Binomial Travel Model

The binomial travel model adds exposure between nodes without permanently moving the population to a visited node. A traveler leaves their home node for the day’s contact calculation and returns home afterward. The population count assigned to each node therefore remains unchanged the entire simulation.

Travel is evaluated after within-node disease progression each simulation day. It can create new exposures in either direction for an origin-destination pair:

1. Infectious residents travel from their home node and expose susceptible people at the destination

2. Susceptible visitors travel to another node and encounter infectious residents who remained there

Only the resulting susceptible-to-exposed movements are applied. Travelers themselves are not removed from one node and added to another.

Complete Configuration

"travel_model": {
  "identity": "binomial",
  "parameters": {
    "rho": "1.0",
    "flow_reduction": ["1.0", "1.0", "1.0", "1.0", "1.0"],
    "traveling_compartments": {
      "I": "0.2"
    },
    "transmitting_compartments": {
      "I": "1.0"
    }
  }
}

Parameter	Required	Description
identity	Yes	Travel implementation. The supported value is "binomial".
rho	Yes	Global multiplier on travel-associated transmission. 1.0 leaves the calculated pressure unchanged; 0.0 prevents travel-associated exposure.
flow_reduction	Yes	One positive divisor per susceptible age group. 1.0 means no reduction; 2.0 halves travel-associated transmission for that age group.
traveling_compartments	Yes	Compartment labels and effective weights for infectious residents who can travel and expose people at another node.
transmitting_compartments	Yes	Compartment labels and effective weights for infectious residents who can expose susceptible visitors arriving at their node.

Every compartment label must exist in the selected disease model. Numeric values may be JSON numbers or numeric strings.

Traveling Versus Transmitting

The two dictionaries describe different contact routes:

Setting	Who is infectious?	Who is exposed?
traveling_compartments	A resident of the origin node who travels for the day	Susceptible people in the destination node
transmitting_compartments	A resident who remains associated with their local node	Susceptible visitors arriving from another node

transmitting_compartments applies only to the travel calculation. It does not select compartments for ordinary within-node disease transmission, which is defined by the disease model.

The transmitting weight may reasonably be greater than the traveling weight. Symptomatic people may continue to expose household or local contacts while being less likely to travel.

For a model with one combined infectious compartment:

"traveling_compartments": {
  "I": "0.2"
},
"transmitting_compartments": {
  "I": "1.0"
}

This treats 20% of I as an effective traveling infectious population while all of I contributes to exposure of visitors at the home node. It can approximate a scenario where 20% of infections are asymptomatic and continue traveling even though the model does not have a separate asymptomatic compartment.

Effective Weights

Each value is a multiplier on the number of people in that compartment. It can represent:

• The fraction who make relevant trips

• Infectiousness relative to a reference compartment

• A combined assumption about travel behavior and relative infectiousness

When asymptomatic and symptomatic states are modeled separately, the weights can preserve the disease model’s relative-infectiousness assumptions:

"traveling_compartments": {
  "IA": "0.97",
  "IP": "0.45"
},
"transmitting_compartments": {
  "IA": "0.97",
  "IP": "0.45",
  "IS": "1.0"
}

Here IS is the reference infectious compartment. IA and IP use their infectiousness relative to IS, while symptomatic IS does not travel but can expose visitors locally.

If only a fraction of a compartment travels, combine that fraction with relative infectiousness. For example, if T is half as infectious as I and 40% of treated people travel, its effective traveling weight is:

\[0.5 \times 0.4 = 0.2.\]

The model does not separately identify those two components, so scenario notes should record how each configured weight was derived.

Exposure Draw

Travel flow, weighted infectious populations, the contact matrix, beta, relative susceptibility, rho, and flow_reduction are combined into an age-specific probability. New exposures in each susceptible age, risk, and vaccine group are then drawn as:

\[X_{\mathrm{travel}} \sim \operatorname{Binom}(S, p_{\mathrm{travel}}).\]

Vaccine effectiveness reduces the probability for vaccinated susceptible groups. The probability is capped between 0 and 1, and the binomial draw cannot expose more people than are currently susceptible.

Because this draw is stochastic, using a deterministic disease model does not make the complete network simulation deterministic while binomial travel is enabled.