Emergency Responders

Our model is based on a generalized model of contagion proposed by Dodds and Watts (50 (link), 58 (link)). Here, we have reformulated the original model in terms of activation rates to describe behavioral contagion dynamics in continuous time. This allows us to more easily constrain parameters based on experimentally determined timescales and networks of influence, derived from the logistic regression’s predictions for response probabilities given fish positions at the time of the initial startle. We then simulate the model using a standard Euler discretization.
Individual fish, as nodes in a network, are connected by weighted directed edges $w_{ij}\in \left[\mathrm{0,1}\right]$ that define the rate of signaling doses received by individual $i$ when individual $j$ startles. Each individual $i$ can be in 1 of 3 states $s_i$ that we call susceptible, active, and recovered. Susceptible nodes may become activated due to inputs received from active neighbors. After a fixed activation time ${\tau }_{act}$ , activated individuals transition into the recovered state. The activation time is set to ${\tau }_{act}=0.5$ s, matching the experimentally observed average startle duration. For simplicity, we consider the recovered state as an absorbing state with no outward transitions, which restricts the model dynamics to single, nonrecurrent cascades. A simulation run is terminated when no active individuals remain.
As an initial condition we set all individuals as susceptible, and at time $t=0$ a single individual is activated (spontaneous startle). A susceptible individual $i$ receives from an active neighbor $j$ stochastic doses of activating signal of size $d_a$ at a rate $r_{ij}={\rho }_{\text{max}}{w}_{ij}$ , with ${\rho }_{\text{max}}$ being the maximal rate of sending activation doses for $w_{ij}=1$ . The maximal activation rate is bounded by limits on response times due to physiological constraints and neuronal processing of sensory cues which trigger a startling response in fish (59 (link)). The fastest startling responses to artificial stimuli were reported to be of the order of few milliseconds. Therefore, we assume ${\rho }_{\text{max}}=10^3$ s⁻¹, which allows in our model for fastest response times of the order of 1 ms (for $w_{ij}\approx 1$ ). To be able to resolve this timescale, we choose the numerical time step accordingly to $\mathrm{\Delta }t=1$ ms ( ${\rho }_{\text{max}}=1/\mathrm{\Delta }t$ ).
Thus, with small $\mathrm{\Delta }t$ , the activation signal received from individual $j$ is a stochastic time series $d_{ij}\left(t\right)$ with 2 possible values, $d_a$ and 0, whereby the probability of receiving an activation dose per simulation time step $\mathrm{\Delta }t$ is $p_a=r_{ij}\mathrm{\Delta }t$ . Each agent integrates all inputs over a finite memory ${\tau }_m=2$ s. The agent becomes activated if the cumulative dose $D_i\left(t\right)=\frac{1}{K_i}\sum _j{\int }_{t-{\tau }_m}^t{d}_{ij}\left(t\prime \right)dt\prime$ received by a susceptible agent $i$ within its memory time exceeds its internal threshold ${\theta }_i$ . Here, $K_i$ is the in degree of the focal individual, such that the doses received by the focal individual are rescaled by the number of its network neighbors, a form supported by prior work in a similar system (28 (link)). The individual thresholds are drawn from a uniform distribution with minimum 0 and maximum $2\overline{\theta }$ , producing an average threshold of $\overline{\theta }$ . This accounts for stochasticity due to inaccessible internal states of individuals at the time of initial startle.
The expected value of the cumulative activation dose received by agent $i$ due to the activation of a single neighbor $j$ ( $K_i=1$ ) over the activation time ${\tau }_{act}$ is thus $⟨D_i⟩=d_a{\rho }_{\text{max}}{w}_{ij}{\tau }_{act}$ . We choose the weights $w_{ij}$ to be equal to the probability that $i$ responds and is the first responder to an initial startle of $j$ , inferred using the logistic regression model depicted in Fig. 3. The linear relationship between the cumulative dose $⟨D_i⟩$ and the weights $w_{ij}$ , along with the uniform distribution of thresholds across fish, guarantees that the complex contagion process produces the correct relative initial response probabilities in the limit of small $\mathrm{\Delta }t$ and $w_{ij}$ (SI Appendix). Without loss of generality, we can set $d_a{\rho }_{\text{max}}=1$ . Thus, based on the maximal rate ${\rho }_{\text{max}}=10^3$ s⁻¹, we set the activation dose $d_a=10^{-3}$ . This leaves us with a single free parameter, the average dose threshold $\overline{\theta }$ , which we fit via maximum likelihood. A total of $10^4$ independent runs were performed for each threshold value to estimate corresponding cascade size probability distributions.

Approximately 50 million people live in a 99 000 km² area of land, where there were multiple regional and local government / hospital organisations: in 2015, there were 17 provinces and 253 local health departments (including 253 local health centres), 17 provincial fire departments, 200 local EMS agencies (966 ambulance stations and 1282 ambulances), and 546 emergency departments (EDs) (20 level one regional EDs, two specialty EDs, 124 level two local EDs, 274 level three emergency rooms, and 126 level four non-designated urgent facilities).
The Ministry of Health and Welfare EMS programme is responsible for emergency care services, acts and regulations, budgeting and policy planning. The Korea Centres for Disease Control and Prevention (CDC) is responsible for the community CPR programme by developing national standards and education programs. The National Medical Centre is responsible for hospital-based emergency care through the ED evaluation programme and reimbursement programs for hospital emergency care. The Central Fire Services (CFS) is responsible for pre-hospital ambulance services related to EMS.9 10 (link)
The 2005 and 2010 CPR guidelines recommended by the International Liaison Committee on Resuscitation (ILCOR) were accepted by the academic societies and implemented in the CPR training for lay persons, first responders, and EMS providers in 2006 and 2011, respectively.11 12 (link) The EMS CPR protocol was developed by EMS medical directors in 2011 on the basis of 2010 guidelines. The protocol allowed the EMS providers to perform chest compression and automatic defibrillation, and endotracheal intubation or supraglottic airway under direct medical control during prehospital CPR. The epinephrine or other resuscitation drugs were not permitted to infuse. The termination of resuscitation declared by emergency medical technicians was not allowed and all OHCAs should be transported to the emergency department with providing CPR on ambulance transport if the patients did not achieve the prehospital return of spontaneous circulation.