Two-stage calibration, scenario selection and posteriors

The model is calibrated by Approximate Bayesian Computation (ABC) in two stages (Section 6). Stage 1 selects trajectories consistent with the early cross-border onsets in Uganda and with early activity in Beni. Stage 2 fits the reported DRC counts. Because cases detected before and around the May alert were partly added retrospectively, the cumulative level up to the first August report is not used as a target; the model is fitted to the increase in reported cases since 31 July at seven situation-report dates up to 30 September. Ascertainment, the fraction of symptomatic cases that is reported, is inferred jointly with the transmission parameters under the assumption that it tracks the isolation rate. Cases enter the reported counts after a delay from symptom onset to report, assumed to follow a gamma distribution with a mean of 5 days (Section 6).

Six isolation scenarios (20 % to 75 %) were compared on the same data, using Bayes factors: the ratio of the probability of the data under each scenario to that under the best-supported one. The 60 % scenario is the best supported. Relative to it, the Bayes factor is 0.55 for 50 % and 0.38 for 75 % isolation, so both remain plausible and are retained as lower and upper brackets. The 40 % scenario is clearly disfavoured (Bayes factor 0.11), and the 20 % and 30 % scenarios are effectively excluded (below 0.01). The ranking is unchanged for ABC tolerances between 3 % and 10 %.

The calibration also provides a posterior distribution for the ascertainment rate (Methods). Over the entire epidemic up to 10 October, 69 % [53 – 88] of all symptomatic cases have been reported under 60 % isolation (median and 90 % credible interval), against 65 % [45 – 84] under 50 % and 81 % [68 – 94] under 75 % isolation.

Posterior R₀ and doubling time in the early phase, before the interventions

R₀ and the doubling time describe the early phase of the outbreak, in the regime without interventions. R₀ is the basic reproduction number in a fully susceptible population with no isolation, and T_d is measured on the simulated epidemic before the isolation ramp starts (up to 20 May 2026). Neither describes current transmission, which is measured by the effective reproduction number R_t (Section 4). In the 60 % scenario, the posterior basic reproduction number is R₀ = 1.87 [1.69 – 2.09] and the empirical doubling time is T_d = 13.2 [9.8 – 17.6] days (Figure 1).

Although both quantities refer to the pre-intervention regime, the posterior of R₀ depends on the isolation scenario: it increases from 1.71 [1.57 – 1.87] at 50 % to 2.13 [1.88 – 2.36] at 75 %. The calibration reproduces the later reported counts with each scenario's isolation in place, and stronger isolation removes more transmission, so a higher intrinsic transmissibility is needed to match the same observed growth. The doubling time is nearly the same in all scenarios (13.6 days at 50 % and 13.5 days at 75 %), since it is measured directly on the early epidemic, before isolation started.

Figure 1 — Posterior R₀ and empirical doubling time in the early phase, before the interventions · 60 % isolation scenario

Posterior densities in the 60 % isolation scenario; both quantities characterise transmission before the interventions. Dark band: 50 % credible interval; light band: 90 % credible interval; dashed line: median; ticks: accepted trajectories. T_d is measured per trajectory by log-linear fit to cumulative DRC symptomatic onsets from the first day with at least 10 cumulative cases to 20 May 2026, before the isolation ramp starts.

Model consistency and out-of-sample check

All three retained scenarios reproduce the fitted counts and the 10 October count, which was held out of the fit (Figure 2). For the 60 % scenario the held-out reported cumulative count and the mean number of reported cases per day between the 30 September and 10 October situation reports both fall near the centre of the predictive distributions, at the 40th percentile and the 46th percentile (Figure 3). Under 50 % isolation they fall at the 20th percentile and 23th percentile, and under 75 % at the 68th percentile and 74th percentile. The daily value is an average over the 10-day period: 678 new cases were reported between the two situation reports (8,300 to 8,978), or 67.8 per day. It is computed in the same way from the model and is not independent of the cumulative count.

Figure 2 — Fit to the reported counts and out-of-sample check · DRC · three isolation scenarios

Reported cumulative cases under the inferred ascertainment and the assumed reporting delay. Square: 31 July anchor; dots: situation-report counts used in the fit; open diamond: 10 October count, not used in the fit. Bands: 50 % and 90 % prediction intervals; line: median.

Figure 3 — Posterior predictive distributions on 10 October 2026 vs observed values · 60 % isolation

Reported cumulative cases on 10 October (left) and mean reported new cases per day between the 30 September and 10 October situation reports (right), i.e. the difference between the two cumulative counts divided by 10 days, in the data and in the model. Dark band: 50 % prediction interval; light band: 90 %; dashed line: model median; solid black line: observed value.

Effective reproduction number · 1 June – 30 November 2026

The effective reproduction number R_t falls from about 1.6–1.8 in early June to about 1 in August, as the isolation ramp takes effect (Figure 4). Since then it has remained close to the epidemic threshold: in October the median is 1.00 under 50 %, 0.95 under 60 % and 0.86 under 75 % isolation. If the isolation levels are maintained, R_t in November is 1.00, 0.94 and 0.84 respectively. The 90 % intervals include 1 in all three scenarios.

Figure 4 — Effective reproduction number R_t in DRC · 1 June – 30 November 2026

Cori estimator on simulated true daily onsets, 7-day sliding window, serial interval Gamma with mean 15.3 days and standard deviation 9.3 days. Median (line), 50 % and 90 % intervals (bands); dashed line: R = 1; dotted line: last data point (10 October).

Isolation	August	October	November
50 %	1.00 [0.91 – 1.09]	1.00 [0.88 – 1.11]	1.00 [0.88 – 1.10]
60 %	0.98 [0.89 – 1.08]	0.95 [0.82 – 1.09]	0.94 [0.80 – 1.08]
75 %	0.99 [0.91 – 1.10]	0.86 [0.69 – 1.08]	0.84 [0.63 – 1.05]
Median of Rt over each month per sample; median and 90 % interval across samples.

Projections

Short-term projections · 31 October 2026

Three weeks after the last situation report, the 60 % scenario projects 15,225 [12,151 – 19,694] true symptomatic cases in DRC by 31 October, of which 10,465 [9,433 – 11,835] are expected to be reported, and about 83 [47 – 150] new symptomatic cases per day (Table 1). The scenarios differ more in the true burden than in the reported counts: higher isolation goes with higher ascertainment, so the same reported counts correspond to fewer true cases (16,493 under 50 % and 12,941 under 75 % isolation). The median reported cumulative counts on 31 October differ by only about 1,100 cases between the 50 % and 75 % scenarios.

Long-term projections · 30 November 2026

The number of newly reported cases per day, averaged between consecutive situation reports, ranged from 68 to 91 in August and from 59 to 86 in September (Figure 5). Single intervals move with reporting batches, but over whole periods the trend is clear: about 80 reported cases per day in August, 71 in September and 68 in the first ten days of October, a slowdown of about 16 %. Cumulative cases are still rising, but fewer new cases are reported each day than in August. This is consistent with an effective reproduction number that has been close to, and possibly just below, 1 since August (Section 4).

The data capture the slowdown itself, not yet its outcome. The three scenarios agree on the recent past and differ in direction: under 50 % isolation the number of reported cases per day stays roughly flat (about 80 on 31 October and 80 on 30 November), under 60 % it declines slowly (64 and 56) and under 75 % it declines faster (47 and 34). The central 50 % prediction intervals of the 50 % and 75 % scenarios no longer overlap from 18 September, but the 60 % scenario overlaps with both until 30 November and the 90 % intervals of all three scenarios overlap widely. Situation reports over the coming weeks are therefore needed to tell whether the epidemic is levelling off or starting to decline.

Under 60 % isolation, reported cases are projected to reach 12,259 [10,446 – 15,059] by 30 November, corresponding to about 17,741 true symptomatic cases. The 50 % and 75 % scenarios bracket this projection at 13,382 and 11,071 reported cases.

Figure 5 — Reported new cases per day in DRC · observed between situation reports and projected to 30 November 2026

Black bars: observed mean number of newly reported cases per day between consecutive situation reports, i.e. the difference between consecutive cumulative counts divided by the number of days (values labelled); the dashed bar (30 September – 10 October) was not used in the fit. Lines: model median of reported new cases per day (7-day mean) for each isolation scenario. Shaded bands: 50 % and 90 % prediction intervals for the 60 % scenario.

Metric, 30 Nov	50 %	60 %	75 %
Reported cases · comparable with situation reports
Reported cumulative	13,382 [11,132 – 15,950]	12,259 [10,446 – 15,059]	11,071 [9,528 – 13,442]
Reported new / day	80 [40 – 134]	56 [27 – 117]	34 [12 – 84]
True cases · all symptomatic cases, including unreported · not comparable with situation reports
True cumulative	19,728 [14,711 – 29,049]	17,741 [13,821 – 23,352]	14,399 [11,174 – 18,147]
True new / day	108 [48 – 200]	73 [33 – 160]	41 [12 – 99]
Median and 90 % prediction interval. Daily values are 7-day means. Reported cases include the assumed reporting delay and the inferred ascertainment; true cases count every symptomatic case in the model, whether reported or not.

Probability of a large outbreak by 30 November 2026

Reported cases are very likely to exceed 10,000 by 30 November under 50 % and 60 % isolation (> 99 % and 99 %) and likely under 75 % (82 %). Exceeding 20,000 reported cases is very unlikely in all three scenarios (< 1 %). In terms of true symptomatic cases, the probability of exceeding 20,000 is 48 % (50 %), 27 % (60 %) and 1 % (75 %); exceeding 30,000 is very unlikely (3 % at most).

Figure 6 — Probability of a large reported outbreak in DRC by 30 November 2026

Probability that reported cumulative cases exceed 10,000 (left) and 20,000 (right) by 30 November 2026, by isolation scenario.

Isolation	P(≥ 10,000)	P(≥ 20,000)
50 %	> 99 %	< 1 %
60 %	99 %	< 1 %
75 %	82 %	< 1 %

Figure 6b — Probability of a large outbreak in true symptomatic cases by 30 November 2026

Probability that true cumulative symptomatic cases in DRC exceed 20,000 (left) and 30,000 (right) by 30 November 2026.

Isolation	P(≥ 20,000)	P(≥ 30,000)
50 %	48 %	3 %
60 %	27 %	< 1 %
75 %	1 %	< 1 %

Continued transmission by 30 November 2026

At least 10 new symptomatic cases per day remain almost certain at the end of November in all three scenarios (at least 96 %). The probability of 50 or more new cases per day is 94 % under 50 %, 79 % under 60 % and 36 % under 75 % isolation. Under none of the scenarios is transmission expected to end by 30 November.

Figure 7 — Probability of continued transmission in DRC by 30 November 2026

Probability that true new symptomatic onsets in DRC, averaged over 24–30 November 2026, exceed 10 (left) and 50 (right) per day.

Isolation	P(≥ 10 / day)	P(≥ 50 / day)
50 %	> 99 %	94 %
60 %	> 99 %	79 %
75 %	96 %	36 %

Methods

Model framework

The framework is GLEAM (Global Epidemic and Mobility Model) [5], an Africa-wide metapopulation network coupled by daily commuting matrices and origin-destination passenger flows from IATA Passenger Intelligence Services and OAG. Latent individuals (E₁, E₂) are fully mobile. Symptomatic individuals: 50 % of community and community-hospital-bound cases remain mobile (health-care-seeking travel and continued commuting), the other 50 % stay in their home basin; isolated (I_iso), hospitalised (H, H_ETC) and ETC compartments do not travel. Note: from OAG Aviation Analytics. The within-basin compartmental dynamics are simulated as a discrete-time multinomial chain-binomial process. At each time step the number of individuals exiting a compartment is drawn from a binomial with exit probability 1 − exp(−Σᵢ λᵢ · Δt), and exits are partitioned across the available destination compartments by a multinomial whose probabilities are proportional to the per-route hazards. We do not assume any mobility reductions between subpopulations: no behavioral reduction, no border closure is explicitly modeled. Transmission is overdispersed: the number of secondary cases generated by an infectious individual is not assumed to be Poisson distributed. Individual transmissibility follows a negative-binomial offspring distribution with dispersion k = 0.1, so that a small fraction of cases generates most secondary infections (see Compartmental structure).

Compartmental structure

The compartmental structure follows a Legrand-like SEIHFR scheme [7,8]. To model the impact of isolation and safe burial protocols, it incorporates three potential outcomes for an infectious individual (Figure 8):

1. Community Branch: the individual does not get admitted to any healthcare facility. They are able to infect people in the community in their infectious stage and, if death occurs, through unsafe burial practices.
2. HCF-only Branch: the infected individual is infectious for an average time of 5 days until they are admitted to a HCF where they can generate new infections through nosocomial transmission and, if death occurs, through unsafe burial practices.
3. Isolation Branch: individuals are infectious for an average time of 2 days before they are moved to a HCF for an average time of 3 days and have a transmissibility that is 10 % of individuals in a HCF in the HCF-only branch. They are then moved to an ETC, where they no longer contribute to ongoing transmission.

The funeral compartment F is fed only by community deaths and regular-HCF deaths (deaths in ETC receive safe and dignified burial and bypass F). Transmission rates by compartment: β_I in all three community-infectious compartments (I_com, I_comH, I_iso), β_H in regular-track H, β_H,iso = 0.1 · β_H in the HCF → ETC transit compartment H_ETC, zero in ETC, and β_F in F.

Individual transmissibility is overdispersed: each community-infectious compartment (I_com, I_comH) and the funeral compartment F is split into four classes with different transmissibility, a discrete approximation of a negative-binomial offspring distribution with dispersion k = 0.1. A small share of cases therefore generates most secondary infections. Isolated cases are not split.

Natural-history parameters

Compartmental dwell times and severity values are based on literature. The Legrand-type SEIHFR formulation [7,8] supplies the framework, Wamala et al. [9] are the source for the original 2007–2008 Uganda BVD outbreak data on which some of the BVD-specific natural-history estimates rest. Isolation-pathway case-finding timings (T_iso and T_he) follow the 2018 North Kivu RVEAP response [6].

Figure 8 — Compartmental structure of the model

Twelve compartments, three potential outcomes at E₂ exit. Latent stages E₁ → E₂ feed three parallel infectious-community sub-compartments: I_com (community-only fate, dwell T_I), I_comH (regular HCF fate, dwell T_sh = 5 d) and I_iso (isolation fate, dwell T_iso = 2 d). Routine cases progress to H with full nosocomial transmission rate β_H; isolated cases progress through H_ETC (residual rate 0.1 · β_H) to ETC (no transmission, safe burial). The funeral compartment F (transmission rate β_F) is fed only by community and regular-HCF deaths. In the current model I_com, I_comH and F are further split into four transmissibility classes (not shown).

Seeding

The epidemic originates in Ituri, DRC, with 5 infectious cases on the inferred start date. Every other basin, including all of Uganda, begins fully susceptible and is reached only through mobility coupling.

Inference: two-stage Approximate Bayesian Computation

Stage 1 samples R₀ ~ U(1.2, 4.0) and the outbreak start date ~ U(1 February, 15 March 2026) and keeps trajectories consistent with the early epidemiological evidence. Three calibration chains share these priors and differ in the evidence imposed: one conditioned on 2–4 early cross-border onsets in Uganda (23,638 trajectories), one conditioned on 2–80 early cumulative onsets in Beni (32,541) and one conditioned on both (7,235). The three chains are pooled without reweighting (63,414 trajectories).

Stage 2 fits the reported DRC cumulative counts. The projected reported count is Reported(t) = 3,674 + c × [I_iso(t) − I_iso(31 Jul)], where I_iso(t) is the simulated cumulative number of isolated symptomatic onsets that have been reported by day t, given the reporting delay (below). The constant c is sampled 200 times per trajectory from its prior (below). The distance is the mean absolute percentage error over the increments since 31 July at 11, 20 and 25 August and 1, 9, 21 and 30 September 2026 (+882, +1,701, +2,039, +2,576, +3,268, +4,099, +4,626 cases). Samples with distance ≤ 5 % are accepted, and trajectories must have at least 3,674 true cumulative cases by 31 July. The 10 October count (8,978) is held out for validation. Bayes factors between isolation scenarios are the ratios of their Stage-2 acceptance rates at this common tolerance.

Reporting delay

New cases are not reported on the day of symptom onset. The delay from symptom onset to report is assumed to follow a gamma distribution with a mean of 5 days and a standard deviation of 3.5 days, a typical delay from symptom onset to admission to a hospital or ETC and consistent with the onset-to-HCF time of the routine care pathway in the model (5 days). The distribution is discretised to whole days and held constant over time. The simulated daily symptomatic onsets are convolved with this distribution to obtain the expected number of cases reported on each day; the delayed series is used for the fit, the reported-count projections and the ascertainment rate. Standard deviations of 2.5 and 5 days give the same results.

Ascertainment

Reporting of new cases is modelled as proportional to isolation, α(t) = c × Q(t), where Q(t) is the isolation rate of each trajectory. Every isolated case is assumed to be reported (c ≥ 1) and ascertainment cannot exceed 1 (c ≤ 1/Q_cap). Because Q(t) rises with the isolation ramp, ascertainment is low early in the epidemic and increases as isolation scales up. The overall ascertainment rate over the entire epidemic is obtained by dividing the cumulative reported count on 10 October (8,978) by the simulated cumulative number of symptomatic cases that have had time to be reported by that date, given the reporting delay, in each accepted sample: 65 % [45 – 84] under 50 %, 69 % [53 – 88] under 60 % and 81 % [68 – 94] under 75 % isolation (median and 90 % credible interval). Because the epidemic grew, the early, weakly detected period accounts for a small share of all cases (about 5 % occurred before 20 May under 60 % isolation), so the overall rate is dominated by the more recent, better-detected cases. The early epidemic size is only loosely constrained, which is why the intervals are wide.

Isolation mechanism

Each scenario sets a target isolation level Q_cap (50 %, 60 % or 75 %). Each DRC basin starts its own ramp of 1 percentage point per day toward the target when its cumulative onsets first reach 80; Bunia keeps a fixed start on 20 May 2026, and Uganda is held at 80 % throughout. The isolation level Q determines the probability with which each new symptomatic case is routed to the isolation pathway (I_iso → H_ETC → ETC). Isolated cases are identified faster than routine cases (onset to HCF 2 days instead of 5) and progress to the ETC compartment, where transmission stops and deaths receive safe and dignified burial. A residual nosocomial channel (10 % of the baseline HCF rate) is retained during the 3-day HCF → ETC transit.

Doubling time and reproduction number

The doubling time T_d is measured on each accepted trajectory by ordinary least squares on log C(t), where C(t) is the cumulative number of DRC symptomatic onsets plus the 5 seed cases, from the first day C(t) ≥ 10 to 20 May 2026 (at least 14 days), with T_d = ln 2 / slope. R_t is the Cori estimator on simulated true daily onsets with a 7-day sliding window and a gamma serial interval (mean 15.3 days, standard deviation 9.3 days) discretised over 1–60 days. R₀ and T_d therefore characterise the early epidemic in the absence of interventions, whereas R_t describes transmission over time with the isolation of each scenario in place.

Limitations and Assumptions

Ascertainment model.

Reporting of new cases is assumed proportional to isolation with a constant factor per trajectory. The delay from symptom onset to report is an assumption (gamma, mean 5 days) and is held constant; changes in the delay over time and batch updates of the reported counts are not modelled. The level of the epidemic before 31 July is only indirectly constrained, so the overall ascertainment and the true number of cases carry wide intervals.

Patients in isolation.

The model occupancy of the hospital and isolation compartments is not compared with the reported number of patients in isolation in this report. The comparison is deferred until the definition of the reported figure and the length of stay in treatment centres have been checked.

Calibration.

The tolerance of the ABC step (5 %) was chosen to retain good fits only; the scenario ranking is the same for tolerances between 3 % and 10 %. Fewer simulations are accepted under 75 % isolation, so its estimates are less precise.

Scope.

All figures and statistics are aggregated to DRC (17 DRC basins plus the Goma catchment). Cross-border spillover to Uganda, Rwanda, South Sudan and other countries is not reported here (see Report #8 for international dissemination).

Mobility, seasonality and interventions.

Mobility is held static, with no behavioural reduction, no border closure and no seasonality in transmissibility. Isolation and case-finding timings are applied homogeneously within each basin; real-world coverage varies by location and over time. No vaccination is modelled.

References

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