On the exact and population bi-dimensional reproduction numbers in a stochastic SVIR model with imperfect vaccine

M. Gamboa, M. López-García and M.J. Lopez-Herrero

Applied Mathematics and Computation, 2024, vol. 468, issue C

Abstract: We aim to quantify the spread of a direct contact infectious disease that confers permanent immunity after recovery, within a non-isolated finite and homogeneous population. Prior to the onset of the infection and to prevent the spread of this disease, a proportion of individuals was vaccinated. But the administered vaccine is imperfect and can fail, which implies that some vaccinated individuals get the infection when being in contact with infectious individuals. We study the evolution of the epidemic process over time in terms of a continuous-time Markov chain, which represents a general SIR model with an additional compartment for vaccinated individuals. In our stochastic framework, we study two bi-dimensional variables recording infection events, produced by a single infectious individual or by the whole infected group, taking into account if the newly infected individual was previously vaccinated or not. Theoretical schemes and recursive algorithms are derived in order to compute joint probability mass functions and factorial moments for these random variables. We illustrate the applicability of our techniques by means of a set of numerical experiments.

Keywords: Stochastic epidemic model; Markov chain; Basic reproduction number; Imperfect vaccine (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:468:y:2024:i:c:s0096300323006951

DOI: 10.1016/j.amc.2023.128526

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