stochastic SVIR model with a pre-epidemic vaccination program and imperfect vaccine protection \cite{Gamboa2024}. The model is formulated as an absorbing continuous-time Markov chain with susceptible, vaccinated, infected, and recovered compartments. We focus on two key epidemiological quantities: the peak number of infections and the final epidemic size, defined as the total number of infections among both susceptible and vaccinated individuals \cite{Black2015}. Recursive schemes are derived to compute the corresponding probability mass functions, enabling the quantification of outbreak risk and variability through relevant summary measures. This approach is particularly well-suited for populations of moderate size, such as hospitals or nursing homes, where stochastic effects play a crucial role. Numerical results illustrate how imperfect vaccination shapes epidemic intensity and overall impact. Finally, some applications are presented to support decision-making in epidemic management under resource constraints \cite{Gomez-Corral2023} and to inform the assessment of vaccine effectiveness \cite{Orenstein1985}. This work is based on a manuscript currently under review.
Bibliography
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author = {María Gamboa and M. L{\'o}pez-Garc{\'\i}a and M. J. Lopez-Herrero},
title = {On the exact and population bi-dimensional reproduction numbers in a stochastic SVIR model with imperfect vaccine},
journal = {Applied Mathematics and Computation},
volume = {468},
pages = {128526},
year = {2024}
}
@article{Orenstein1985,
author = {W. A. Orenstein and R. H. Bernier and T. J. Dondero and others},
title = {Field evaluation of vaccine efficacy},
journal = {Bulletin of the World Health Organization},
volume = {63},
number = {6},
pages = {1055--1068},
year = {1985}
}
@article{Gomez-Corral2023,
author = {A. G{\'o}mez-Corral and M. J. Lopez-Herrero and D. Taipe},
title = {A Markovian epidemic model in a resource-limited environment},
journal = {Applied Mathematics and Computation},
volume = {458},
pages = {128252},
year = {2023}
}
@article{Black2015,
author = {A. J. Black and J. V. Ross},
title = {Computation of epidemic final size distributions},
journal = {Journal of Theoretical Biology},
volume = {367},
pages = {159--165},
year = {2015}
}
