Renaissance model of an epidemic with quarantine

Quarantine is one possible solution to limit the propagation of an emerging infectious disease. Typically, infected individuals are removed from the population by avoiding physical contact with healthy individuals. A key factor for the success of a quarantine strategy is the carrying capacity of the facility. This is often a known parameter, while other parameters such as those defining the population structure are more difficult to assess. Here we develop a model where we explicitly introduce the carrying capacity of the quarantine facility into a susceptible-infected-recovered (SIR) framework. We show how the model can address the propagation and control of contact and sexually transmitted infections. We illustrate this by a case study of the city of Zurich during the 16th century, when it had to face an epidemic of syphilis. After Swiss mercenaries came back from a war in Naples in 1495, the authorities of the city addressed subsequent epidemics by, among others, placing infected members of the population in quarantine. Our results suggest that a modestly sized quarantine facility can successfully prevent or reduce an epidemic. However, false detection can present a real impediment for this solution. Indiscriminate quarantine of individuals can lead to the overfilling of the facility, and prevent the intake of infected individuals. This results in the failure of the quarantine policy. Hence, improving the rate of true over false detection becomes the key factor for quarantine strategies. Moreover, in the case of sexually transmitted infections, asymmetries in the male to female ratio, and the force of infection pertaining to each sex and class of sexual encounter can alter the effectiveness of quarantine measures. For example, a heterosexually transmitted disease that mainly affects one sex is harder to control in a population with more individuals of the opposite sex. Hence an imbalance in the sex ratios as seen in situations such as mining colonies, or populations at war, can present impediments for the success of quarantine policies.