Compute the derivatives for SIS compartmental model:
\(S\) is the density of susceptible humans (or hosts)
\(I\) is the density of infected humans (or hosts)
\(H=S+I\) is human (or host) population density
The clearance rate for infections is \(r\), and by assumption, individuals are assumed to be susceptible to infection after clearing infections.
The model has a port to model mass treatment, in equations \(\xi(t)\).
The xds implementation computes \(dH/dt\)
rather than \(dS/dt.\) In the functions get_XH_vars
and parse_XH_orbits,
\(S\) is computed as \(S=H-I\) and listed as a variable. The
derivatives computed are:
$$ \begin{array}{rl} dH/dt = & B(t,H) + D \cdot H \\ dI/dt = & h (H-I) - r I - \xi(t) + D \cdot I \end{array} $$ where \(S=H-I\);
\(\xi(t)\) is a function to simulate mass treatment; \(B(t, H)\) is the time-dependent birth rate; and \(D\) is a linear operator, a matrix describing demographic changes, including mortality, migration, and aging;
Usage
# S3 method for class 'SIS'
dXHdt(t, y, xds_obj, i)