Derivatives for the queuing model \(M/M/\infty\)

This queuing model \(M/M/\infty\) tracks the MoI in a cohort of humans as it ages. It assumes a time- and age-dependent hazard rate for infection, called the force of infection (FoI, \(h_\tau(a)\)). Infections do not affect each other, and each one clears independently at the rate \(r\).

Let \(\zeta_i\) the fraction of the population with MoI = i, then $$\frac{d\zeta_0}{da}= -h_\tau(a) \zeta_0 + r \zeta_1$$ and for \(i\geq 1\) $$\frac{d\zeta_i}{da}= h_\tau(a) \left( \zeta_{i-1} - \zeta_i \right) - ri \zeta_i + r(i+1)\zeta_{i+1}$$

This function computes the derivatives in a form that can be used by deSolve::ode.

dMoIda(a, M, pars, FoIpar)

Arguments

a

the host age

M

the state variables

pars

the parameters

FoIpar

\(h_\tau(a)\), a list formatted to compute FoI

Value

the derivatives as a list

See also

solveMMinfty