Mobility restrictions for the control of epidemics: When do they work?

Abstract

Background: Mobility restrictions-trade and travel bans, border closures and, in extreme cases, area quarantines or cordons sanitaires-are among the most widely used measures to control infectious diseases. Restrictions of this kind were important in the response to epidemics of SARS (2003), H1N1 influenza (2009), Ebola (2014) and, currently in the containment of the ongoing COVID-19 pandemic. However, they do not always work as expected.

Methods: To determine when mobility restrictions reduce the size of an epidemic, we use a model of disease transmission within and between economically heterogeneous locally connected communities. One community comprises a low-risk, low-density population with access to effective medical resources. The other comprises a high-risk, high-density population without access to effective medical resources.

Findings: Unrestricted mobility between the two risk communities increases the number of secondary cases in the low-risk community but reduces the overall epidemic size. By contrast, the imposition of a cordon sanitaire around the high-risk community reduces the number of secondary infections in the low-risk community but increases the overall epidemic size.

Interpretation: Mobility restrictions may not be an effective policy for controlling the spread of an infectious disease if it is assessed by the overall final epidemic size. Patterns of mobility established through the independent mobility and trade decisions of people in both communities may be sufficient to contain epidemics.

Fig 1. Single community COVID-19 disease dynamics.

The rates associated with the pathways are included in Table 1.

Fig 2. Patch-specific, global final size and global basic reproductive number in the presence of HRC mobility.

(A) Community specific and total final epidemic size with unidirectional mobility (t₂ = 0). (B) Global ${\mathcal{R}}_0$ for different LRC risk scenarios, (${\mathcal{R}}_{02}=1.1,1$ and 0.9), with unidirectional mobility (t₂ = 0).

Fig 3. Total attack rate under differential LRC risk levels.

The mobility thresholds $t_1^{-}$ and $t_1^{+}$ are highly sensitive to ${\mathcal{R}}_{02}$, under one-way mobility and ${\mathcal{R}}_{01}=2.3$.

Fig 4. Cordon Sanitaire effectiveness as a function of LRC risk of infection.

(A) The cordon sanitaire mobility threshold as a function of HRC mobility defines ${\mathcal{R}}_{02}\left(t_1\right)$ values for which the cordon sanitaire is recommended, conditionally recommended or not recommended. (B) HRC traveling time reduces or increases the total attack rate as a function of the LRC risk of infection, (${\mathcal{R}}_{01}=2.3$).

Fig 5. Cordon sanitaire level curves for population density ratios N1N2=5,1 and 15.

The higher the HRC population size, the minimum mobility level required to drop the total attack rate below the cordon sanitaire under unidirectional mobility from the HRC.

Fig 6. Global basic reproductive number level curve R0=1 in the plane (t1,R02).

Unidirectional mobility from HRC can eradicate a COVID-19 outbreak, (${\mathcal{R}}_{01}=2.3$ and, N₁ = N₂).