Methods for determining the quarantine period of infectious diseases; Estimation of the epidemiological ripple effects

This study proposes a few different methods to determine the length of quarantine against infectious diseases and develops their theoretical foundation. Quarantine measure, which refers to compulsory physical separation, including restriction of movement, of healthy indiviuduals who have been potentially exposed to an infectious disease, is one of the essential countermeasures as a border control against newly emerging infectious diseases. Although diagnostic tests and legal enforcement of quarantine have been discussed, little has been done on the determination of the optimal length. Practical implications of the length of quarantine are clarified by means of mathematical modelling of infectious disease dynamics. Various effectiveness measures are defined as a function of quarantine period, identifying differences between different evaluation measures and specifying the required epidemiological information to attain the estimation. Although the optimal durations for quarantine period have previously been discussed using the incubation period alone, more useful determination is attainable, accounting for the presence of asymptomatic individuals. Moreover, the present study does not only suggest the direct effectiveness of quarantine, but also quantifies the impact of quarantine on the resulting epidemic dynamics. In particular, the probability of extinction and delay-effect of invasion are explicitly modelled. As an example, numerical illustrations are made for pandemic influenza control, demonstrating that the proposed methods would be useful for decision-making of quarantine period for many infectious diseases.