calc_risk: Calculate risk from one pathogen exposure

In bryanmayer/multdr: Simulating and fitting multiple exposure infectious disease dose-response models

Description

This function takes a pathogen exposure and calculates the risk of infection over its persistence within host

Usage

calc_risk(exposure, survival_time = Inf, hazard_risk, clr)

Arguments

exposure	The initial level of the pathogen exposure
survival_time	The range of time to calculate the risk over (default infinity)
hazard_risk	The per time risk of exposure during persistence
clr	The clearance rate of exposure

Details

The risk is derived using a surival function. exposure = p, survival_time = T, hazard_risk = β, and clearance rate = c. Note: every calculation assumes that time starts at 0

The pathogen is assumed to be cleared exponentially (P(0) = p)

dP/dt = -cP

The pathogens pose a risk of infection during their persistance that can be used to calculate the survival function

λ(t) = β * P(t)

S(T) = exp(-integral(0, T) λ(t)dt)

S(t) = exp(-β/c * p * (1 - exp(-cT))

which simplifies as T -> Inf to

S(T) = exp(-β/c * p)

The risk is 1 - S(T).

Value

risk calculation over the time specified in survival time

See Also

calc_risk_mult for mulitple exposures.

Examples

calc_risk(1e8, 1, 1e-8, 1)
calc_risk(exposure = 1e8, hazard_risk = 1e-8, clr = 1)

bryanmayer/multdr documentation built on May 13, 2019, 8:11 a.m.