Iran, Hormuz, and War as a Network

A tanker hit at Hormuz, a sanction against an Iranian company, and a blocked nuclear inspection change the same problem through different channels. Damage to the ship may make its passage harder to insure; the sanction may prevent the purchase of its cargo; denied access for inspectors may weaken the political agreement on which reopening depends. Those facts are geographically and institutionally distant, but their consequences can meet in the availability of energy.

The war that began on February 28 involves Iran, the United States, and Israel, and runs through a network of bases, ports, facilities, routes, and mediators. Hormuz concentrates energy transport; Qatar and Oman combine civilian, logistical, and diplomatic functions; Lebanon and Bab el-Mandeb introduce constraints that a ceasefire limited to Iran can leave unresolved. One side’s military superiority describes only part of this network.

The problem becomes clear in the September 25 proposal: Tehran offers a seven-day sequence for reopening Hormuz and resuming nuclear talks, conditional on American concessions over the naval blockade, sanctions, and the ceasefire, including Lebanon. The timetable would start after American acceptance. On September 30, Iran reports receiving a response; its terms remain unknown. A proposal with a short deadline can therefore leave the constraints preventing ships from passing unchanged for a long time.

From a narrative graph to a falsifiable model

The map of actors remains useful for orientation, but it cannot do three jobs at once: describe geopolitics, identify causes, and produce a risk number. States, institutions, prices, and infrastructure are not homogeneous variables; summing their activations on a 0–100 scale turns the analyst’s choices into a precision the data do not have.

The model therefore starts with a stricter chain. Events change operational risk; that risk conditions Hormuz’s effective capacity; capacity determines missing flows and diversions; only then come prices, the energy bill, and macroeconomic dynamics. An arrow is allowed only if it can be associated with data, an estimable equation, and a forecast error.

Causal chain From an event to its economic effect

The model separates observations, latent states, physical constraints, and economic consequences. Each transition needs its own data and estimate.

01 Observed
Verified events
Source provenance, attacks, blockades, mines, agreements, and measurable event features.
02 Latent
Operational risk
Escalation probabilities and transitions among normal, coercive, selective, or dysfunctional transit.
03 Estimated
Hormuz capacity
Executable traffic relative to a normal counterfactual, estimated separately for oil and LNG.
04 Physical
Missing flows
Unserved demand, bypass capacity, activation delays, and rerouting costs.
05 Market
Energy prices
Revision in expected scarcity; Brent, TTF, and insurance premia remain downstream variables.
06 Economy
Impact on Italy
Import bill, sectoral pass-through, inflation, and output with uncertainty intervals.

Define the prediction target first

For each fuel $f\in\{\mathrm{oil},\mathrm{LNG}\}$ , $Q_{f,t}$ is the flow observed on day $t$ . The term $Q^0_{f,t}$ is the traffic that a model trained on ordinary periods would have predicted in the absence of the crisis. It cannot be a recent moving average: once the corridor is disrupted, that average incorporates the shock it should be measuring.

The ratio of the two flows defines effective operational capacity, used here as an indicator of feasible traffic relative to the ordinary reference. It does not describe the strait’s navigable width; it measures how much traffic remains feasible after accounting for crews, war-risk cover, waiting times, escorts, and restrictions. The ratio can exceed one and also responds to demand: separating capacity from utilization requires observations on waiting times and rejected cargoes, beyond the number of passages. The event $A_f(h,\delta,d;t)$ indicates that, within a horizon of $h$ days, capacity falls below $1-\delta$ for at least $d$ consecutive days. The main outputs thus become an explicit probability and a loss in physical units.

\begin{aligned} Q^0_{f,t} &= \mathbb E\!\left[Q_{f,t}\mid\text{ordinary conditions}\right],\\ C_{f,t} &= \frac{Q_{f,t}}{Q^0_{f,t}},\\ p_f(h,\delta,d;t) &= \Pr\!\left[A_f(h,\delta,d;t)\mid\mathcal F_t\right],\\ L^f_{h,t} &= \mathbb E_t\!\left[ \sum_{\tau=1}^{h}Q^0_{f,t+\tau} \left[1-C_{f,t+\tau}\right]_+ \right]. \end{aligned}

Here $[x]_+=\max(x,0)$ and $\mathcal F_t$ contains only information available by $t$ . Thresholds must remain visible: a predictive publication will need to show several combinations of horizon, decline, and duration. For oil, $L^f_{h,t}$ is expressed in barrels; for LNG, in a consistent physical measure, without pretending that alternative oil pipelines can replace an LNG carrier.

From sources to the operational state

A war report does not automatically correspond to a true event. The database must retain the original source, distinguish republications, and assign each episode a confirmation probability $r_i$ . Satellite images, maritime authorities, and shipowners can corroborate one another; ten articles derived from the same statement remain a single information chain. The model then receives observable features — distance from the route, target, tonnage, duration, damage, mines, ports, or bases involved — weighted by the event’s credibility, rather than an arbitrary score.

Verified events feed a parsimonious daily process, such as a negative-binomial process, split into a few classes: threats to traffic, coastal or energy attacks, attacks on Gulf bases and logistical nodes, coercive measures, and verified signs of de-escalation. A marked Hawkes process would make sense only with many precisely dated episodes; for a single crisis, it would produce more parameters than information.

Capacity is governed by a latent state $S_t\in\{0,1,2,3\}$ : normal, open but coercive, selective interdiction, and generalized dysfunction. Transition probabilities depend on events and the previous regime; a ship being hit does not add points, but can increase the probability of moving from one state to another. The continuous value $C_{f,t}$ is inferred jointly from transit counts, AIS tonnage, waiting times, diversions, and cancellations. Satellite data from IMF PortWatch provide a useful sensor, not an infallible measure: reception, reported draught, coverage, and revisions must remain within the model’s uncertainty.

The relevant network is physical

Downstream of the operational state, network theory acquires a narrower meaning. Oil and LNG require separate graphs with production areas, terminals, pipelines, routes, ports, storage, and final markets. Each edge has a nominal capacity $\bar q_{e,f,t}$ , an operational fraction $R_{e,f,t}$ , and a unit cost $c_{e,f,t}$ ; on the Hormuz edge, the constraint must be converted into the same units as the flow. If $Q^0_{f,t}$ is below nominal capacity, a ratio $C_{f,t}>1$ can be consistent with a facility still below full utilization. The linking assumption is $R_{\mathrm H,f,t}=\min\!\left(1,C_{f,t}Q^0_{f,t}/\bar q_{\mathrm H,f,t}\right)$ ; it must be checked against operational data, because observed traffic alone does not identify available capacity.

The model requires solving a minimum-cost flow problem, explicitly retaining unmet demand $u_{v,f,t}$ . A bypass is therefore not counted merely because it exists on a map: it must have spare capacity, a compatible origin, available terminals, and enough time to become operational.

\begin{aligned} J^\star_{f,t} &= \min_{\{q_e,s_v,u_v\}} \left[ \sum_{e\in E_f}c_{e,f,t}q_{e,f,t} + \sum_{v\in V_f}V_{v,f}u_{v,f,t} \right],\\ s_{v,f,t}+\sum_{e\in\delta^-(v)}q_{e,f,t} &= d_{v,f,t}-u_{v,f,t} +\sum_{e\in\delta^+(v)}q_{e,f,t},\\ 0\le q_{e,f,t} &\le \bar q_{e,f,t}R_{e,f,t},\\ 0\le s_{v,f,t} &\le \bar s_{v,f,t}, \qquad 0\le u_{v,f,t}\le d_{v,f,t},\\ U_{f,t}&=\sum_v u_{v,f,t}. \end{aligned}

$s_{v,f,t}$ is the supply used, bounded by availability $\bar s_{v,f,t}$ ; $d_{v,f,t}$ is demand and $V_{v,f}$ is the penalty for one unmet unit. $U_{f,t}$ is the physical loss the next step must explain. If $k_{\mathrm H,f,t}=\bar q_{\mathrm H,f,t}R_{\mathrm H,f,t}$ , the marginal value of additional capacity is $-\partial J^\star/\partial k_{\mathrm H,f,t}$ : increasing the capacity constraint can reduce the minimum cost. The minimum cut has its technical meaning here: the sum of operational capacities crossing a partition of the physical network, not a metaphor for the number of domains involved. The EIA estimate of around 20 million barrels per day transiting in 2024 and, in its June 2025 assessment, 2.6 million of spare capacity in the main alternative paths provides a historical reference. Spare capacity during the 2026 war requires a new measurement.

Alternative capacity changes over time. A pipeline project enters the network on the date it becomes usable, with its own terminals, supply, and limits. Pipelines can divert some crude oil; they do not replace LNG transport. A node on the map is not a reserve of immediately available capacity.

Prices remain downstream

The market responds mainly to revisions in future scarcity. Let $M^H_{f,t}$ be the expected cumulative deficit over the next $H$ days: $\xi^H_{f,t}$ measures the revision of that deficit between two information sets, keeping the future days being compared fixed. Subtracting two rolling windows with different endpoints would mix new information with the passage of time. An attack that does not change the distribution of flows can produce much news and little price news; a sudden shift towards selective interdiction can do the opposite.

\begin{aligned} M^H_{f,t} &= \mathbb E_t\!\left[\sum_{\tau=1}^{H}U_{f,t+\tau}\right],\\ \xi^H_{f,t} &= \mathbb E\!\left[\sum_{\tau=1}^{H}U_{f,t+\tau}\mid\mathcal F_t\right]\\ &\quad - \mathbb E\!\left[\sum_{\tau=1}^{H}U_{f,t+\tau}\mid\mathcal F_{t-1}\right],\\ \log P_{f,t+h}-\log P_{f,t-1} &= \alpha_h+\beta_h\xi^H_{f,t} +\boldsymbol{\gamma}_h^\top\mathbf Z_t +\varepsilon_{t,h}. \end{aligned}

Jordà’s local projections allow responses to be estimated at multiple horizons without imposing the full dynamics of a VAR. $\mathbf Z_t$ must separate global demand, OPEC+ production, inventories, the dollar, and financial risk. Bank of Italy research shows why identifying supply, demand, and expectations shocks is crucial. Brent, TTF, volatility, and insurance premia therefore remain variables to be explained or auxiliary sensors: they cannot enter upstream into an index then used to predict those same prices.

Transmission to the Italian economy

Italy can suffer the shock even if no ship bound for an Italian port is stopped: a change in the marginal price of energy is enough. The first channel is the import bill. If $e_t=\mathrm{USD}/\mathrm{EUR}$ , a weaker euro amplifies the price in euros. $V_{f,t}^{\mathrm{IT}}$ is the initial value of imports in euros, not their physical volume. The approximation initially holds imported quantities fixed; freight, insurance, and diversions enter separately in $\Delta F_t^{\mathrm{IT}}$ .

\begin{aligned} \Delta B_t^{\mathrm{IT}} &\simeq \sum_f V_{f,t}^{\mathrm{IT}} \left( \Delta\log P^{\$}_{f,t}-\Delta\log e_t \right) +\Delta F_t^{\mathrm{IT}},\\ \Delta\mathbf p &= \left(I-RA^\top\right)^{-1} RB^\top\Delta\mathbf p_E. \end{aligned}

The second line propagates energy prices through the input-output matrix: $A$ contains intersectoral inputs, $B$ exposure to imported energy, and $R$ is the diagonal matrix of price pass-through shares, between zero and one. The inverse requires $\rho(RA^\top)<1$ . Inflation, production, consumption, and wages then need a separate dynamic model, estimated with local projections and specifications that depend on the state of the economy. This is consequential: Eurostat attributes 36% of Italy’s available energy in 2024 to gas, while the Bank of Italy finds effects of energy shocks that vary with the size of the shock and the inflation regime.

Uncertainty is a result

Uncertain events, unobserved states, and persistent regimes make Bayesian estimation natural. Each draw from the posterior distribution simulates events, state, capacity, the physical network, prices, and the Italian impact; the output is a probability distribution, not a privileged trajectory. Priors favouring small parameters should constrain edges the data do not support, while joint estimation across several crises avoids learning an entire dynamic process from a few months.

The model can produce usable forecasts only if it outperforms simple benchmarks on data excluded from estimation. Interruption probabilities must be evaluated with Brier and log scores; transits, flows, and prices with MAE, RMSE, and CRPS. The main test leaves one crisis out of estimation in turn, alongside placebo tests, removal of individual model components, sensitivity to priors, and checks for inadvertent use of future information. If the full system does not beat a seasonal transit forecast or a logistic regression with few parameters, the correct conclusion is to reduce it, not defend its complexity.

An open route can remain unusable

Passage permitted on paper can be impractical for a company: an unavailable crew, withdrawn insurance cover, or a wait incompatible with the cargo is enough. The number of ships passing is therefore necessary but insufficient. We need to know what cargoes they carry, which route they take, and how many other ships have abandoned the passage.

The IMO register as of September 30 counts 88 confirmed incidents and 24 seafarer deaths in the strait and the Middle East. It includes three ships damaged on September 28 and 29. The count has a regional scope and a precise date: it is not the number of attacks in the last week, nor a measure of the share of traffic lost.

On October 1, AP reports a notification received by UKMTO: a tanker hit by an unknown projectile, a fire, and a safe crew. The ship’s name and responsibility are not established in that source. The report and the confirmed incident register belong to different levels of verification. A page without current warnings also describes its own list, not the absence of danger in the surrounding sea.

The IMO assessment of August 28 indicated up to 400 ships and around 6,000 seafarers unable to leave the Gulf safely. It is a dated snapshot of the blockade’s human cost, separate from the death toll. Exhausted crews and disrupted crew-change procedures can reduce operational capacity even when material damage to ships remains limited.

Descriptive map Actors and dependencies in the crisis

Coercion
US-Israel alliance
Mediation
Hosting and rear area
Energy
Verification / rules
Regional spillover

Edges represent military, energy, and diplomatic relationships. The United States and Israel are linked by their alliance; Kharg is the terminal for Iranian exports; Hormuz concentrates the transit constraint; Qatar and Oman offer diplomatic channels. The physical network proposed for forecasting instead requires capacities, costs, and oil or LNG flows.

The map connects actors and functions; the flow model instead needs terminals, capacities, times, and goods. Confusing the two networks would allow the same weight to be assigned to a diplomatic statement and an idle facility. The former can change expectations; the latter directly limits production or transport.

Military and economic pressure overlap

The United States and Israel share intelligence, supplies, military cooperation, and missile defence. American support expands Israeli capabilities; Gulf bases and logistics allow Washington to sustain regional operations. This interdependence also exposes personnel, infrastructure, and governments that must reconcile protection, economic continuity, and diplomatic relations.

The American reinforcement described by AP on October 1 comprises about 9,000 personnel aboard a group of ships with the USS Theodore Roosevelt. According to an anonymous official, a third aircraft carrier could reach the region by the end of the month. The transfer expands the available options; it does not demonstrate that all units are already present or that an order for a new campaign has been issued.

The U.S. Treasury sanctions of October 1 extend OFAC sectoral determinations to the automotive and railway industries and target companies such as Iran Khodro and SAIPA, alongside railway operators and industrial networks. This is a verifiable formal decision. The statement’s claims about its economic effects instead require checking against data on revenue, production, and payments.

In the physical network, sanctions and attacks have different effects. A terminal can remain operational and lose buyers, banks, or insurers; a ship can have a cargo that can legally be purchased and fail to find a safe route. The effective constraint emerges from their combination, not just the number of targets or sanctioned entities.

The Gulf must also protect alternative paths

Gulf ports, airports, bases, and energy facilities perform several functions in the same territory. Hitting a logistical node can increase the cost of a military campaign and interrupt civilian activities. Reinforcing its defence requires resources that could otherwise protect routes or other facilities. Alternative paths reduce exposure to Hormuz only while they remain operational, supplied, and reachable.

Qatar makes this overlap visible. It is an LNG producer, hosts American forces, and maintains mediation channels. In its September 4 letters to the UN, Doha contests Iran’s justifications for attacks, asserts its right to self-defence and compensation, and cites its diplomatic initiatives. These are Qatar’s official positions, not an independent ruling on legal responsibility.

A mediator under attack can continue passing messages, but faces domestic pressures and defence obligations that restrict its freedom of action. Its contribution should be assessed through outcomes: agreed access, enforceable guarantees, ships that have left, and attacks that have ceased. The frequency of meetings alone does not measure room for negotiation.

Nuclear verification conditions the credibility of commitments

Nuclear verification and safe navigation are linked in negotiating proposals. A reopening supported by promises that cannot be checked can be revoked as soon as one side alleges a violation. Inspectors help reduce that scope for interpretation through access, inventories, and continuity of observations.

On September 9, the IAEA Board of Governors adopts resolution GOV/2026/61, which requests the transmission of documents on Iranian non-compliance to the UN Security Council and General Assembly. The joint statement by Canada, Australia, and New Zealand describes the lack of access to declared facilities during the reporting period and the inability to verify the material inventory. The lack of verification leaves decisive questions open; it does not by itself prove that a nuclear weapon exists.

Radiological safety is a separate problem. In his September 7 statement, Grossi reports radiation levels in the Gulf region within normal background levels, based on data communicated to the Agency. A normal radiological observation does not reconstruct uranium quantities or replace inspections. It answers a different question.

Energy measures the persistence of damage

In its September 11 oil market report, the IEA estimates Gulf oil exports in August at around 13 million barrels per day, about half the pre-war level, with more than 10 million barrels per day of regional production still shut in. The full return of supplies is pushed back to 2027 in the report’s forecast scenario. The recovery date is a conditional forecast, not an observed reopening.

The IEA analysis of September 18 also shows how the system has absorbed part of the shock: higher production outside the Gulf, alternative routes, lower demand, and the release of more than 300 million barrels from member countries’ emergency reserves. These responses allow consumption to continue while supplies remain reduced, but draw down safety margins. Prices can fall for a few weeks without the original capacity being restored.

The chart retains the historical collection through September 4. It separates the EIA spot series from subsequent observations of oil contracts, which include quotes of different kinds. That discontinuity prevents the plot from being treated as a homogeneous series for estimating a causal response. The IEA monthly data just cited have a different scope and are not added as if they were daily prices.

Historical observations Brent through September 4, 2026

US dollars per barrel. The collection combines EIA spot prices and Brent contract quotes; sources and price types change over the period.

Final point in the collection $96.28 September 4, 2026 · MarketWatch settlement

EIA spot · through June 29 Contract quotes · July 10-September 4

From July 10, the points include intraday, delayed, and settlement quotes. They do not form a homogeneous series: the segments connect available observations. Global demand, OPEC+, inventories, the dollar, and liquidity can move prices alongside events in Hormuz.

For Italy, the economic connection runs through international marginal prices even when the stopped ship is not bound for an Italian port. Oil, LNG, freight, and insurance affect importers, transport, and energy-intensive industries; exchange rates, contracts, and substitution capacity change the transmission. The import-bill formula and input-output matrix define an estimation pathway. Quantifying inflation or GDP still requires Italian data, estimated parameters, and uncertainty intervals.

The transitions that changed the conflict

The full chronology remains in the documentary dossier. The relevant transitions here explain the situation without repeating every episode.

Period	Change	Unresolved constraint
February 28–March	U.S.-Israeli attacks and Iran’s response involve the Gulf, navigation, and energy facilities.	Military superiority does not automatically protect every civilian and logistical node.
April–May	Ceasefires, the blockade of Iranian ports, and armed protection of traffic overlap.	Reduced fire does not restore ordinary passage.
June 17	A U.S.-Iran memorandum opens a phase of negotiation and implementation.	Inspection access, sanctions, and route control require verification and enforceable agreements.
July–August	New incidents and coercive measures interrupt the expected stabilization.	Alternative routes and logistical capacities limit only part of the losses.
September 9–18	The IAEA resolution and energy data document verification and supply problems.	Economic costs persist even during diplomatic openings.
September 25–October 1	Iranian proposal, U.S. response reported by Tehran, and American naval reinforcement.	Terms of a possible agreement remain unknown; troop transfers and a new incident do not establish a negotiating outcome.

What would distinguish the scenarios

Prolonged attrition. Attacks and restrictions keep traffic below the ordinary reference for weeks. Waiting times, diversions, and insurance cover remain abnormal. A stable recovery in flows and commercial conditions would contradict this reading.

Route interdiction. Selective permits, the port blockade, and attacks reinforce one another, increasing unmet demand. The scenario requires a verified reduction in traffic and feasible capacity; statements about control of the strait alone are insufficient.

Negotiated reopening. The diplomatic proposal becomes a sequence of implemented commitments: less selective transits, crew protection, sustainable insurance conditions, and verifiable inspection access. Acceptance of a timetable is a first step; recovered capacity is the outcome to measure.

Regional expansion. Attacks on bases, infrastructure, or alternative paths produce further losses outside Hormuz. Verification requires the geographical spread of events and constraints on flows to increase together. A single alert in a new location does not establish a change of scale.

Five observations help distinguish these possibilities: actual transits and cargoes; incidents and crews; capacity of terminals and alternative routes; IAEA access and implemented commitments; prices, import quantities, and exchange rates. Each needs a date, unit, scope, and provenance. The map indicates where to look. The model becomes useful when those observations allow its arrows to be tested or rejected.