Control Strategies

This page describes the disease control interventions implemented in MHASpread, their mechanisms, parameters, and interaction effects.

Overview of Control Actions

MHASpread implements four complementary control strategies applied across three nested spatial zones. Control actions are triggered upon detection of infected farms and operate simultaneously to contain and eliminate infection.

Control Zone Architecture

Zone Definitions

Three concentric zones with increasing distance from detected infected farms:

Zone Radius Primary Purpose Key Actions
Infected Zone 3 km Rapid containment Depopulation + vaccination + surveillance
Buffer Zone 3–7 km Prevent spread Vaccination + surveillance + trade restrictions
Surveillance Zone 7–15 km Early detection Active detection + movement monitoring

Zone Establishment

Zones are established around each newly detected infected farm, creating overlapping containment regions in multi-farm outbreaks.

Control Action 1: Depopulation

Mechanism

Infected farms within the infected zone are completely depopulated (all animals culled) and excluded from subsequent simulation.

Implementation

Priority Ordering

Farms are prioritized for depopulation by:

  1. Primary criterion: Total herd size (largest farms first)
  2. Rationale: Maximize removal of infectious animals per day within capacity limits

Daily Capacity

The number of farms depopulated per day is a scenario parameter (e.g., 1, 3, 5 farms/day).

Scheduling

If depopulation capacity is exceeded:

  • Farms scheduled for subsequent days maintain current dynamics
  • Queued farms remain infectious until culling
  • Creates realistic simulation of logistical bottlenecks

Transmission Impact

By removing $I_i(t)$ (all infectious animals), depopulation eliminates:

  • Within-farm transmission: No more internal spread
  • Between-farm kernel contributions: Farm $i$ no longer contributes to $P_E$ for neighbors
  • Trade network transmission: Depopulated farms cannot ship animals

Disease Duration

Time from detection to removal varies. If a farm takes 3 days to depopulate and infectious period is ~5 days, ~40% of infectious life occurs pre-removal.

Control Action 2: Emergency Vaccination

Eligibility

Vaccinated populations: Bovine (cattle) only

Geographic scope: Infected zone + Buffer zone

Timing: 15 days after control zone establishment

Rationale for 15-Day Lag

  1. Logistical mobilization: Time to transport vaccine, train personnel, establish vaccination sites
  2. Epidemiological window: Balance between early action and realistic implementation

Implementation Details

Daily Vaccination Capacity

Specified as number of farms vaccinated per day (e.g., 5 farms/day).

Prioritization Within Zones

Farms prioritized by:

  1. Largest herds first (maximize animals vaccinated)
  2. Infected zone first (higher risk)
  3. Geographic proximity (reduce travel time)

Progressive Immunization

Within each farm, vaccination occurs over multiple days:

\[a_t = \left\lfloor (S + E + I + R) \cdot \frac{1}{v_t} \right\rfloor\]

where $v_t = 15$ days (duration to vaccinate entire herd).

The number of animals attempted for vaccination per day is:

\[a_t = \min\left(a_t, \max(V^* - V, 0)\right)\]

where $V^* = \lfloor N \cdot \tau \rfloor$ is target vaccinated count and $\tau$ is target coverage (100%).

Vaccine Efficacy

Probability that a vaccinated animal develops protective immunity is $v_e$ (e.g., 0.95 for 95% efficacy).

Number of successful vaccinations:

\[X \sim \text{Binomial}(a_t, v_e)\]

Compartment Allocation

Successfully vaccinated animals are drawn proportionally from $S, E, I, R$ compartments:

\[d_k \sim \text{Hypergeometric}(C_k, U - C_k, r_k)\]

where $C_k$ is count in compartment $k$, $U$ is unvaccinated pool, and $r_k$ is remaining vaccinations to allocate.

Mechanism: Vaccine Protection

Vaccinated animals ($V$ compartment) are:

  • Protected from infection: Cannot transition $S \to E$ (immune-blocked)
  • Never infectious: Do not contribute to transmission kernel
  • Not depopulated: Remain on farm after outbreak resolution

Population Immunity

As vaccination progresses, farm-level infection probability decreases:

\[\text{Effective susceptible proportion} = \frac{S + E}{N} \to \frac{S + E}{N - V}\]

Control Action 3: Movement Standstill

Scope

Duration: 30 days from zone establishment

Geographic scope: Infected zone + Buffer zone + Surveillance zone

Movement Restrictions

Outgoing Movements

Prohibited from infected and buffer zones:

  • Prevents infected animals from being shipped to distant farms
  • Cuts network-mediated transmission pathway

Incoming Movements

Prohibited to surveillance zone:

  • Reduces exposure of uninfected farms in high-surveillance area
  • Limits trade-driven introduction of infection

Implementation

Each movement event is checked against:

  1. Zone status of sending farm
  2. Standstill date range for that zone
  3. Movement direction (outgoing vs. incoming)

If conditions met, movement is blocked.

Interaction with Depopulation

Depopulated farms automatically cannot ship animals (they no longer exist in simulation).

Duration and Termination

Standstill lasts 30 days unless:

  • All zones are dissolved (rare, requires complete elimination)
  • Scenario-specific override (e.g., early termination in sensitivity analysis)

Control Action 4: Contact Tracing & Traceback

Mechanism

Epidemiological tracing identifies farms that received animals from detected infected farms within the past 30 days.

Implementation

For each detected farm $i$:

  1. Query movement history: Identify incoming movements to farm $i$ in past 30 days
  2. Identify senders: Origin farms of those movements
  3. Classify traceback farms: Senders are added to detected farms list
  4. Apply zones: Control zones established around traceback farms

Transmission Impact

Traceback farms are treated as:

  • Already infected (even if still latent)
  • Immediately under surveillance (if in surveillance zone)
  • Eligible for depopulation (if detection confirmed)

Limitation

Model does not include false positives from traceback. All traceback identifies real infection (reflects best-case scenario).

Detection Capability

Active Surveillance

Farms in surveillance zones are inspected on a rolling basis:

Inspection Intensity

Number of farms inspected per day:

\[k_i = \max\left(1, \left\lfloor \frac{P_i}{3} \right\rfloor\right)\]

where $P_i$ = farms under surveillance at iteration $i$.

This ensures:

  • At least 1 farm inspected daily if surveillance active
  • One-third of population examined per day across full cycle

Detection Process

Newly infected farms detected via hypergeometric sampling:

\[E_i \sim \text{Hypergeometric}(M = P_i, n = I_i, N = k_i)\]

where:

  • $M$ = total farms under surveillance
  • $n$ = infected farms present
  • $N$ = farms inspected

Diagnostic Sensitivity

Detected farms are subject to diagnostic testing with sensitivity $s$:

\[E_i^* \sim \text{Binomial}(E_i, s)\]

If $s = 1$: perfect diagnostics; $s < 1$: imperfect tests (reflects subclinical cases, sampling error).

Scenario Parameters: A Summary

Key control parameters that users can specify:

Parameter Example Values Impact
Depopulation capacity (farms/day) 1, 3, 5, 10 Speed of infected farm removal
Vaccination capacity (farms/day) 2, 5, 10 Cattle herd protection rate
Vaccination efficacy 0.85, 0.95 Proportion animals protected
Diagnostic sensitivity 0.80, 0.95, 1.0 Detection accuracy
Standstill duration Fixed 30 days Network-mediated transmission blockade
Detection lag Varies with inspection Time before control action

Control Effectiveness: Conceptual Framework

What Drives Success?

Successful containment requires:

  1. Rapid detection (low diagnostic lag)
  2. Adequate depopulation capacity (removes infection before spread)
  3. Ring vaccination (protects susceptible cattle before exposure)
  4. Movement restrictions (blocks long-distance spread)
  5. Coordination (zones align with actual farming landscape)

What Undermines Control?

  • Slow detection (infection establishes widely before awareness)
  • Low depopulation capacity (queued farms remain sources)
  • Vaccination delays (animals become infected during lag)
  • Movement rule violations (non-compliance or smuggling)
  • Network clustering (farms in tight spatial clusters, rapid spread)

Sensitivity Considerations

MHASpread allows systematic variation of all parameters to assess robustness of strategies across different outbreak contexts.

Multi-Farm Outbreaks: Zone Interaction

When multiple farms are detected simultaneously or sequentially:

  1. Zones established around each farm (3, 7, 15 km radius)
  2. Zones may overlap (especially in dense farming regions)
  3. Most stringent rule applied (intersection takes minimum control intensity)

Example: Two farms detected 5 km apart:

  • Farm A infected zone (3 km) overlaps Farm B buffer zone (7 km)
  • Overlapping region subject to both infected zone and buffer zone rules
  • Most restrictive controls apply (e.g., both require depopulation consideration)

Temporal Dynamics of Control

Phase 1: Silent Spread (Days 0–20)

  • No control active
  • Infection spreads unimpeded
  • No detection

Phase 2: Detection & Zone Establishment (Day ~21–25)

  • First infected farm detected
  • Zones established
  • Depopulation and tracing initiated
  • Vaccination logistics mobilized

Phase 3: Active Control (Days 25–50+)

  • Depopulation proceeds
  • Vaccination ongoing
  • Standstill enforced
  • New infections may occur if control insufficient

Phase 4: Resolution

  • New infections cease
  • Remaining infectious animals recover or are removed
  • Zones dissolved after sufficient time with no new infections

Cost-Effectiveness Perspective

Control actions impose costs:

  • Depopulation: Direct loss (animal value) + labor + disposal
  • Vaccination: Vaccine + personnel + logistics + time loss
  • Standstill: Lost trade revenue + market disruption
  • Surveillance: Personnel, testing, equipment

MHASpread outputs (final farm count, animal losses, epidemic duration) feed into downstream economic models for cost-benefit analysis.

Next Steps