Agent Multigroup

A Multi-group SEIR Model

Parameter values

  # the transmission rate matrix
  beta = matrix(c(0.4, 0.2, 0.2, 0.3), nrow=2)
  # the recovery rate
  gamma = newExpWaitingTime(0.2)
  # the rate leaving the latent stage and becoming infectious
  sigma=0.5
  # the population size
  N = 10000

Create the Simulation and Initialize the agents

  # initialize a simulation with N agents
  sim = Simulation$new(N)
  for (i in 1:n) {
    sim$setState(i, list(if (i <= 20) "I" else "S", group=i %% 2))
  }

Add Loggers

A counter counts a specific type of event changes. It take three arguments

• name: the name of the counter, which is the name of the observation variable
• from: its meaning depends on the following argument.
• to: optional. If to is NULL, then counter counts the number of agents in the state that matches from. Otherwise, it logs the transitions that agent jumped from a state that matched "from" to one matched "to".

A state matches if the the corresponding domains in "from" (or "to") have identical values as the agent's state.

  sim$addLogger(newCounter("S1", from=list("S", group=0)))
  sim$addLogger(newCounter("S2", list("S", group=1)))
  sim$addLogger(newCounter("E1", list("E", group=0)))
  sim$addLogger(newCounter("E2", list("E", group=1)))
  sim$addLogger(newCounter("I1", list("I", group=0)))
  sim$addLogger(newCounter("I2", list("I", group=1)))
  sim$addLogger(newCounter("R1", list("R", group=0)))
  sim$addLogger(newCounter("R2", list("R", group=1)))

Mixing Pattern

We create a random mixing object and add it to the simulation

  m = newRandomMixing()
  sim$addContact(m)

Transitions

There are two types of transitions.

• Spontaneous transitions, e.g., showing system or recovery.
• Transitions caused by contacts.

The transition rules are specified by a formula:

• "->" denotes the direction of transition.
• A contact transition needs to have two agents state specified, the agent who initiates the contact, and the contacting agent. There states are specified by the "+" operator. The first is the state of the initiator, the second is the state of the contact.
• A contact transition is always associated with a contact object, which determines the contacts of an agent. The contact is specified after "~".

Each transition has to have a waiting time, which must be exponentially distributed. It can be a number specifying the rate. Though not used in the example, a transition can have a to_change_callback and a changed_callback. The first callback is a function that return a logical value. If TRUE, the transition will occur. Otherwise the transition will be prevented. The latter callback is executed after the state change happened.

  sim$addTransition("E"->"I", sigma)
  sim$addTransition("I"->"R", gamma)
  sim$addTransition(list("I", group=0) + list("S", group=0) -> 
                      list("I", group=0) + list("E", group=0) ~ m, beta[1, 1]) 
  sim$addTransition(list("I", group=0) + list("S", group=1) -> 
                      list("I", group=0) + list("E", group=1) ~ m, beta[1, 2]) 
  sim$addTransition(list("I", group=1) + list("S", group=0) -> 
                      list("I", group=1) + list("E", group=0) ~ m, beta[2, 1]) 
  sim$addTransition(list("I", group=1) + list("S", group=1) -> 
                      list("I", group=1) + list("E", group=1) ~ m, beta[2, 2]) 

Run the Simulation

  result = sim$run(0:250)
  print(result)