Sensitivity Analysis in Veterinary Disease Models

By Dr. Zubair Khalid, DVM, MS, PhD · 2026-08-11

Key Takeaways

• Sensitivity analysis is crucial for veterinary disease models to identify which uncertain parameters (e.g., transmission rate $\beta$, recovery rate $\gamma$, diagnostic test sensitivity/specificity) most influence model outputs like peak prevalence or time to extinction, thereby guiding data collection and intervention prioritization.
• One-way sensitivity analysis, while simple and computationally inexpensive, can miss critical parameter interactions (e.g., between contact rate and pathogen shedding duration) and is best suited for initial screening or models with few parameters.
• Global sensitivity analysis methods, such as variance-based Sobol indices, are essential for exploring the full parameter space, quantifying the contribution of individual parameters and their interactions to output variance, and are increasingly required for regulatory submissions (e.g., WOAH standards).
• Parameter correlation is a common pitfall; when parameters like pathogen infectiousness and host susceptibility are biologically linked, standard sensitivity methods can misattribute influence, necessitating multi-way or global approaches that account for joint distributions.
• The choice of sensitivity analysis method (one-way, multi-way, global) should be driven by the model's purpose, the number of uncertain parameters, computational resources, and the decision context, with variance-based methods favored for high-stakes decisions like resource allocation for outbreak response.
• Documenting sensitivity analyses rigorously, including parameter sources, ranges, distributions, correlation structures, and the chosen method, is vital for reproducibility and regulatory compliance, especially for models informing notifiable disease control strategies.

Veterinary disease models translate assumptions about transmission, host susceptibility, and intervention efficacy into quantitative predictions. Those predictions support decisions about surveillance design, outbreak response, and resource allocation. Yet every model rests on parameters that are measured with error, estimated from limited field data, or borrowed from related species. Sensitivity analysis is the discipline of determining how strongly model outputs depend on each input, and therefore which uncertainties actually matter for the decisions the model informs.

This article provides a procedural reference for veterinary researchers who construct or evaluate disease models. It covers local methods, including one-way and multi-way approaches, and global methods that explore the full parameter space. It also addresses the relationship between sensitivity analysis and uncertainty analysis, practical workflows for reporting, and common failure modes in veterinary applications. The intended reader is assumed to be comfortable with compartmental models, differential equations, and basic statistical inference. Model construction and validation are excluded, the focus is exclusively on interrogating an existing model's behavior.

The central question answered here is practical: when a model's output changes, which parameters should the investigator suspect first, and how should that suspicion be quantified and communicated? The answer determines whether a surveillance program samples more animals, whether a culling policy is adjusted, or whether a model is judged fit for regulatory use. International standards for animal health surveillance and reporting, such as those maintained by the World Organization for Animal Health, increasingly expect model outputs to be accompanied by explicit statements of uncertainty and sensitivity, making this analysis a reporting requirement instead of an academic exercise.

At a Glance

The Logic of Sensitivity in Epidemiological Models

A disease model is a function that maps input parameters to output quantities. The basic reproduction number, peak prevalence, time to extinction, and total cases are all outputs of interest in veterinary epidemiology. Each output is a function of transmission rate, contact structure, recovery or removal rate, latent period, and population size. The sensitivity of an output to an input is the rate at which the output changes when the input changes, holding other inputs fixed or allowing them to vary according to a specified scheme.

The distinction between sensitivity analysis and uncertainty analysis is frequently blurred in the veterinary literature. Uncertainty analysis asks what the output distribution looks like when input uncertainty is propagated through the model. Sensitivity analysis asks which inputs contribute most to that output uncertainty. The two are complementary. A model can have large uncertainty in a parameter that has negligible effect on the output, in which case refining that parameter estimate is wasted effort. Conversely, a parameter estimated with high precision can dominate output uncertainty if the output is extremely sensitive to it. The principles of epidemiological measurement and study design that underpin these distinctions are formalised in standard public health training materials, including the self-study course on epidemiology published by the Centers for Disease Control and Prevention.

The biological basis for parameter sensitivity is often traceable to nonlinear dynamics. In a susceptible-infected-recovered model, the transmission rate appears multiplicatively in the force of infection, so its influence on epidemic peak is nonlinear and interacts with population size and contact structure. Parameters that appear in exponents or denominators, such as the latent period in an SEIR model, can produce threshold behavior where small changes flip the system between outbreak and extinction. Sensitivity analysis is the tool that reveals these nonlinearities systematically instead of by intuition.

One-Way Sensitivity Analysis

One-way sensitivity analysis varies a single parameter across a plausible range while all other parameters remain at their baseline values. The output is recorded at each value, and the resulting curve or table shows the output's response to that parameter alone. This is the simplest and most commonly reported form of sensitivity analysis in veterinary models.

The method has clear advantages. It is computationally inexpensive, easy to interpret, and straightforward to present to stakeholders. A tornado diagram, in which each parameter's output range is displayed as a horizontal bar sorted by width, is the standard visualization. The parameter with the widest bar has the greatest individual influence on the output.

The limitations are equally clear. One-way analysis cannot detect interactions between parameters. Two parameters may each have small individual effects but a large joint effect, and one-way analysis will miss this entirely. The method also depends heavily on the chosen baseline values and the chosen ranges for each parameter. If the range for a parameter is too narrow, its sensitivity will be underestimated, if too wide, overestimated. The ranges must therefore be justified by data or expert opinion, and the justification should be reported alongside the results. For veterinary models, parameter ranges are often derived from field studies in the target species, experimental infection studies, or extrapolation from related species, and each source carries different uncertainty.

Multi-Way Sensitivity Analysis

Multi-way sensitivity analysis extends the one-way approach by varying two or more parameters simultaneously. The simplest form is two-way analysis, where two parameters are varied across a grid of values and the output is displayed as a contour plot or heat map. This reveals whether the two parameters interact, meaning whether the effect of one parameter depends on the value of the other.

Three-way and higher analyzes are possible but quickly become difficult to visualize and interpret. A three-way analysis can be displayed as a series of two-way plots at different values of the third parameter, but beyond that the graphical options are limited. Multi-way analysis is most useful when the investigator has a specific hypothesis about an interaction, such as between transmission rate and culling efficacy, or between diagnostic test sensitivity and the frequency of testing.

The computational cost of multi-way analysis grows geometrically with the number of parameters and the number of values per parameter. For models with many parameters, full multi-way grids are impractical, and the investigator must either select a subset of parameters for joint analysis or move to global methods. The selection of parameters for multi-way analysis should be guided by the results of a prior screening exercise, such as a Morris design, instead of by intuition alone.

Global Sensitivity Analysis

Global sensitivity analysis treats all parameters as random variables with specified distributions and explores the full joint parameter space. The output is evaluated at many points sampled from the joint distribution, and the resulting output variance is decomposed among the inputs. Variance-based methods, most commonly Sobol indices, provide a quantitative partition of output variance into first-order effects, which are attributable to each parameter alone, and total effects, which include interactions with other parameters.

The Sobol first-order index for a parameter is the fraction of output variance that would remain if all other parameters were fixed at their true values. The total-order index is the fraction of output variance that would remain if all other parameters were fixed but this parameter varied, which includes all interactions involving the parameter. The difference between total and first-order indices for a parameter indicates the strength of its interactions with other parameters.

Global methods require substantially more model evaluations than local methods. A typical Sobol analysis requires thousands of evaluations, and for computationally expensive models this can be prohibitive. Screening methods, particularly the Morris design, offer a computationally cheaper alternative. The Morris method samples trajectories through the parameter space and computes elementary effects for each parameter, which are then summarized by their mean and standard deviation. A high mean indicates a strong main effect, a high standard deviation indicates interactions or nonlinearity. The Morris method does not provide the quantitative variance decomposition of Sobol indices, but it ranks parameters reliably at a fraction of the computational cost, making it the method of choice for initial screening of models with many parameters.

The choice of input distributions for global sensitivity analysis is a substantive scientific decision. Parameters measured in controlled experiments may be assigned normal or log-normal distributions. Parameters estimated from field data may be assigned beta distributions bounded by plausible minima and maxima. Parameters borrowed from other species should be assigned wider distributions to reflect the additional uncertainty from interspecies extrapolation. The correlation structure among parameters should also be considered, since parameters estimated from the same data set are often correlated, and ignoring that correlation can distort sensitivity indices.

Selecting a Sensitivity Analysis Method

The choice of sensitivity analysis method depends on the model's purpose, the number of uncertain parameters, the computational budget, and the decisions the model will inform. For veterinary disease models, the practical question is whether the analysis must identify influential parameters, quantify interactions, or map the full response surface.

One-way analysis suits models with few parameters and limited computational resources. It answers the question of which single parameter most affects the output when others remain fixed. Multi-way analysis extends this to pairs or small groups, revealing interactions that one-way methods miss. Global methods, including variance-based approaches such as Sobol indices and regression-based techniques, apportion output variance across all parameters simultaneously and account for interactions across the full parameter space.

The decision sequence begins with the model's end use. If the model informs emergency response resource allocation, global methods are warranted because parameter interactions can materially change predicted outcomes. If the model screens candidate parameters for a more detailed study, one-way or multi-way methods provide adequate initial ranking at lower computational cost.

Parameter count drives the next decision. Models with fewer than ten uncertain parameters can often be examined with full factorial multi-way designs or elementary effects screening. Models with dozens of parameters benefit from variance-based global methods that rank parameters by their contribution to output variance without requiring exhaustive combinations.

Computational cost matters in veterinary applications where models may simulate large populations over long time horizons. A single run of a stochastic between-herd transmission model may take minutes to hours. Variance-based global methods typically require hundreds to thousands of runs. Screening designs, such as the method of Morris, require far fewer runs and can identify non-influential parameters before a full global analysis.

The following table summarizes selection criteria.

Species and production system alter the correct choice. A model of a slow-spreading disease in a national cattle population may justify computationally intensive global analysis because the consequences of misallocating control resources are large. A model of an acute outbreak in a single swine herd may need rapid results, favouring screening methods that identify the dominant transmission parameters within a constrained time frame. Models used for regulatory submissions or trade decisions, where the WOAH terrestrial animal health standards require transparent uncertainty characterization, should use methods that produce interpretable variance decompositions.

Worked Example: Sensitivity of an SIR Model for Foot-and-Mouth Disease

Consider a deterministic SIR model of foot-and-mouth disease spread within a single cattle herd. The model has three parameters: the transmission rate beta, the recovery rate gamma, and the initial proportion of infectious animals. The output of interest is the peak prevalence of infectious animals.

The model is simple enough that a full factorial multi-way design is feasible. Assign each parameter three levels representing plausible low, central, and high values based on published ranges. The full factorial design requires 27 model runs. The results show that peak prevalence is most sensitive to beta, moderately sensitive to the initial infectious proportion, and relatively insensitive to gamma within the tested range.

This finding has direct management implications. Control measures that reduce transmission, such as movement restrictions and biosecurity, should be prioritized over measures that shorten the infectious period, such as early culling, if the model's parameter ranges reflect the local situation. The analysis also identifies which parameters warrant further data collection. Reducing uncertainty in beta, through transmission studies or outbreak data, would reduce uncertainty in the model output more than additional data on gamma.

A one-way analysis of the same model would rank beta first, but it would not reveal whether beta and the initial infectious proportion interact. If the interaction is strong, the optimal control strategy may depend on the initial disease state, which is often poorly known at the start of an outbreak. The multi-way design captures this interaction and informs a more robust decision framework.

For a stochastic version of the same model, the analysis must account for output variability arising from demographic stochasticity. Each parameter combination requires multiple stochastic runs, and the sensitivity measures should be computed on the mean or a quantile of the output distribution. The CDC principles of epidemiology in public health practice provide the underlying logic for interpreting such output distributions in outbreak settings.

Interpreting Sensitivity Results for Decision-Making

Sensitivity analysis output must be translated into decisions. A parameter that ranks high in sensitivity but cannot be influenced by intervention is less actionable than a moderately sensitive parameter that corresponds to a feasible control measure. The analysis should therefore be paired with a list of intervention levers and their associated parameters.

For example, in a model of antimicrobial resistance spread in a feedlot, the transmission rate between animals may be highly sensitive, but the practical lever is the rate of antimicrobial use, which may map to a different parameter. The sensitivity analysis identifies where uncertainty matters, and the intervention mapping identifies what can be done about it.

Threshold effects deserve specific attention. A model may show little sensitivity to a parameter across most of its range, but cross a threshold where the output changes sharply. One-way and multi-way analyzes can miss such thresholds if the parameter levels do not bracket the critical value. Global methods that sample across the full parameter space are more likely to reveal threshold behavior. When thresholds are present, the analysis should report the parameter values at which the output changes regime, also the average sensitivity.

The evidence base for parameter values varies by disease and production system. For well-studied diseases in major livestock species, published estimates may exist for transmission and recovery parameters. For emerging diseases or wildlife hosts, parameter estimates may be sparse or derived from related pathogens. Sensitivity analysis is particularly valuable in the latter case because it identifies which parameters most affect conclusions despite the uncertainty. The WOAH animal health surveillance standards emphasize structured data collection that can reduce such parameter uncertainty over time.

Documenting Sensitivity Analyzes

Documentation should allow another researcher to reproduce the analysis and understand its limitations. Record the parameter ranges and their sources, the sampling design, the number of model runs, and the sensitivity measures computed. State whether the analysis was local or global and justify the choice.

Report the results as a ranked list of parameters with their sensitivity indices or effect sizes. Include the range of output values across the parameter space, as this communicates the practical importance of uncertainty. A parameter with a high sensitivity index but a narrow plausible range may contribute less to output uncertainty than a parameter with a moderate index and a wide range.

Document the model version and the software used. Veterinary disease models are often implemented in specialised packages or custom code, and version differences can change sensitivity results. Note any approximations, such as the use of a deterministic model where a stochastic one would be more realistic, and state how these approximations affect the interpretation of the sensitivity measures.

Where the analysis informs a specific decision, such as the choice between vaccination and culling strategies, record the decision context and the criteria used to judge the output. This allows the sensitivity results to be revisited if the decision context changes, for example if new MSD Veterinary Manual guidance on disease control becomes available or if the production system changes.

Limitations and Common Pitfalls

Correlated parameters violate the assumptions of variance-based sensitivity methods. If two parameters are biologically correlated, such as transmission rate and contact rate, the variance decomposition cannot uniquely attribute output variance to either. The analysis should report the correlation structure and consider methods that accommodate correlated inputs, such as regression-based approaches with correlated predictors.

Extrapolating sensitivity results across scales is risky. A parameter that dominates in a single-herd model may be less important in a regional model where spatial structure and movement patterns dominate. Sensitivity analyzes should be repeated at each scale of interest instead of assumed to transfer.

Model structural uncertainty is not captured by parameter sensitivity analysis. Two models with different structures, such as an SIR model and a model with an explicit latent period, may produce different sensitivity rankings even with identical parameter ranges. The analysis should acknowledge that it addresses parameter uncertainty only, and that structural choices remain a source of unquantified uncertainty.

The AVMA practice resources note that professional judgment remains necessary when applying model outputs to individual animals or specific herds. Sensitivity analysis improves the transparency of model-based reasoning, but it does not replace clinical or epidemiological judgment about the applicability of a model to a particular setting.

Recognized Complications and Failure Modes

Sensitivity analysis fails in characteriztic ways that produce misleading inference. The most common failure is parameter correlation masking. When two parameters move together, as transmission rate and contact rate often do in livestock movement models, one-way analysis attributes all effect to whichever parameter is varied first. The analyst sees a large sensitivity index for transmission rate and concludes it dominates, when the true driver is the correlated pair. Detection requires inspecting the correlation matrix before analysis and running multi-way or global methods that sample the joint parameter space.

A second failure mode is extrapolation beyond the parameter range the model was built to represent. A model calibrated on intensive pig production data will not tolerate parameters spanning extensive outdoor systems without structural breakdown. The model may return plausible outputs for parameter values that produce impossible within-herd dynamics, such as a basic reproduction number below zero or above the theoretical maximum for the pathogen. Discriminating checks include plotting model outputs against parameter values and confirming monotonic behavior where biology demands it, and verifying that extreme parameter combinations do not produce negative compartment sizes or oscillating solutions in a model that should equilibrate.

A third failure is treating sensitivity results as if they were uncertainty results. Sensitivity analysis orders parameters by influence on output. Uncertainty analysis quantifies the confidence interval around the output given parameter distributions. A parameter can be highly sensitive and precisely known, making it irrelevant to output uncertainty, while a moderately sensitive parameter with wide uncertainty dominates the prediction interval. Confusing the two leads to misplaced data collection effort.

Common Errors in Application

Less experienced analysts frequently vary parameters one at a time around a baseline and report the resulting output range as a sensitivity analysis. This approach misses interactions and depends heavily on the chosen baseline. The corrective action is to adopt a global method when more than three parameters are under study, or when the model is nonlinear. A second common error is using arbitrary ranges for parameter variation instead of ranges derived from the literature or expert elicitation. Arbitrary ranges produce sensitivity rankings that reflect the analyst's choice of bounds, not the biology. Each parameter range should be justified and recorded with its source.

A third error is interpreting sensitivity indices as causal effects. A high sensitivity index for the culling rate in a foot-and-mouth disease model does not prove that culling drives outbreak size. It shows that the model output responds strongly to that input. Causal claims require experimental or quasi-experimental evidence outside the model. A fourth error is failing to test the model's structural assumptions before running sensitivity analysis. If the compartmental structure is wrong, sensitivity analysis quantifies the behavior of a model that does not represent the system. The CDC principles of epidemiology in public health practice provide the observational grounding needed to check whether model structure matches field patterns.

Limitations of Current Evidence

The evidence base for sensitivity analysis in veterinary disease models is uneven. Methodological guidance is well developed for human infectious disease modeling, but veterinary applications face additional constraints. Livestock population data are often aggregated at herd level, movement data are incomplete, and reporting delays vary by species and production system. These data limitations propagate into parameter distributions and widen uncertainty in ways that sensitivity analysis can quantify but cannot resolve.

Expert opinion still differs on how to handle parameters that cannot be estimated from available data. Some groups advocate wide, weakly informative distributions to reflect ignorance. Others argue for narrow ranges based on analogous pathogens or production systems. The choice materially affects sensitivity rankings. A parameter given a wide range will appear more influential than the same parameter given a narrow range. This is not a technical problem with a unique solution. It is a modeling judgment that should be documented and defended.

There is also unresolved debate about the appropriate complexity of sensitivity analysis for regulatory submissions. International standards for animal health surveillance and trade require transparent reporting of model assumptions, but they do not prescribe a specific sensitivity method. The WOAH terrestrial animal health code sets expectations for scientific justification without mandating a particular analytical approach. In practice, reviewers accept one-way analysis for simple models and expect global methods for models that inform major control decisions.

Escalation and Consultation

Sensitivity analysis results warrant escalation when they reveal that model conclusions depend on parameters the analyst cannot defend. If the ranking of control strategies reverses across the plausible range of a single uncertain parameter, the model cannot support a recommendation without further data collection or expert review. This situation calls for consultation with a quantitative epidemiologist or a specialist in the specific production system.

Laboratory involvement is indicated when parameter uncertainty stems from diagnostic test performance. Sensitivity and specificity of diagnostic tests directly affect prevalence estimates and transmission parameters. If sensitivity analysis identifies test performance as a dominant driver, the appropriate response is to consult diagnostic laboratories for validated test characteriztics instead of to widen the parameter range.

Regulatory reporting is required when sensitivity analysis informs notifiable disease control. Models used to support culling zones, movement restrictions, or vaccination strategies should be documented to the standard expected by the relevant animal health authority. The AVMA practice resources and WOAH standards provide guidance on the level of documentation expected. When model results conflict with field observations, the discrepancy should be reported to the authority responsible for disease control, because the model may be missing a transmission pathway that field data reveal.

Frequently Asked Questions

How Much Computational Expertise Is Required for Global Sensitivity Analysis?

Global sensitivity analysis methods such as variance-based decomposition and Latin hypercube sampling require more programming skill than one-way or multi-way approaches. For a veterinary researcher comfortable with statistical software, the learning curve is moderate, and most modern epidemiological packages include built-in routines for these procedures. If your team lacks this expertise, start with one-way analysis for the parameters you suspect matter most, then progress to global methods as familiarity grows. The CDC principles of epidemiology provide a useful foundation for understanding the underlying sampling and inference concepts. Collaboration with a biostatistician is often the most efficient path when model complexity outpaces local capacity.

What Can Be Done When Computational Resources Are Limited?

When running thousands of model iterations is impractical, reduce the parameter space before performing sensitivity analysis. Use expert elicitation to fix parameters with well-established values from the literature, then focus computational effort on the parameters with greatest biological uncertainty. Screening designs such as the Morris method require far fewer model runs than full variance-based approaches while still identifying influential parameters. For herd-level models, consider aggregating subpopulations to reduce state variables. The WOAH animal health surveillance standards describe how surveillance data can inform parameter ranges, which helps prioritize which parameters deserve the computational investment.

How Do Sensitivity Results Transfer Between Species or Production Systems?

Sensitivity findings from one species do not transfer directly to another because the underlying biology, contact structure, and management practices differ. A parameter that dominates transmission dynamics in intensively housed swine may have negligible influence in pasture-based cattle systems. Re-run the sensitivity analysis for each new context instead of assuming portability. The rank ordering of influential parameters often changes more than the model structure itself. When publishing results, state clearly which species and production system the analysis covers. The MSD Veterinary Manual provides species-specific guidance on biological parameters such as incubation periods and transmission routes, which can inform whether your parameter ranges are appropriate for a new target population.

What Records Should Be Kept for Regulatory or Audit Purposes?

Document the model version, the software and version used, the full list of parameters with their distributions and sources, and the random number generator seed for reproducibility. Record the date of each analysis run and the exact parameter ranges tested. For notifiable disease models, regulatory bodies may request this documentation during outbreak investigations or trade disputes. The WOAH terrestrial animal health code outlines expectations for surveillance and risk assessment documentation that apply to member countries. Keep version-controlled code and output files in a shared repository so that any team member can reproduce a given analysis. This practice also protects against loss of institutional knowledge when staff change.

How Should Sensitivity Findings Be Explained to a Client or Supervisor?

Frame the explanation around decisions instead of mathematics. State which parameters most influence the outcome of interest, what that means for the specific control question, and how much confidence can be placed in the model predictions. Use visual aids such as tornado diagrams or scatter plots instead of tables of variance indices. Explain that sensitivity analysis identifies where additional data collection would most reduce uncertainty, which is often the most actionable message for a producer or regulatory body. The AVMA practice resources offer guidance on communicating complex technical information to non-specialist audiences in veterinary practice settings.

When Is Sensitivity Analysis Not Worth the Effort?

If the model is used only for a single, time-sensitive decision and the outcome is robust to plausible parameter variation, a full sensitivity analysis may be unnecessary. Similarly, if the model is purely illustrative for teaching purposes, informal exploration of parameter effects may suffice. Sensitivity analysis adds the most value when model outputs inform high-stakes decisions such as culling strategies, vaccination campaigns, or trade restrictions, and when parameter estimates carry substantial uncertainty. For low-stakes decisions with well-characterized parameters, the cost of the analysis may exceed its benefit. The WOAH animal health surveillance standards emphasize proportionate investment of resources relative to the risk being managed, a principle that applies equally to analytical effort.

Related Clinical & Scientific Guides

• Evaluating Veterinary Surveillance System Attributes
• Network Analysis for Infectious Disease Spread in Animal Populations
• Randomized Controlled Trials in Veterinary Field Settings

References and Further Reading

• Chronic mild stress-induced anhedonia: a realistic animal model of depression.. 1992.
• Current approaches for assessing insulin sensitivity and resistance in vivo: advantages, limitations, and appropriate usage.. 2008.
• Serum FGF21 levels are increased in obesity and are independently associated with the metabolic syndrome in humans.. 2008.
• The wavelengths in sunlight effective in producing skin cancer: a theoretical analysis.. 1974.
• The inflammasome-mediated caspase-1 activation controls adipocyte differentiation and insulin sensitivity.. 2010.
• The contribution of gliosis to diffusion tensor anisotropy and tractography following traumatic brain injury: validation in the rat using Fourier analysis of stained tissue sections.. 2011.
• WOAH Animal Health Surveillance Standards. WOAH.
• CDC Principles of Epidemiology in Public Health Practice. CDC.
• MSD Veterinary Manual, Professional Edition. MSD Veterinary Manual.

Related Articles

• Compartmental Models in Veterinary Disease Dynamics
• Risk Factor Analysis for Disease in Animal Populations
• Time Series Analysis for Veterinary Disease Surveillance
• Bayesian Hierarchical Models for Veterinary Disease Mapping
• Network Analysis for Infectious Disease Spread in Animal Populations

This article is educational professional reference material for veterinary audiences. It is not a substitute for veterinary diagnosis, individual clinical judgment, current product labeling, or applicable regulatory requirements.