Analytical estimation of maximum fraction of infected individuals with one-shot non-pharmaceutical intervention in a hybrid epidemic model.

BACKGROUND: Facing a global epidemic of new infectious diseases such as COVID-19, non-pharmaceutical interventions (NPIs), which reduce transmission rates without medical actions, are being implemented around the world to mitigate spreads. One of the problems in assessing the effects of NPIs is that different NPIs have been implemented at different times based on the situation of each country; therefore, few assumptions can be shared about how the introduction of policies affects the patient population. Mathematical models can contribute to further understanding these phenomena by obtaining analytical solutions as well as numerical simulations. METHODS AND RESULTS: In this study, an NPI was introduced into the SIR model for a conceptual study of infectious diseases under the condition that the transmission rate was reduced to a fixed value only once within a finite time duration, and its effect was analyzed numerically and theoretically. It was analytically shown that the maximum fraction of infected individuals and the final size could be larger if the intervention starts too early. The analytical results also suggested that more individuals may be infected at the peak of the second wave with a stronger intervention. CONCLUSIONS: This study provides quantitative relationship between the strength of a one-shot intervention and the reduction in the number of patients with no approximation. This suggests the importance of the strength and time of NPIs, although detailed studies are necessary for the implementation of NPIs in complicated real-world environments as the model used in this study is based on various simplifications.

The association between the dynamics of COVID-19, related measures, and daytime population in Tokyo.

In Japan, a novel coronavirus has been prevalent since January 2020. The Japanese and local governments have implemented various measures, including declaring a state of emergency, according to the epidemic situation in each region. This study estimated the effective reproduction number (Rt) using the number of confirmed positive cases and positivity rates in Tokyo and examined the association between Rt and the rate of increase/decrease in the number of people across 12 sites. In Tokyo, there were five waves in which Rt was persistently estimated as approximately 1.0. The fourth and fifth waves started under the declaration of the state of emergency and coincided with an increase in the number of people. However, the contribution of the number of people to Rt was inconsistent, even when the number of people was of the same magnitude. A possible reason for this is difference in the countermeasures content, as the impact of vaccination was considered to be minor at the time. Where vaccination is insufficient, the wave is terminated by controlling the number of people leaving their homes. It is suggested that infection could be controlled more efficiently, depending on the content of the countermeasures.