R/equilibrium-epiSEIR.R
equilibrium_SEI_SEIR.RdGiven prevalence of disease in humans (modeled as an SEIR: Susceptible-Latent-Infected-Recovered process with birth and death) and entomological parameters of transmission, this function calculates the quasi-stationary distribution of adult female mosquitoes across SEI (Susceptible-Exposed-Infectious) stages, allowing for Erlang distributed E stage.
equilibrium_SEI_SEIR( params, node_list = "b", NF = NULL, phi = 0.5, NH = NULL, log_dd = TRUE, spn_P, pop_ratio_Aq = NULL, pop_ratio_F = NULL, pop_ratio_M = NULL, pop_ratio_H = c(1, 0, 0, 0), cube )
| params | a named list of parameters (see details) |
|---|---|
| node_list | a character vector specifying what type of nodes to create; (m = a node with only mosquitoes, h = a node with only humans, b = a node with both humans and mosquitoes) |
| NF | vector of female mosquitoes at equilibrium, for mosquito-only nodes |
| phi | sex ratio of mosquitoes at emergence |
| NH | vector of humans at equilibrium, for human-only nodes |
| log_dd | Boolean: TRUE implies logistic density dependence, FALSE implies Lotka-Volterra model |
| spn_P | the set of places (P) (see details) |
| pop_ratio_Aq | May be empty; if not, a named vector or matrix. (see details) |
| pop_ratio_F | May be empty; if not, a named vector or matrix. (see details) |
| pop_ratio_M | May be empty; if not, a named vector or matrix. (see details) |
| pop_ratio_H | Prevalence in human-only nodes, default is all susceptible |
| cube | an inheritance cube from the |
a vector of the equilibrium number of females in each SEI stage
This function handles 3 types of nodes: Human only, mosquito only, and nodes
with both. These nodes are set using the node_list parameter.
Mosquito-only node equilibrium calls equilibrium_lifeycle, which
follows one of two models: classic logistic dynamics or the Lotka-Volterra
competition model. This is determined by the parameter log_dd, and it
changes elements of the return list: K is returned for logistic dynamics,
or gamma is returned for Lotka-Volterra dynamics. This
is parameterized with the NF parameter to define the adult female numbers.
This parameter only needs to be supplied if there are mosquito-only nodes.
Human-only nodes don't require any equilibrium calculations. These nodes use
the NH and pop_ratio_H to set adult human populations and
infection rates in nodes. These two parameters only need to be supplied
if there are human-only nodes. pop_ratio_H needs to be a matrix with the
number of rows equal to the number of human-only patches, and 4 columns. The
columns are assumed to be fractions of the population in "S", "E", "I", or "R"
states, and every row must sum to 1.
For human and mosquito nodes, this function calls make_Q_SEI to construct the
infinitesimal generator matrix which is used to solve for the quasi-stationary
(stochastic) or equilibrium (deterministic) distribution of mosquitoes over stages.
Parameters are provided by params.
For information on the method used to solve this distribution, see section "3.1.3 Nonsingularity of the Subintensity Matrix" of:
Bladt, Mogens, and Bo Friis Nielsen. Matrix-exponential distributions in applied probability. Vol. 81. New York: Springer, 2017.
The places (spn_P) object is generated from one of the following:
spn_P_lifecycle_node, spn_P_lifecycle_network,
spn_P_epiSIS_node, spn_P_epiSIS_network,
spn_P_epiSEIR_node, or spn_P_epiSEIR_network.
The initial population genotype ratios are set by supplying the pop_ratio_Aq,
pop_ratio_F, and pop_ratio_M values. The default value is NULL,
and the function will use the wild-type alleles provided in the cube
object. However, one can supply
several different objects to set the initial genotype ratios. All genotypes provided
must exist in the cube (this is checked by the function). If a single, named vector
is provided, then all patches will be initialized with the same ratios. If a
matrix is provided, with the number of columns (and column names) giving the
initial genotypes, and a row for each patch, each patch can be set to a different
initial ratio. The three parameters do not need to match each other.
The params argument supplies all of the ecological and epidemiological
parameters necessary to calculate equilibrium values. This is used to set the
initial population distribution and during the simulation to maintain equilibrium.
This params must include the following named parameters, noted as being
the same as lifecycle parameters, or new for the epidemiological equilibrium
(Lifecycle parameters)
qE: inverse of mean duration of egg stage
nE: shape parameter of Erlang-distributed egg stage
qL: inverse of mean duration of larval stage
nL: shape parameter of Erlang-distributed larval stage
qP: inverse of mean duration of pupal stage
nP: shape parameter of Erlang-distributed pupal stage
muE: egg mortality
muL: density-independent larvae mortality
muP: pupae mortality
muF: adult female mortality
muM: adult male mortality
beta: egg-laying rate, daily
nu: mating rate of unmated females
(Epidemiological parameters)
NH: number of humans, can be a vector
X: SEIR prevalence in humans, can be a vector of length 4 for 1 node, or a matrix for many nodes
NFX: number of female mosquitoes, only required if any prevalence (X) is zero
b: mosquito to human transmission efficiency, can be a vector
c: human to mosquito transmission efficiency, can be a vector
r: rate of recovery in humans (1/duration of infectiousness)
muH: death rate of humans (1/avg lifespan)
f: rate of blood feeding
Q: human blood index
qEIP: related to scale parameter of Gamma distributed EIP (1/qEIP is mean length of EIP)
nEIP: shape parameter of Gamma distributed EIP
delta: inverse duration of the latent stage (E)
The return list contains all of the parameters necessary later in the simulations.
For equilibrium without epidemiological parameters, see equilibrium_lifeycle.
For equilibrium without latent humans (SIS dynamics), see equilibrium_SEI_SIS.