Éboli Model: Ebola Dynamics & Collider EFT

Updated 5 July 2026

Éboli Model is a designation for both tractable Ebola compartmental models and a specific SMEFT framework for anomalous quartic gauge couplings.
It encapsulates enhanced SIR/SEIR dynamics with additional features like incubation, hospitalization, and spatial effects, optimizing control measures such as vaccination.
In collider physics, the model specifies a constrained dimension-8 operator basis that probes CP-even anomalous gauge couplings while addressing unitarity and positivity limits.

Éboli Model is an ambiguous designation in the arXiv literature. In mathematical epidemiology it denotes Ebola-virus compartmental models, ranging from basic SIR and SEIR systems to hospitalization-, funeral-, mobility-, and control-augmented formulations; in collider phenomenology it denotes the dimension-8 anomalous quartic gauge-coupling basis associated with Éboli, Gonzalez-Garcia, and collaborators and used in SMEFT analyses of vector-boson scattering and triboson production (Rachah et al., 2016, Rachah et al., 2015, Collaboration, 19 Mar 2026). The two usages are mathematically unrelated, but both are technically well defined and both have acquired stable roles in their respective research domains.

1. Nomenclature and scope

The epidemiological usage appears in work that explicitly labels a compartmental Ebola system as an “Ebola model” or “Ébola model,” with the central example being a SIR model with vital dynamics, Ebola-induced mortality, and vaccination control calibrated to Guinea 2015 data (Rachah et al., 2016). Closely related papers compare SIR and SEIR formulations for West African Ebola, extend the state space to hospitalization and unsafe burial, or embed transmission in spatial and metapopulation structures (Rachah et al., 2015, Diaz et al., 2016, D'Silva et al., 2015, Ivorra et al., 2014).

The collider-physics usage is narrower. In the ATLAS combination of anomalous quartic gauge-coupling measurements, the “Éboli model” is the dimension-8 SMEFT basis used to parameterise CP-even quartic electroweak gauge-boson self-couplings, with scalar-, mixed-, and tensor-type operators and Wilson coefficients quoted as $f_i/\Lambda^4$ (Collaboration, 19 Mar 2026). This usage is not metaphorical: it refers to a specific EFT operator basis and a specific implementation strategy in VBS and triboson analyses.

2. Epidemiological usage: compartmental Ebola dynamics

The simplest epidemiological formulation is the basic SIR system

$\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$

with $S(0)=S_0>0$ , $I(0)=I_0>0$ , $R(0)=0$ , and constant population $N=S+I+R$ (Rachah et al., 2016). In this representation, $\beta$ is the transmission rate and $\mu$ is the recovery or removal rate. Comparative work on West African Ebola uses exactly this SIR structure alongside a basic SEIR extension,

$\begin{cases} \dfrac{d\hat{S}(t)}{dt} = -\hat{\beta}\, \hat{S}(t)\, \hat{I}(t),\[0.3cm] \dfrac{d\hat{E}(t)}{dt} = \hat{\beta}\, \hat{S}(t)\, \hat{I}(t) - \hat{\gamma}\, \hat{E}(t),\[0.3cm] \dfrac{d\hat{I}(t)}{dt} = \hat{\gamma}\, \hat{E}(t) - \hat{\mu}\, \hat{I}(t),\[0.3cm] \dfrac{d\hat{R}(t)}{dt} = \hat{\mu}\, \hat{I}(t), \end{cases}$

to isolate the effect of an explicit latent compartment $\hat{E}$ (Rachah et al., 2015).

A central modeling distinction is whether incubation is represented explicitly. The SIR-with-vital-dynamics formulation assumes that Ebola’s incubation is short enough that, for modeling the early outbreak, individuals become infectious immediately after infection; hence no exposed $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$0 class is used (Rachah et al., 2016). By contrast, the SIR-versus-SEIR comparison states that SEIR is “closer to the reality of Ebola virus, characterized by a period of incubation described by the exposed group,” and therefore “describes better the propagation of the virus” when that latent period is epidemiologically relevant (Rachah et al., 2015).

More elaborate Ebola-specific state spaces add hospitalization, funeral transmission, or both. A modified deterministic SEIR system for Guinea, Liberia, and Sierra Leone uses $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$1, where $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$2 is hospitalized infectious, $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$3 is removed but still infectious dead, $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$4 is buried, and $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$5 is recovered immune (Diaz et al., 2016). A stage-structured model instead distinguishes early infectious $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$6, late infectious $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$7, funeral transmissible $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$8, and recently recovered $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$9, thereby resolving the clinical course rather than hospitalization status (Eisenberg et al., 2015). Be-CoDiS further embeds an EVD-specific SEIHRDB system inside a between-country mobility model, with $S(0)=S_0>0$ 0 for dead but not yet buried and $S(0)=S_0>0$ 1 for buried (Ivorra et al., 2014).

3. SIR with vital dynamics, endemic equilibria, and optimal vaccination

The “Ebola model” in "Modeling, dynamics and optimal control of Ebola virus spread" is the SIR system with births, natural deaths, and disease-induced mortality,

$S(0)=S_0>0$ 2

where $S(0)=S_0>0$ 3 is inflow of newborn susceptibles, $S(0)=S_0>0$ 4 is natural mortality, and $S(0)=S_0>0$ 5 is Ebola-induced mortality in the infected class (Rachah et al., 2016). Its basic reproduction number is

$S(0)=S_0>0$ 6

so the epidemic threshold is determined by the ratio of effective infection pressure to total removal from $S(0)=S_0>0$ 7 (Rachah et al., 2016).

The model has two biologically meaningful equilibria. The disease-free equilibrium is

$S(0)=S_0>0$ 8

and the endemic equilibrium $S(0)=S_0>0$ 9 satisfies

$I(0)=I_0>0$ 0

$I(0)=I_0>0$ 1

The qualitative threshold statement is standard: if $I(0)=I_0>0$ 2, the disease-free equilibrium is obtained in the long run; if $I(0)=I_0>0$ 3, the endemic equilibrium is obtained (Rachah et al., 2016).

The controlled version introduces vaccination $I(0)=I_0>0$ 4 with $I(0)=I_0>0$ 5,

$I(0)=I_0>0$ 6

and minimizes

$I(0)=I_0>0$ 7

over a finite horizon, with $I(0)=I_0>0$ 8 days and $I(0)=I_0>0$ 9 in the reported simulations (Rachah et al., 2016). Vaccination moves individuals directly from $R(0)=0$ 0 to $R(0)=0$ 1, and the quadratic term penalizes vaccine usage. The implementation is numerical rather than analytic: ACADO and BocopHJB are used, and the coincidence of their solutions is taken to suggest global optimality of the computed control (Rachah et al., 2016).

For Guinea 2015, the model is calibrated to WHO data with fitted parameters $R(0)=0$ 2, $R(0)=0$ 3, $R(0)=0$ 4, $R(0)=0$ 5, demographic inflow $R(0)=0$ 6, and normalized initial conditions $R(0)=0$ 7, $R(0)=0$ 8, $R(0)=0$ 9 using population $N=S+I+R$ 0 (Rachah et al., 2016). The uncontrolled simulation approaches $N=S+I+R$ 1, with damped oscillations and endemic persistence consistent with $N=S+I+R$ 2 (Rachah et al., 2016). Under optimal vaccination, the maximum infected fraction is reduced from about $N=S+I+R$ 3 to about $N=S+I+R$ 4, the significant infection period shortens from more than $N=S+I+R$ 5 days to about $N=S+I+R$ 6 days, and the optimal $N=S+I+R$ 7 is high initially and then decreases (Rachah et al., 2016).

A recurrent point of disagreement in Ebola modeling is whether a closed, homogeneous, low-dimensional compartmental system is sufficient. The SIR-versus-SEIR comparison shows that if the latent period is very short and the initial exposed fraction is small, the SEIR infectious curve can be made to coincide very closely with the SIR curve; specifically, with $N=S+I+R$ 8, the two infectious trajectories have the same peak size, peak time, and nearly identical time course, although the recovered curves still differ (Rachah et al., 2015). The same study concludes that the models are not fully interchangeable for control design and that SEIR recommends earlier and stronger vaccination because it resolves the exposed pipeline explicitly (Rachah et al., 2015).

Hospitalization and funeral transmission alter both mechanism and control leverage. In the modified SEIR model with $N=S+I+R$ 9 and $\beta$ 0, susceptibles are infected through community infectious $\beta$ 1 at rate $\beta$ 2, unburied dead $\beta$ 3 at rate $\beta$ 4, and hospitalized infectious $\beta$ 5 at rate $\beta$ 6, yielding

$\beta$ 7

with country-specific values $\beta$ 8 for Guinea, $\beta$ 9 for Liberia, and $\mu$ 0 for Sierra Leone (Diaz et al., 2016). Local sensitivity analysis in that framework shows that increasing hospitalization rate $\mu$ 1 has a much larger impact on $\mu$ 2 than increasing burial rate $\mu$ 3, whereas the active-subspace analysis indicates that global prioritization can differ from local prioritization, with Liberia favored for small-to-moderate changes and Sierra Leone for large, transformative changes in hospitalization capacity (Diaz et al., 2016).

Spatial and strain heterogeneity directly challenge homogeneous mixing and uniform transmissibility. Using migration-informed effective distance, arrival time of EVD across West African countries is more strongly correlated with effective distance than with geodesic distance, with Spearman $\mu$ 4, $\mu$ 5, $\mu$ 6, and inferred effective velocity $\mu$ 7 (Burghardt et al., 2016). At finer administrative resolution, the initial logistic growth parameter $\mu$ 8 decreases with population density, with Spearman $\mu$ 9, $\begin{cases} \dfrac{d\hat{S}(t)}{dt} = -\hat{\beta}\, \hat{S}(t)\, \hat{I}(t),\[0.3cm] \dfrac{d\hat{E}(t)}{dt} = \hat{\beta}\, \hat{S}(t)\, \hat{I}(t) - \hat{\gamma}\, \hat{E}(t),\[0.3cm] \dfrac{d\hat{I}(t)}{dt} = \hat{\gamma}\, \hat{E}(t) - \hat{\mu}\, \hat{I}(t),\[0.3cm] \dfrac{d\hat{R}(t)}{dt} = \hat{\mu}\, \hat{I}(t), \end{cases}$0, $\begin{cases} \dfrac{d\hat{S}(t)}{dt} = -\hat{\beta}\, \hat{S}(t)\, \hat{I}(t),\[0.3cm] \dfrac{d\hat{E}(t)}{dt} = \hat{\beta}\, \hat{S}(t)\, \hat{I}(t) - \hat{\gamma}\, \hat{E}(t),\[0.3cm] \dfrac{d\hat{I}(t)}{dt} = \hat{\gamma}\, \hat{E}(t) - \hat{\mu}\, \hat{I}(t),\[0.3cm] \dfrac{d\hat{R}(t)}{dt} = \hat{\mu}\, \hat{I}(t), \end{cases}$1, and KDE-based strain analysis indicates that some strains, including SL1 in Guinea, occur more often than expected under a common-transmissibility null (Burghardt et al., 2016). A plausible implication is that country-scale single-$\begin{cases} \dfrac{d\hat{S}(t)}{dt} = -\hat{\beta}\, \hat{S}(t)\, \hat{I}(t),\[0.3cm] \dfrac{d\hat{E}(t)}{dt} = \hat{\beta}\, \hat{S}(t)\, \hat{I}(t) - \hat{\gamma}\, \hat{E}(t),\[0.3cm] \dfrac{d\hat{I}(t)}{dt} = \hat{\gamma}\, \hat{E}(t) - \hat{\mu}\, \hat{I}(t),\[0.3cm] \dfrac{d\hat{R}(t)}{dt} = \hat{\mu}\, \hat{I}(t), \end{cases}$2 models can obscure both place-based and lineage-based heterogeneity.

Gravity-coupled models make this spatial critique operational. A country- and district-level gravity model with latent infection, two infectious stages, and funeral transmission reproduces multiple waves in Guinea and distinguishes local from long-range transmission (D'Silva et al., 2015). In that framework, eliminating local transmission in Liberia yields about $\begin{cases} \dfrac{d\hat{S}(t)}{dt} = -\hat{\beta}\, \hat{S}(t)\, \hat{I}(t),\[0.3cm] \dfrac{d\hat{E}(t)}{dt} = \hat{\beta}\, \hat{S}(t)\, \hat{I}(t) - \hat{\gamma}\, \hat{E}(t),\[0.3cm] \dfrac{d\hat{I}(t)}{dt} = \hat{\gamma}\, \hat{E}(t) - \hat{\mu}\, \hat{I}(t),\[0.3cm] \dfrac{d\hat{R}(t)}{dt} = \hat{\mu}\, \hat{I}(t), \end{cases}$3 fewer cumulative cases across the three countries by 31 October 2014, whereas eliminating long-range transmission into Sierra Leone yields about $\begin{cases} \dfrac{d\hat{S}(t)}{dt} = -\hat{\beta}\, \hat{S}(t)\, \hat{I}(t),\[0.3cm] \dfrac{d\hat{E}(t)}{dt} = \hat{\beta}\, \hat{S}(t)\, \hat{I}(t) - \hat{\gamma}\, \hat{E}(t),\[0.3cm] \dfrac{d\hat{I}(t)}{dt} = \hat{\gamma}\, \hat{E}(t) - \hat{\mu}\, \hat{I}(t),\[0.3cm] \dfrac{d\hat{R}(t)}{dt} = \hat{\mu}\, \hat{I}(t), \end{cases}$4 fewer cases (D'Silva et al., 2015). The same analysis introduces “spatial herd protection” and “intervention-amplifying regions”; for example, Dubreka accounts for only $\begin{cases} \dfrac{d\hat{S}(t)}{dt} = -\hat{\beta}\, \hat{S}(t)\, \hat{I}(t),\[0.3cm] \dfrac{d\hat{E}(t)}{dt} = \hat{\beta}\, \hat{S}(t)\, \hat{I}(t) - \hat{\gamma}\, \hat{E}(t),\[0.3cm] \dfrac{d\hat{I}(t)}{dt} = \hat{\gamma}\, \hat{E}(t) - \hat{\mu}\, \hat{I}(t),\[0.3cm] \dfrac{d\hat{R}(t)}{dt} = \hat{\mu}\, \hat{I}(t), \end{cases}$5 of total baseline cases but its elimination reduces total cases across all regions by about $\begin{cases} \dfrac{d\hat{S}(t)}{dt} = -\hat{\beta}\, \hat{S}(t)\, \hat{I}(t),\[0.3cm] \dfrac{d\hat{E}(t)}{dt} = \hat{\beta}\, \hat{S}(t)\, \hat{I}(t) - \hat{\gamma}\, \hat{E}(t),\[0.3cm] \dfrac{d\hat{I}(t)}{dt} = \hat{\gamma}\, \hat{E}(t) - \hat{\mu}\, \hat{I}(t),\[0.3cm] \dfrac{d\hat{R}(t)}{dt} = \hat{\mu}\, \hat{I}(t), \end{cases}$6 (D'Silva et al., 2015). Be-CoDiS generalizes the same logic to 176 countries by coupling within-country SEIHRDB dynamics through travel rates $\begin{cases} \dfrac{d\hat{S}(t)}{dt} = -\hat{\beta}\, \hat{S}(t)\, \hat{I}(t),\[0.3cm] \dfrac{d\hat{E}(t)}{dt} = \hat{\beta}\, \hat{S}(t)\, \hat{I}(t) - \hat{\gamma}\, \hat{E}(t),\[0.3cm] \dfrac{d\hat{I}(t)}{dt} = \hat{\gamma}\, \hat{E}(t) - \hat{\mu}\, \hat{I}(t),\[0.3cm] \dfrac{d\hat{R}(t)}{dt} = \hat{\mu}\, \hat{I}(t), \end{cases}$7, allowing estimation of country-specific export and introduction risks, hospital burden, and a global $\begin{cases} \dfrac{d\hat{S}(t)}{dt} = -\hat{\beta}\, \hat{S}(t)\, \hat{I}(t),\[0.3cm] \dfrac{d\hat{E}(t)}{dt} = \hat{\beta}\, \hat{S}(t)\, \hat{I}(t) - \hat{\gamma}\, \hat{E}(t),\[0.3cm] \dfrac{d\hat{I}(t)}{dt} = \hat{\gamma}\, \hat{E}(t) - \hat{\mu}\, \hat{I}(t),\[0.3cm] \dfrac{d\hat{R}(t)}{dt} = \hat{\mu}\, \hat{I}(t), \end{cases}$8 for the 2014–2015 epidemic (Ivorra et al., 2014).

5. Collider-physics usage: the Éboli dimension-8 EFT basis

In collider phenomenology, the Éboli model is a SMEFT truncation designed for anomalous quartic gauge couplings. The ATLAS combination writes

with dimensionless Wilson coefficients $\hat{E}$ 0 and heavy scale $\hat{E}$ 1, and expands the cross section as

$\hat{E}$ 2

The basis is restricted to C-even, P-even, $\hat{E}$ 3-invariant dimension-8 operators that specifically produce anomalous quartic gauge couplings (Collaboration, 19 Mar 2026).

The paper groups the 21 operators into scalar-type operators containing only derivatives of the scalar Higgs field, $\hat{E}$ 4; tensor-type operators containing only electroweak boson field strengths, $\hat{E}$ 5; and mixed-type operators $\hat{E}$ 6 (Collaboration, 19 Mar 2026). It then reduces the working set by dropping $\hat{E}$ 7 as redundant, excluding $\hat{E}$ 8 and $\hat{E}$ 9 because the MG5_aMC implementation was not available in all analysis publications, and imposing $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$00, leaving 17 independent Wilson coefficients (Collaboration, 19 Mar 2026).

A distinctive phenomenological feature of the Éboli basis is that the SM-interference term is highly suppressed because of helicity structure, so sensitivity is driven mainly by quadratic $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$01 terms (Collaboration, 19 Mar 2026). Scalar and mixed operators are most strongly constrained by semileptonic VBS channels, whereas tensor operators are dominated by photon-rich high-energy channels, especially $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$02 (Collaboration, 19 Mar 2026). The paper also notes a block structure in cross-terms, with strong suppression between scalar, mixed, and tensor families and approximate orthogonality inside parts of the mixed sector.

6. Experimental constraints, unitarity, and positivity

The ATLAS combination uses seven VBS analyses and one triboson analysis at $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$03 TeV with $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$04–$\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$05, including semileptonic $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$06, $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$07, same-sign $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$08, $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$09, $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$10, $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$11, $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$12, and $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$13 channels (Collaboration, 19 Mar 2026). Confidence intervals are extracted with simultaneous profiled likelihood fits in one or more Wilson coefficients, with nuisance parameters for experimental and theoretical systematics and with asymptotic Wilks-theorem inference cross-checked by pseudo-experiments (Collaboration, 19 Mar 2026).

Because dimension-8 amplitudes grow with energy, the paper overlays perturbative partial-wave unitarity and positivity constraints. Unitarity is enforced with a clipping prescription: EFT contributions are set to zero above a chosen partonic cutoff $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$14, defined as $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$15 for VBS and $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$16 for triboson production (Collaboration, 19 Mar 2026). The reported “unitarized” interval is the intersection between the $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$17 CL interval as a function of $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$18 and the theoretical unitarity bound. No unitarized confidence interval is found for $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$19, because the experimental interval is always weaker than the unitarity constraint (Collaboration, 19 Mar 2026).

Observed unitarized $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$20 CL intervals include $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$21, $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$22, $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$23, $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$24, $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$25, and $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$26, with corresponding unitarization cutoffs typically in the $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$27–$\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$28 range (Collaboration, 19 Mar 2026). In the simultaneous 17-parameter profiled fit without clipping, representative observed $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$29 CL intervals are $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$30, $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$31, and $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$32 (Collaboration, 19 Mar 2026). The combined results improve previous published confidence intervals by $\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$33–$\begin{cases} \dfrac{dS(t)}{dt} = -\beta S(t) I(t),\[0.2cm] \dfrac{dI(t)}{dt} = \beta S(t) I(t) - \mu I(t),\[0.2cm] \dfrac{dR(t)}{dt} = \mu I(t), \end{cases}$34, depending on the coefficient (Collaboration, 19 Mar 2026).

Across both domains, the term therefore designates a compact but not unique modeling tradition. In epidemiology, it denotes tractable Ebola transmission systems whose realism increases by adding incubation, hospitalization, funeral transmission, spatial coupling, or control. In collider EFT, it denotes a specific dimension-8 operator basis for anomalous quartic gauge couplings whose interpretation now depends explicitly on high-energy validity criteria such as unitarity and positivity (Rachah et al., 2016, Burghardt et al., 2016, Collaboration, 19 Mar 2026).