On the General Epidemic Model with Inmigration of Susceptibles and Infections
DOI:
https://doi.org/10.11145/250Abstract
We investigate the time to reach a critical number of infections in the Ridler-Rowe (1967) model, a general stochastic epidemic model with inmigration of susceptibles and infections. We focus on the study of the distribution of the exact reproduction number (i. e., the exact number of secondary cases produced by a typical infective individual during its entire infectious period) and the distribution of population transmission numberВ (i. e., the exact number of secondary cases produced by all infective individuals). Both descriptors were defined by Artalejo and Lopez-Herrero (2013) and are alternative stochastic versions of the well-known basic reproduction number. We firstly characterize the distribution of the time to reach a critical number of infections, as well as the probability mass functions andВ expected values ofВ the above-mentioned numbers.В Then we derive an iterative procedure to evaluate these distributions by using percentiles of the maximum number of susceptibles and infections simultaneously present in the population.
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