Abstract

We study an epidemic model for a generic infectious disease with an ongoing spread in a closed community. The disease is assumed to not cause additional mortality and without providing immunity. We also assume the availability of a preventive measure that is both scarce and only partially effective in reducing the infection risk. We analyze the model focusing on the effect of a class of susceptibles that chooses to quarantine itself from the epidemic while waiting for the preventive measure to be available. Of particular interest is the case when the model exhibits bi-stability between the disease-free equilibrium and an endemic state which indicates that the disease may persist even if the epidemic reproductive number is less than one. We investigate the conditions whereby increasing the quarantine rate eliminates the bi-stability scenario thereby improving the predictive value of the model when assessing whether the disease evolves toward an endemic state or not.