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Facing a global epidemic of new infectious diseases such as COVID-19,non-pharmaceutical interventions (NPIs), which reduce transmission rateswithout medical actions, are being implemented around the world to mitigatespreads. One of the problems in assessing the effects of NPIs is that differentNPIs have been implemented at different times based on the situation of eachcountry; therefore, few assumptions can be shared about how the introduction ofpolicies affects the patient population. Mathematical models can contribute tofurther understanding these phenomena by obtaining analytical solutions as wellas numerical simulations. In this study, an NPI was introduced into the SIRmodel for a conceptual study of infectious diseases under the condition thatthe transmission rate was reduced to a fixed value only once within a finitetime duration, and its effect was analyzed numerically and theoretically. Itwas analytically shown that the maximum fraction of infected individuals andthe final size could be larger if the intervention starts too early. Theanalytical results also suggested that more individuals may be infected at thepeak of the second wave with a stronger intervention. This study providesquantitative relationship between the strength of a one-shot intervention andthe reduction in the number of patients with no approximation. This suggeststhe importance of the strength and time of NPIs, although detailed studies arenecessary for the implementation of NPIs in complicated real-world environmentsas the model used in this study is based on various simplifications.

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