This implements a delay differential equation model for adult mosquito ecology and
infection dynamics that is consistent with the model published by George
Macdonald in 1952. A generalized version of this model, the MY module GeRM,
was developed to handle exogenous forcing by weather and vector control. This model
should be used only for educational purposes.
Variables:
\(M\): the density of adult mosquitoes
\(Y\): the density of infected adult mosquitoes
\(Z\): the density of infectious adult mosquitoes
Parameters and Terms:
\(\Lambda\) or
Lambda: the emergence rate of adult mosquitoes (fromF_emerge)\(f\) or
f: the blood feeding rate\(q\) or
q: maturation rate\(\tau\) or
eip: the extrinsic incubation period\(\Omega\) or
Omega: an adult mosquito demographic matrix, including mortality and migration\(\Upsilon\) or
Upsilon: survival and dispersal through the eip, \(\Upsilon= e^{-\Omega \tau}\)
Dynamics: In the delay equation, we use the subscript to denote the lagged value of a variable or term: e.g., \(M_\tau = M(t-\tau)\).
$$ \begin{array}{rl} dM/dt &= \Lambda - \Omega \cdot M \\ dY/dt &= fq\kappa(M-Y) - \Omega \cdot Y \\ dZ/dt &= \Upsilon \cdot (fq\kappa)_\tau(M_\tau-Y_\tau) - \Omega \cdot Y \\ \end{array}$$
This model was included mainly for the historical interest. It has been updated to handle
exogenous forcing by weather and vector control in the module GeRM
Usage
# S3 method for class 'macdonald'
dMYdt(t, y, xds_obj, s)Value
a numeric vector