malariaEquilibriumVivax

Often we are interested in the state of a given malaria transmission model at equilibrium. However, some models (e.g. the Griffin et al. 2014 model, the White et al. 2018 model) are quite complex, and can result in equilibrium solutions that are fairly in-depth. In these situations it is useful to have a “canonical” equilibrium solution that is tried and tested, and can be used reliably by multiple users. This package complements the malariaEquilibrium package to store canonical equilibrium solutions for Plasmodium vivax malaria models.

How to interact with this repos

If you have a new model with an equilibrium solution that you would like to host here, then please go ahead and do so in a new branch. The master branch, on the other hand, should always correspond to the current most active model used by the malaria group (currently the White et al. 2018 model). This should generally be left alone unless you know what you’re doing.

Any changes that you propose to branches that you did not create yourself (e.g. the master branch) should be done through pull requests, rather than editing directly. This gives others the opportunity to review your changes before they are implemented in code.

NB. These stipulations are in place because there are other R packages that test against the equilibrium solutions from this package, and so any changes here may cause other packages to fail if they are not know about beforehand.

Installation

You can install from the master branch of malariaEquilibriumVivax with:

# install.packages("devtools")
devtools::install_github("mrc-ide/malariaEquilibriumVivax")

Or from a specific branch with:

# install.packages("devtools")
devtools::install_github("mrc-ide/malariaEquilibriumVivax", ref = "mybranch")

Finally, don’t forget to load the package with:

library(malariaEquilibriumVivax)
library(malariasimulation)

Example

Working with parameters

It’s possibly easiest to begin with the default vivax parameter set as found in malariasimulation.

vivax_params <- get_parameters(parasite = "vivax")

We can modify parameter values exactly as we would with a named list:

vivax_params$eta <- 0.1
head(vivax_params)
#> $dd
#> [1] 5
#> 
#> $dt
#> [1] 1
#> 
#> $da
#> [1] 10
#> 
#> $dpcr_max
#> [1] 70
#> 
#> $dpcr_min
#> [1] 10
#> 
#> $kpcr
#> [1] 4.602

These do not have parameter names that are consistent with Michael White’s model and must be translated for use in the equilibrium solution.

vivax_eq_params <- malariasimulation:::translate_vivax_parameters(vivax_params)

Getting the equilibrium solution

Now we can calculate the equilibrium solution using the vivax_equilibrium() function. This assumes a fixed EIR and treatment rate (ft), and takes model parameters as input. It calculates the equilibrium solution for a defined age range:

eq <- vivax_equilibrium(EIR = 10, ft = 0.2, p = vivax_eq_params, age = 0:10)

We have two equilibrium solutions: a full solution that loops over hypnozoite batch numbers until reaching a limit (the default limit is set to 10 hypnozoite batches), and a simplified, approximate, version that calculates the average for each age and biting heterogeneity group.

eq <- vivax_equilibrium(EIR = 10, ft = 0.2, p = vivax_eq_params, age = 0:10, v_eq = "simplified")

The output elements are “states” and “FOIM”. The former is a matrix with age brackets in rows, and model states or other downstream calculations in columns. For example, the column “S” gives the equilibrium proportion of humans in the susceptible state.

head(eq$states[[1]])
#>   age       prop            S            U            A            D
#> 1   0 0.04347126 8.761186e-05 0.0001821670 0.0001778841 2.704346e-05
#> 2   1 0.04158151 8.125013e-05 0.0001506895 0.0002141042 1.417579e-05
#> 3   2 0.03977391 6.917851e-05 0.0001696545 0.0001952529 8.791530e-06
#> 4   3 0.03804489 6.131761e-05 0.0001909988 0.0001654373 6.787005e-06
#> 5   4 0.03639103 5.552787e-05 0.0002068250 0.0001384096 5.742089e-06
#> 6   5 0.03480906 5.073966e-05 0.0002167239 0.0001165638 5.050992e-06
#>              T            P       ID          IDM       ICA          ICM
#> 1 1.367281e-06 1.330026e-05 10.57063 3.998968e-01  18.34678 2.714350e+00
#> 2 7.022980e-07 7.178265e-06 22.33676 1.235799e-05  43.05848 8.388141e-05
#> 3 4.368955e-07 4.436999e-06 34.00066 3.818982e-10  70.75929 2.592182e-09
#> 4 3.384367e-07 3.407793e-06 45.14801 1.180178e-14  99.90119 8.010607e-14
#> 5 2.866831e-07 2.877534e-06 55.62886 3.647096e-19 129.66663 2.475513e-18
#> 6 2.523018e-07 2.529270e-06 65.39694 1.127060e-23 159.58217 7.650064e-23
#>          HH EIR       inf       E_M       I_M  inf_rvoir      mv0       psi
#> 1  3.093588  10 0.3404829 0.4828513 0.2377735 0.01254184 258.7219 0.3090514
#> 2  6.138467  10 0.3404829 0.4828513 0.2377735 0.02794163 258.7219 0.4529588
#> 3  8.988822  10 0.3404829 0.4828513 0.2377735 0.04860308 258.7219 0.5799565
#> 4 11.588919  10 0.3404829 0.4828513 0.2377735 0.07346903 258.7219 0.6920317
#> 5 13.927406  10 0.3404829 0.4828513 0.2377735 0.10152487 258.7219 0.7909376
#> 6 16.013886  10 0.3404829 0.4828513 0.2377735 0.13200393 258.7219 0.8782218
#>     phi_clin phi_patent       dPCR
#> 1 0.19089373  0.8042138 0.03026526
#> 2 0.05938605  0.5571232 0.08782813
#> 3 0.03199827  0.3375802 0.09799606
#> 4 0.02450078  0.2112293 0.09944715
#> 5 0.02162766  0.1422464 0.09978762
#> 6 0.02027758  0.1027153 0.09989899

The “FOIM” element gives the onward force of infection from humans to mosquitoes, which is a single number:

eq$FOIM
#> [1] 0.1423578