Investigating duration and intensity of Covid-19 social-distancing strategies

Abstract

The exponential character of the recent Covid-19 outbreak requires a change in strategy from containment to mitigation. Meanwhile, most countries apply social distancing with the objective to keep the number of critical cases below the capabilities of the health care system. Due to the novelty and rapid spread of the virus, an a priori assessment of this strategy was not possible. In this study, we present a model-based systems analysis to assess the effectiveness of social distancing measures in terms of intensity and duration of application. Results show a super-linear scaling between intensity (percent contact reduction) and required duration of application to have an added value (a lower number of fatalities). This holds true for an effective reproduction of [Formula: see text] and is reverted for [Formula: see text]. If R is not reduced below 1, secondary effects of required long-term isolation are likely to unravel the added value of disease mitigation. If an extinction is not feasible, we recommend moderate social-distancing that is well balanced against capability limits of national health-care systems.

Figure 1

Schematic diagram of the adapted SIR model: susceptible S(t), infected - infection unknown I(t), infected in isolation II(t), resistant symptomatic RS(t), resistant asymptomatic RA(t), deaths D(t), deaths caused by lack of ICU DL(t), compare Eqs. (1)–(8).

Figure 2

Delay effect of mitigation interventions ($a_f=0$).

Figure 3

Relationship between effective reproduction R and peak occurrence $\mu$ in days after disease outbreak ($a_f=0$). The parameter $\lambda$ is calculated to 238.

Figure 4

Relationship between effective reproduction R and standard deviation $\sigma$. ($a_f=0$) The parameter $\tau$ is calculated to 12.46.

Figure 5

Relationship between effective reproduction, peak occurrence ($\mu$) and number of infected at model initialization ($a_f=0$).

Figure 6

Relative fatalities (fatalities with contact reduction divided by fatalities without contact reduction, i.e. a relative fatality of 1 indicates that measures have no added value) plotted against social contact reduction in percent and duration of measure application.

Figure 7

Relative fatalities (fatalities with contact reduction divided by fatalities without contact reduction, i.e. a relative fatality of 1 indicates that measures have no added value) in Scenario 2, (R0 = 2.1) with constant duration (200 days) and varying intensity of contact reduction.

Figure 8

Policy based mitigation of new infections to meet capabilities of national health care systems.

Figure 9

Mitigation and herd immunity strategy in a high performance health care system (Scenario 11 Austria, R0 = 1.4) and low rates of ICU admissions (2.2% of confirmed infected).