Critical mobility in policy making for epidemic containment

TL;DR

This paper addresses how mobility drives epidemic spread and proposes policy strategies that exploit a critical mobility threshold to prevent large outbreaks. It introduces an agent-based, mobility–contact coupling with a COVID-19–like SEIR process, using the radius of gyration $R_g$ as the mobility metric and identifying a boundary $R_{g,c}$ that delineates outbreak from containment as a function of immune fraction $x$ and infectivity $\beta$. By comparing incidence-threshold traffic-light interventions with $R_g$-based controls, including a staircase approach that tracks the moving $R_{g,c}$, the work shows how policy can maintain near-threshold mobility to suppress peaks while reducing oscillations and societal burden. Vaccination shortens outbreak duration and shifts the threshold but does not qualitatively alter the mobility–epidemic relationship, suggesting mobility-guided strategies can complement vaccination campaigns. Together, the framework provides a practical, data-driven avenue for policy makers to minimize health-system overload and economic disruption while steering communities toward herd immunity, albeit with data and behavioral- response caveats.

Abstract

When considering airborne epidemic spreading in social systems, a natural connection arises between mobility and epidemic contacts. As individuals travel, possibilities to encounter new people either at the final destination or during the transportation process appear. Such contacts can lead to new contagion events. In fact, mobility has been a crucial target for early non-pharmaceutical containment measures against the recent COVID-19 pandemic, with a degree of intensity ranging from public transportation line closures to regional, city or even home confinements. Nonetheless, quantitative knowledge on the relationship between mobility-contagions and, consequently, on the efficiency of containment measures remains elusive. Here we introduce an agent-based model with a simple interaction between mobility and contacts. Despite its simplicity our model shows the emergence of a critical mobility level, inducing major outbreaks when surpassed. We explore the interplay between mobility restrictions and the infection in recent intervention policies seen across many countries, and how interventions in the form of closures triggered by incidence rates can guide the epidemic into an oscillatory regime with recurrent waves. We consider how the different interventions impact societal well-being, the economy and the population. Finally, we propose a mitigation framework based on the critical nature of mobility in an epidemic, able to suppress incidence and oscillations at will, preventing extreme incidence peaks with potential to saturate health care resources.

Figures (11)

• Figure 1: Summary of model. A Sketch of zones where agents can be seen during the day. H and W represent house and workplace respectively, with fixed mobility between them represented in black arrows. $\textit{T}_1$ and $\textit{T}_2$ represent extra trips that may occur with a probability p, represented with curved white arrows. B Trip distance statistics from our model employing equation \ref{['eq:cauchy']} and relationship between our mobility metric $R_g$ and the trip probability p. C Compartmental model. Transition rates and other parameters are listed in Table \ref{['tab:rates']}. The compartments consist of the following states: susceptible $S$, exposed $E$, infected $I$ and recovered $R$.
• Figure 2: Epidemic size, i.e., the fraction of infected individuals at the end of the simulation, as a function of the population mobility $R_g$ and the initial immunity levels for infectivity $\beta = 0.1$. The dashed white line shows eq. (\ref{['eq:fit']}) performed to points with epidemic size between $1.3\%$ and $2.5\%$, used to estimate the critical mobility threshold $R_{g,c}$ based on immunity. Equivalently, the dashed orange line is another fit performed to mark the boundary below which mobility induces at least a 5% outbreak.
• Figure 3: Examples of incidence threshold-based interventions for infectivity $\beta = 0.1$. The first uncontrollable epidemic wave is removed due to being completely uncoupled from the dynamics the different interventions induce. (A and B) Incidence per 100 000 inhabitants and mobility curves throughout a realisation of strict traffic light interventions without vaccination. Mobility is adjusted every $T_r=30$ timesteps and adopts the values stated in Table \ref{['tab:traffic_light']} immediately. The grey dashed line in A and C represents an incidence rate of 10 daily cases per 100 000 individuals. (C and D) Epidemic and mobility curves throughout a realisation of lenient traffic light interventions without vaccination. Mobility aims to adopt the values stated in Table \ref{['tab:traffic_light']} progressively, in changes of $\Delta p = 10\%$ revised every $T_r=60$ timesteps. B and D include the 5% outbreak mobility limit plus a 90 timestep moving average of $R_g$ as a measure of an effective mobility.
• Figure 4: Examples of $R_g$-based interventions for infectivity $\beta =0.1$. The first uncontrollable epidemic wave is removed due to being completely uncoupled from the dynamics the different interventions induce. (A and B) Incidence per 100 000 inhab. and mobility curves throughout a realisation of an $R_g$-based intervention with theoretically estimated $R_{g,c}$ and $\epsilon_p = 0.025$ without vaccination. Mobility is adjusted every $T_r=30$ timesteps following \ref{['eq:rgc-measure']}. (C and D) Epidemic and mobility curves throughout a realisation of staircase interventions without vaccination. The mobility parameter $p$ is forced to be monotonically increasing through time in steps of $\Delta p = 0.3\%$ every $T_r=30$ timesteps. The grey dashed line in A and C represents an incidence rate of 10 daily cases per 100 000 individuals. B and D include the 5% outbreak mobility limit plus a 90 timestep moving average of $R_g$ as a measure of an effective mobility. The 90 t.s. average completely overlaps $R_g$ as changes are too slow for them to be distinguishable.
• Figure 5: Violin and strip plots for statistics of the different metrics and interventions tested. The parameters of each intervention are detailed in figures \ref{['fig:main_res']} and \ref{['fig:main_res_2']}. Violin plots include lines to mark median and quartiles of the distribution. The first epidemic wave happens with $p=0$ and thus is uncontrollable. Therefore it is excluded when computing the present statistics to avoid dilution of the results produced in the regions where interventions are acting. The number of simulations for each intervention is 200. A Average Incidence per 100 000 inhab. B Surplus Incidence as a percentage of the total population. C Distribution of Peak Incidences by intervention type. D Deviation of mobility from the optimum, characterised as the standard deviation of the relative mobility $\Theta (t) := R_{g}(t) - R_{g,c}(t)$. E Cumulative effective mobility (moving average of $R_g$ with a 90t.s. window) above the 5% outbreak mobility level. F Example trajectories in the phase diagram of Fig. \ref{['fig:imm_map']} for interventions shown in Fig. \ref{['fig:main_res']} and \ref{['fig:main_res_2']}.