Trace Functions

library(ramp.xds)
library(viridisLite)

As part of the plug-and-play modular design for ramp.xds, each dynamical component includes a trivial model that has no variables. The outputs required by other components are passed as a trace function. These trace functions have three parts:

• a mean value, or a scaling argument

• a function that returns a F_seasonal signal, configured with a line in the appropriate options list, F_season = function(t){...}

• a function that returns a F_trend, configured with a line in the appropriate options list, F_trend = function(t){...}

The trivial modules each returns different values:

• $\cal L$ - The trivial aquatic module is set up by create_Lpar_trivial. The function F_emerge() returns Lambda*F_season(t)*F_trend(t). To override the defaults, Lopts must be a named list that sets the values of the elements:

  • Lambda = c(...) is the

  • F_season = function(t){...}

  • F_trend = function(t){...}

• $\cal MYZ$ - The trivial adult mosquito module is setup by create_MYZpar_trivial. The values will return either F_fqZ or F_eggs

  • Both F_fqZ and F_eggs use the same seasonality and trend functions:

    • F_season = function(t){...}

    • F_trend = function(t){...}

  • the function F_fqZ() returns f*q*Z*F_season(t)*F_trend(t). To configure, MYZopts should be a named list that sets the values of the elements:

    • f = c(...)

    • q = c(...)

    • Z = c(...)

  • the function F_eggs() returns eggs*F_season(t)*F_trend(t); to override the defaults, MYZopts must be a named list that sets the values of the elements:

    • eggs = c(...)

• $\cal X$ - The trivial module for human / host infection and immunity is set up by create_Xpar_trivial. F_X calls F_H and then returns H*kappa*F_season(t)*F_trend(t)

  • F_H is configured in xds_setup by passing HPop = ...

  • To configure F_X, Xopts must be a named list that sets the values of the elements. The values of F_X should be in the interval $[0,H]:$

    • kappa = c(...)

    • F_season = function(t){...}

    • F_trend = function(t){...}

Emergence

The following adult mosquito model is forced by emergence and net infectiousness:

• Lo configures the adult mosquito emergence rate to rise initially, but then to decline with a F_seasonal signal:

Lo = list(F_season = function(t){1+sin(2*pi*t/365)}, 
          F_trend = function(t){(1+t/250)*exp(-t/1000)}, 
          Lambda =5)

• Xo configures the net infectiousness to rise to 80% over time.

Xo = list(kappa = 0.8, 
          F_trend = function(t){exp(t/500)/(10+exp(t/500))})

rm = xds_setup(Xname = "trivial", Xopts = Xo, HPop=10, 
               Lname = "trivial", Lopts = Lo)
rm <- xds_solve(rm, 3650, dt=10)

xds_plot_M(rm)
xds_plot_Y(rm, add=T)
xds_plot_Z(rm, add=T)