Motivated by modelling epidemics like COVID-19, this paper proposes a generalized chain binomial process which integrates two types of infectives, those with symptoms and those without. Testing of infectives and vaccination of susceptibles are then incorporated as preventive protective measures. Our interest relates to the distribution of the state of the population at the end of infection and to the reproduction number [Formula: see text] with the associated extinction condition. The method uses the construction of a family of martingales and a branching approximation for large populations, respectively. A more general branching process for epidemics is also constructed and studied. Finally, some results obtained are illustrated by numerical examples.
Keywords: Approximation by branching; Final population state; Reproduction number; Symptomatic infected or not; Testing and vaccination.
© 2021. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.