r0_conversions {finalsize}

Converts between epidemiological parameters related to R_0

Description

Converts between R_0 and the transmission rate \lambda, or calculates the effective reproduction number R_\text{eff} for a population, while accounting for population characteristics including demographic heterogeneity in social contacts, heterogeneity in the demographic distribution, and heterogeneity in susceptibility to infection.

Uses the R0 (R_0), contact matrix (C), population (N), and infectious period (\gamma) to calculate the transmission rate using the following equation.

\lambda = R_0 / ({Max}(EV(C)) \gamma)

where EV(C) denotes the eigenvalues of the matrix C which is calculated from the social contacts matrix scaled by the number of individuals in each demographic and susceptibility group in the population.

Usage

lambda_to_r0(
  lambda,
  contact_matrix,
  demography_vector,
  susceptibility,
  p_susceptibility,
  infectious_period = 1.8
)

r0_to_lambda(
  r0,
  contact_matrix,
  demography_vector,
  susceptibility,
  p_susceptibility,
  infectious_period = 1.8
)

r_eff(r0, contact_matrix, demography_vector, susceptibility, p_susceptibility)

Arguments

lambda

The transmission rate of the disease, also called the 'force of infection' (\lambda). This is different from the effective transmission rate (\beta).

contact_matrix

Social contact matrix. Entry m_{ij} gives average number of contacts in group i reported by participants in group j

demography_vector

Demography vector. Entry v_{i} gives proportion of total population in group i.

susceptibility

A matrix giving the susceptibility of individuals in demographic group i and risk group k.

p_susceptibility

A matrix giving the probability that an individual in demography group i is in risk (or susceptibility) group k. Each row represents the overall distribution of individuals in demographic group i across risk groups, and each row must sum to 1.0.

infectious_period

Duration of the infectious period in days. Default value is 1.8 days.

r0

The basic reproductive number R_0 of the infection.

Details

Given the transmission rate (\lambda), social contacts matrix (c), demography (N), the distribution P of each demographic group i into susceptibility groups S, and the infectious period (\gamma)

• r_eff() calculates the effective reproductive number;

• lamda_to_r0() calculates the R_0 from the transmission rate as

  R_0 = {Max}(EV(C)) \times \lambda \gamma

• r0_to_lambda() calculates the transmission rate as

  \lambda = R_0 / ({Max}(EV(C)) \gamma)

  Note that this is also called the 'force of infection' and is different from the effective transmission rate often denoted \beta.

Here, EV(C) denotes the eigenvalues of the matrix C which is calculated from the social contacts matrix scaled by the number of individuals in each demographic and susceptibility group in the population.

Value

Returns a single number for the calculated value.

Examples

#### Prepare data ####
# Get example dataset and prepare contact matrix and demography
data(polymod_uk)
contact_matrix <- polymod_uk$contact_matrix
demography_vector <- polymod_uk$demography_vector

# define lambda
lambda <- 0.3

# define infectious period of 5 days
infectious_period <- 5
# define the number of age and susceptibility groups
n_demo_grps <- length(demography_vector)
n_risk_grps <- 3

# In this example, risk varies across groups
susceptibility <- matrix(
  data = c(0.5, 0.7, 1.0), nrow = n_demo_grps, ncol = n_risk_grps
)

# risk does not vary within groups
p_susceptibility <- matrix(
  data = 1, nrow = n_demo_grps, ncol = n_risk_grps
)
# p_susceptibility rows must sum to 1.0
p_susceptibility <- p_susceptibility / rowSums(p_susceptibility)

#### Effective R ####
r0 <- 2.0
r_eff(
  r0 = r0,
  contact_matrix = contact_matrix,
  demography_vector = demography_vector,
  susceptibility = susceptibility,
  p_susceptibility = p_susceptibility
)

#### Transmission rate to R0 ####
lambda_to_r0(
  lambda, contact_matrix, demography_vector,
  susceptibility, p_susceptibility,
  infectious_period
)

#### R0 to Transmission rate ####
r0 <- 1.5
r0_to_lambda(
  r0, contact_matrix, demography_vector,
  susceptibility, p_susceptibility,
  infectious_period
)