A mathematical model of H5N1 influenza transmission in US dairy cattle

Abstract

2024 saw a novel outbreak of H5N1 avian influenza in US dairy cattle. Limited surveillance data has made determining the true scale of the epidemic difficult. We present a stochastic metapopulation transmission model that simulates H5N1 influenza transmission through individual dairy cows in 35,974 herds in the continental US. Transmission is enabled through the movement of cattle between herds, as indicated from Interstate Certificates of Veterinary Inspection data. We estimate the rates of under-reporting by state and present the anticipated rates of positivity for cattle tested at the point of exportation over time. We investigate the impact of intervention methods on the underlying epidemiological dynamics, demonstrating that current interventions have had insufficient impact, preventing only a mean 175.2 reported outbreaks. Our model predicts that the majority of the disease burden is, as of January 2025, concentrated within West Coast states. We quantify the uncertainty in the scale of the epidemic, highlighting the most pressing data streams to capture, and which states are expected to see outbreaks emerge next, with Arizona and Wisconsin at greatest risk. Our model suggests that dairy outbreaks will continue to occur in 2025, and that more urgent, farm-focused, biosecurity interventions and targeted surveillance schemes are needed.

Fig. 1. Schematic overview of model format and outputs.

Infection spreads from the initial infected state through export of cattle. A Cattle exports are stochastically generated using trade data from the United States Animal Movement Model (USAMM). B At each time step, a herd has a probability of testing, and notifying of an outbreak. C We aggregate the number of herds with any infected cattle by state, and the number of newly reported outbreaks, at each date. D We fit global epidemiological parameters and an ascertainment scaling parameter via particle Markov Chain Monte Carlo simulation (pMCMC). Using the posterior distributions of these parameters, we are able to produce further model simulations herein. Full methodological details are presented in Supplementary Material Section 2.

Fig. 2. Model simulations.

After fitting model parameters we simulate 20,000 stochastic realizations drawing from the parameter posterior distributions. Displayed is the epidemic trajectory from these simulations for each US state. A shows the date at which the first outbreak is detected in a state, a binary outcome. 0 indicates the state has not yet reported its first outbreak. 1 indicates that it has. Model simulation thus plots the proportion of the 20,000 realizations which have simulated a reported outbreak by this date. B shows the proportion of herds in each state which report new outbreaks per week, assuming no differences in ascertainment (parameter A^asc) between states. Red points depict data. The black line depicts the model mean, lightly shaded grey region depicts the 95% credible interval (95% CrI), and the darker shaded grey region depicts the 50% CrI.

Fig. 3. Ascertainment rate assumptions.

A shows how the modeled baseline probability of reporting an outbreak depends on the number and proportion of infected cattle in a herd. Our model assumes that the probability that an infected herd reports an outbreak depends on the size of the holding, and the number of infected cattle on that date. B shows the mean and 95% CrI per-herd probability a herd reports an outbreak by US state, assuming every herd has 10% of its cattle infected. The credible interval captures the variation in herd sizes and the posterior distribution of the ascertainment rate parameter. C maps the mean values shown in (B).

Fig. 4. Probability of positive border testing.

We calculate the probability of an export of cattle out of each state testing positive from 20,000 stochastic model simulations. When moving cattle inter-state, up to 30 cattle will be tested for H5N1 per export. Panels show the state average per-herd probability that, should a herd export cattle, it would test positive at: A week beginning April 15th 2024, B week beginning August 19th 2024, and C week beginning December 2nd 2024.

Fig. 5. Border testing intervention counterfactuals.

A The number of new reported outbreaks weekly. B The number of herds nationally with any infected cattle. C The total number of infected cows nationally over time. Solid lines show simulation mean. Shaded regions show 95% CrI. Blue (True measures) depicts baseline model assumptions, whereby up to 30 cows in each inter-state export are tested starting from April 29th 2024. Red depicts the scenario with no border testing. Green depicts border testing of up to 100 cows from each export, implemented 28 days earlier, on April 1st 2024.