Optimizing Weekly-Period Cyclical Lockdown Policies: A Simulation Study Using the A-SIR Model

Abstract

This paper presents numerical simulations of COVID-19 cyclical lockdown scenario in which there is an alternating short phase between working days and lockdown days with weekly period. We use an adaptive SIR model with daily varying infection and recovery rates. The model is fitted with United States COVID-19 data. The rates for the model-fitting are obtained using the Method of Variational Imbedding (MVI) and fixed-point iteration that depend on actual COVID-19 data. Subsequently, we use the adaptive model to simulate cyclical lockdown of W working days (normal state) and L lockdown days with weekly cycle W +L = 7. To model the cyclical lockdown scenario, we multiply the infection rate by a piecewise continuous damping function that has value either 1 (when no lockdown is implemented) or 0.175 (when short lockdown is implemented). The numerical simulation shows that allowing up to 5 working days per week can flatten the curve of active cases. We also compare the model for cyclical lockdown scenario against the model for prolonged and continuous lockdown scenario: the simulation of prolonged continuous lockdown without allowing a short period of normal state result in smaller final epidemic size. However, as the number of lockdown L gets higher, the cyclical lockdown seems to converge to the prolonged continuous lockdown. Our result shows that using cyclical lockdown with L = 4 lockdown days per week for 177 weeks, which means 708 days of lockdown, gives total incidence (final epidemic size) of 4.311% (as a percentage of initial susceptible population S(0)), while using prolonged continuous lockdown for 708 consecutive days results in total incidence of 3.111%. Although the latter has smaller total incidence, the difference is not significant, which suggests that we can trade it for social and economic advantages that cyclical lockdown offers.