From 2a42e8c75e76c285794e214936e3fcfd975ea635 Mon Sep 17 00:00:00 2001
From: David Smith
Lambda
or \(\Lambda\) - the emergence rates of adult
+mosquitoes in the patches
kappa
or \(\kappa\)
+- net infectiousness (NI), the probability a mosquito becomes infected
+after blood feeding on a human. The dynamical terms output by \(\cal MYZ\) models are:
F_fqZ
outputs the number of bites by infectious
+mosquitoes, per patch, per day
F_fqM
outputs the number of bites by mosquitoes, per
+patch, per day
F_eggs
outputs the number of eggs laid by
+mosquitoes, per patch, per day
In this vignette, we discuss the challenge of extensibility, +in particular, the challenges of modeling malaria transmission by +mosquitoes as a changing baseline that has been modified by +vector control.
+The models in ramp.xds
were included
+for several reasons:
They serve as an important set of models to test the software;
The basic mosquito models in ramp.xds
-are variants of George Macdonald mathematical models, developed with
-help from P. Armitage. The variables for all the models in
-ramp.xds
are mosquito densities, and the
-default model is from Aron & May, 1982.
These models all use a common set of parameters:
+\(f\) the patch-specific overall +feeding rates
\(q\) the patch-specific human +fraction
\(g\) the patch-specific +mortality rate
\(\sigma\) the patch-specific +emigration rate
\(\mu\) patch-specific mortality +associated with emigration
\(\nu\) patch-specific +egg-laying rates
\(\cal K\) a dispersal +matrix
ramp.xds
there are several versions of
basic models for mosquito infection dynamics. These models make similar
assumptions about mosquito ecology and infection dynamics. (The
equations are in the documentation for The four models are
basicM
- see [dMYZdt.basicM] does not
-include any infection dynamics.basicM
- no infection dynamics (see dMYZdt.basicM)
-basicM <- xds_setup(MYZname = "basicM", Xname = "trivial", Xopts = list(kappa = .1, Y=0, Z=0))
+basicM <- xds_setup(Xname = "trivial", Xopts = list(kappa = .1),
+ MYZname = "basicM")
+
basicM <- xde_solve(basicM, Tmax=80)
si
- A standard SI compartmental model
-for infection, see [dMYZdt.si].
-RM <- xds_setup(MYZname = "RM", Xname = "trivial", Xopts = list(kappa = .1), MYZopts = list(Y=0, Z=0))
+RM <- xds_setup(Xname = "trivial", Xopts = list(kappa = .1),
+ MYZname = "RM", MYZopts = list(Y=0, Z=0))
+
RM <- xde_solve(RM, Tmax=80)
If \(M\) and \(\kappa\) have reached the steady state, then the fraction of infected mosquitoes, \(y=Y/M\) is given by:
\[y =
@@ -341,13 +373,13 @@ This is equivalent to Macdonald’s formula. In Infectiousnessxds_plot_Z(sei, llty=1, clrs="darkblue")
xds_plot_Z(si, add=TRUE, clrs = "darkred")
xds_plot_Z(RM, add=TRUE, clrs = "orange")
-
+
xds_plot_Z_fracs(sei, clrs="darkblue")
xds_plot_Z_fracs(RM, add=T, clrs = "orange")
xds_plot_Z_fracs(sei, add=T, clrs="darkblue")
xds_plot_Z_fracs(si, add=T, clrs = "darkred")
ramp.xds
this set of equations is
implemented. This sets up and solves a model with \(\kappa\) and \(\Lambda\) passed as constant values, and a
@@ -359,7 +391,7 @@ Infectiousnessxds_plot_M(rm)
xds_plot_Y(rm, add=TRUE)
xds_plot_Z(rm, add=TRUE)
-
+
Macdonald’s Formula
@@ -373,11 +405,12 @@
Macdonald’s FormulaLo = list(season = function(t){1+sin(2*pi*t/365)},
trend = function(t){exp(-t/1000)},
Lambda =5)
-rm = xds_setup(Xname = "trivial", Xopts = list(kappa=0.1), Lname = "trivial", Lopts = Lo, HPop=10)
+rm = xds_setup(Xname = "trivial", Xopts = list(kappa=0.1), HPop=10,
+ Lname = "trivial", Lopts = Lo)
rm <- xde_solve(rm, 3680, dt=10)
xds_plot_M(rm)
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