renewal_function: Renewal equation solution to the expectation of the...

In pspc-data-science/branchsim: Gamma negative binomial branching process simulation of epidemics

Description

This function numerically solves the renewal equation for a CMJ process using the properties of the triple (λ_{χ}, ξ_χ, χ). See appendix C of Branching Processes in Biology by Kimmel and Axelrod for more details. Z = G(t) + \int_0^t Z(t - u)\, mu(du)

Usage

renewal_function(dMu, G = 1, Time_limit = 100, nstep = 10000)

Arguments

dMu	The function dMu(t) defines mu(dt) = dMu(t)\,dt. Function as argument.
G	A function that that defines the expectation of the random characteristic of interest. Default G=1 (total number born). Function as argument.
nstep	The number of steps for the integration. Default is 10^4.
T	The maximum of the time interval for integration 0,T. Default is T =100.

Value

A tibble containing the time steps with the solution to the renewal equation.

pspc-data-science/branchsim documentation built on Jan. 19, 2021, 10:10 a.m.