Description Usage Arguments Details Value See Also
View source: R/loglikelihoodepiILM.r
Calculates the log likelihood for the specific compartmental framework of the continuous-time ILMs.
1 2 3 4 5 |
object |
an object of class “datagen” that can be the output of |
distancekernel |
the spatial kernel type when |
control.sus |
a list of values of the susceptibility function (>0):
where, n and n_s are the number of individuals and number of susceptibility parameters, respectively. Default = NULL means the model does not include these parameters. |
control.trans |
it has the same structure as the |
kernel.par |
a scalar spatial parameter for the distance-based kernel (>0), or a vector of the spatial and network effect parameters of the network and distance-based kernel (both). It is not required when the |
spark |
spark parameter (>=0), representing random infections that are unexplained by other parts of the model. Default value is zero. |
gamma |
the notification effect parameter for SINR model. The default value is 1. |
delta |
a vector of the shape and rate parameters of the gamma-distributed infectious period (SIR) or a 2 by 2 matrix of the shape and rate parameters of the gamma-distributed incubation and delay periods (SINR). |
We label the m infected individuals i = 1, 2, …, m corresponding to their infection (I_i) and removal (R_i) times; whereas the N-m individuals who remain uninfected are labeled i=m+1, m+2, …, N with I_i= R_i = ∞. We then denote infection and removal time vectors for the population as I = {I_1, ..., I_m} and R = {R_1,..., R_m}, respectively. We assume that infectious periods follow a gamma distribution with shape and rate δ. The likelihood of the general SIR continuous-time ILMs is then given as follows:
where θ is the vector of unknown parameters; f(.;δ) indicates the density of the infectious period distribution; and D_i is the infectious period of infected individual i defined as D_i= R_i-I_i. The likelihood of the general SINR continuous-time ILMs is given by:
where D^{inc}_i and D^{delay}_i are the incubation and delay periods such that D^{inc}_i = N_i - I_i and D^{delay}_i = R_i - N_i, and
λ_{ij}^{-} = Ω_{S}(j) Ω_{T}(i) k(i,j),
for i in I(t), j in S(t), and
λ_{ij}^{+} = γ (Ω_{S}(j) Ω_{T}(i) k(i,j)),
for i in N(t), j in S(t).
Note, λ_{ij}^{+} is used only under the SINR model.
Returns the log likelihood value.
contactnet, datagen, epictmcmc
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