Stochastic SIB model for infected cases simulation

stochastic_sib_model Stochastic SIB model for infected cases simulation

stochastic_sib_model(
  mu,
  beta,
  rho,
  sigma,
  gamma,
  alpha,
  mu_B,
  m = 0.3,
  theta,
  nnodes,
  POP_node,
  fluxes,
  time_sim,
  y0
)

Arguments

mu	population natality and mortality rate (day^-1)
beta	contact rate
rho	immunity loss rate (day^-1)
sigma	symptomatic ratio, i.e., fraction of infected people that develop symptoms and are infective. (The remaining fraction enters directly the recovered compartment.)
gamma	rate at which people recover from cholera (day^-1)
alpha	cholera induced mortality rate (day^-1)
mu_B	death rate of V.cholerae in the aquatic environment (day^-1)
m	parameter for infection force, default value is 0.3
theta	contamination rate
nnodes	number of nodes/cities
POP_node	vector, length represents number of cities/nodes; vector represents population at each node
fluxes	matrix, number of nodes x number of nodes where each row contains the probabilities a person travels from the given city (by Row Index) to another city (by Column Index).
time_sim	time steps for simulation, e.g., seq(0, 100, 0.1)
y0	initial condition for stochastic_sib_model, output of 'initial_condition_sib_model'

Value

a matrix, nnodes x number of time steps, representing number of new cases at each node, each time step

References

Li, J., Manitz, J., Bertuzzo, E. and Kolaczyk, E.D. (2020). Sensor-based localization of epidemic sources on human mobility networks. arXiv preprint Available online: https://arxiv.org/abs/2011.00138.

Author

Jun Li

Examples

set.seed(2020)
popu <- rep(20000, 10)
sigma <- 0.05
mu_B <- 0.2
theta_max <- 16
theta <- runif(10, 0.1, 0.9) * theta_max
y0 <- initial_condition_sib_model(popu, sigma, mu_B, theta, c(3))
time_sim <- seq(0, 1, by=0.1)
mu <- 4e-05
beta_max <- 1 
rho <- 0
beta <- runif(10, 0.1, 0.9) * beta_max
gamma <- 0.2
alpha <- 0
humanmob.mass <- matrix(runif(100, 0.1, 0.9), 10, 10)
diag(humanmob.mass) <- 0
for (j in 1:10) {
  humanmob.mass[j, ] <- humanmob.mass[j, ]/sum(humanmob.mass[j, ])
}
simu.list = stochastic_sib_model(mu = mu, beta = beta, rho = rho, sigma = sigma, gamma = gamma,
                   alpha = alpha, mu_B = mu_B, theta = theta, nnodes = 10, POP_node = popu,
                   fluxes = humanmob.mass, time_sim = time_sim, y0 = y0)