Model-based analysis on social acceptability and feasibility of a focused protection strategy against the COVID-19 pandemic

Abstract

This paper studies the social acceptability and feasibility of a focused protection strategy against coronavirus disease 2019 (COVID-19). We propose a control scheme to develop herd immunity while satisfying the following two basic requirements for a viable policy option. The first requirement is social acceptability: the overall deaths should be minimized for social acceptance. The second is feasibility: the healthcare system should not be overwhelmed to avoid various adverse effects. To exploit the fact that the disease severity increases considerably with age and comorbidities, we assume that some focused protection measures for those high-risk individuals are implemented and the disease does not spread within the high-risk population. Because the protected population has higher severity ratios than the unprotected population by definition, the protective measure can substantially reduce mortality in the whole population and also avoid the collapse of the healthcare system. Based on a simple susceptible-infected-recovered model, social acceptability and feasibility of the proposed strategy are summarized into two easily computable conditions. The proposed framework can be applied to various populations for studying the viability of herd immunity strategies against COVID-19. For Japan, herd immunity may be developed by the proposed scheme if [Formula: see text] and the severity rates of the disease are 1/10 times smaller than the previously reported value, although as high mortality as seasonal influenza is expected.

Figure 1

Proposed adaptive control measure. The top and middle shows the number of infectious individuals I(t) and infected (infectious or recovered) individuals, respectively, $1-S(t)$ at time t. An uncontrolled case is indicated using the dot-dashed curve, whereas a controlled case is indicated using the black solid curve. An adaptive control that reduces social activity as in the bottom panel is imposed at $T^{\ast }$ and lifted when herd immunity in this group is established at $T^{\ast \ast }$. The area of the gray region below the controlled curve in the top panel presents the final number of infected individuals in the active group, A. As the number of infectious individuals start to decrease at $T^{\ast \ast }$, A will exceed $p^{\ast }=1-{\mathcal{R}}_0^{-1}$.

Figure 2

Minimum level of the control threshold to acquire herd immunity with varying shares of the active group in the whole population, $n=1/N\in (0,1]$. For each n, the condition (6) is satisfied if $I_{\mathrm{c}}\ge I_{min}$. The proposed strategy with any control threshold, $I_{\mathrm{c}}$, that is above the black solid curve can achieve herd immunity as the whole population. The dashed curve indicates the peak number of infectious individuals $I_{\mathrm{peak}}$, which is an increasing function of ${\mathcal{R}}_0$, in the uncontrolled scenario. The assumed control scheme is feasible (in terms of the condition (6) if $)I_{min}\le I_{\mathrm{peak}}$.

Figure 3

solid black curves show $I_{min}$ for Cases 1 to 4. The dashed black curve shows $I_{\mathrm{peak}}$. The marker indicates $I_{max}$ for Case 3, below which the proposed control scheme is feasible in terms of the healthcare system capacity. In Case 3, the proposed control scheme is feasible when ${\mathcal{R}}_0$ and $I_{\mathrm{c}}$ lie in the shaded region. The feasibility condition (7) is thus satisfied for ${\mathcal{R}}_0\le 2.0$ in Case 3.