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The SIS module for the XH component

Source: R/human-XH-SIS.R
SIS.Rd

In the SIS compartmental model, infected individuals are either susceptible (S), or infected and infectious (I). Susceptible individuals become infected at the per-capita rate \(h\). Infected individuals clear infections at the per-capita rate \(r\), and then they become susceptible to infection again.

Human/host population size (H) is a state variable that can be configured.

and \(H=S+I\): the model computes \(dH/dt\) and \(dI/dt\). When outputs are parsed, S is computed as \(S=H-I\).

This module also includes:

  • a model for human demographic changes; and

  • a port for mass treatment, \(\xi(t)\).

State Variables

H

total human (or host) population density

I

density of infected humans

During parsing, the density of susceptibles is computed as: $$S = H - I$$.

Parameters

r

clearance rate for infections

xi

mass treatment rate

B

time-dependent birth rate function \(B(t, H)\)

D

human demographic matrix

Dynamics

$$ \begin{array}{rl} dH/dt &= B(t,H) + D \cdot H \\ dI/dt &= h(H-I) - rI - \xi(t) + D \cdot I \\ \end{array}$$ where \(h\) is the force of infection computed upstream.