Assessing the efficacy of health countermeasures on arrival time of infectious diseases

Public health measures to control the international spread of infectious diseases include strengthening quarantines and sealing borders. Although these measures are effective in delaying the importation of infectious diseases, they also have a significant economic impact by stopping the flow of people and goods. The arrival time of infectious diseases is often used to assess quarantine effectiveness. Although the arrival time is highly dependent on the number of infected cases in the endemic country, direct comparisons have not yet been made. Therefore, this study derives an explicit relationship between the number of infected cases and arrival time. Transmission behavior is stochastic, and deterministic models are not always realistic. In this study, random differential equations, which are differential equations with stochastic processes, were used to describe the dynamics of infection in an endemic country. Furthermore, the flow of travelers from the endemic country was described in terms of survival time, and the arrival time in each country was calculated. A scenario in which PCR kits were distributed between endemic and disease-free countries was also considered, and the impact of different distribution rates on arrival time was evaluated. The simulation results showed that increasing the distribution of PCR kits in the endemic country was more effective in delaying arrival times than using PCR kits in quarantine in disease-free countries. It was also found that increasing the proportion of identified infected persons in the endemic country, leading to isolation, was more important and effective in delaying arrival times than increasing the number of PCR tests.