M. Gamboa Pérez, M. J. López-Herrero
We consider a population of constant size, where individuals are affected by an infectious disease that no confers immunity. Infections can be produced through direct contact with infected individuals within the population and also from an external source of infection. A percentage of the population is vaccinated with an imperfect vaccine. We describe the evolution of the epidemic process in terms of a bi-dimensional continuous-time Markov chain. Due to the imperfect vaccine and the external source of infection, the number of immunized individuals drops down continually and in consequence the herd immunity could be lost. To control the loss of protection, we introduce an alarm threshold on the number of protected individuals. Our main goal is to investigate the size of susceptible group at this time and evaluate if a re-vaccination program could be launched immediately. We provide some numerical results representing the evolution of diphtheria outbreaks.
Palabras clave: Stochastic Markovian epidemic; Imperfect vaccine; Basic reproduction number
Programado
GT17 Procesos Estocásticos y sus Aplicaciones II
7 de junio de 2022 15:30
A26
