# exDE (Extensible Differential Equations for mosquito-borne pathogen modeling)

## What is exDE?

exDE provides tools to set up modular ordinary and delay differential equation spatial models for mosquito-borne pathogens, focusing on malaria. Modularity is achieved by method dispatch on parameter lists for each component which is used to compute the full set of differential equations. The function exDE::xDE_diffeqn computes the gradient of all state variables from those modular components and can be used with the excellent solvers in deSolve, or other differential equation solvers in R. exDE can be regarded as the continuous-time companion to the discrete stochastic Micro-MoB framework.

To get started, please consider reading some of the articles in the drop down panels above, at our website. The 3 sections ending in “Component” describe particular models implementing the interface for each of those components (adult mosquitoes, aquatic mosquitoes, and humans), and show a simulation at their equilibrium values.

The section “Articles” has more in-depth examples, including an extended walk through of how to set up and run a model in vignette("ex_534"), a guide on how to contribute, and an example of running a model in exDE with external forcing under a model of ITN (insecticide treated nets) based vector control in vignette("vc_lemenach").

The section “Functions” documents each function exported by the package.

## Installation

To install from an R session, run the following lines of code.

library(devtools)
devtools::install_github("dd-harp/exDE")

## Contributing

For information about how to contribute to the development of exDE, please read our article on how to contribute at vignette("Contributing")!

## Model building in exDE

Models for mosquito borne pathogen transmission systems are naturally modular, structured by vector life stage, host population strata, and by the spatial locations (patches) at which transmission occurs (see figure below).

Models in the exDE framework are constructed from 3 dynamical components:

• $$\mathcal{M}$$: adult mosquitoes, whose dynamics are described by $$d\mathcal{M}/dt$$
• $$\mathcal{L}$$: aquatic (immature) mosquitoes, whose dynamics are described by $$d\mathcal{L}/dt$$
• $$\mathcal{X}$$: human population, whose dynamics are described by $$d\mathcal{X}/dt$$

The combined state from these 3 components is the entire state of the dynamical model, and their combined dynamics described by their differential equations represents the full endogenous dynamics of the system. In addition there are 2 more components which do not directly contribute to the state of the model, but instead modify parameters and compute intermediate quantities to represent external influences on the system. These are:

• Exogenous forcing: weather, climate, unmodeled populations
• Vector control: public health and mosquito control interventions which affect the dynamical components

There are also functions which handle the exchange of information (flows) between the dynamical components and which couple their dynamics. Bloodfeeding is the process by which adult mosquitoes seek out and feed on blood hosts, and results in the quantities $$EIR$$ (entomological inoculation rate) and $$\kappa$$, the net infectiousness of humans to mosquitoes, which couple the dynamics of $$\mathcal{M}$$ and $$\mathcal{X}$$. Likewise emergence of new adults from aquatic habitats and egg laying by adults into habitats couples $$\mathcal{M}$$ and $$\mathcal{L}$$.

The function exDE::xDE_diffeqn compute the necessary quantities and returns a vector of derivatives of all state variables which can be used to solve trajectories from a model in exDE. The program flow within this function is summarized by this diagram: