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README.md

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# JumpProcesses.jl
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[![Join the chat at https://julialang.zulipchat.com #sciml-bridged](https://img.shields.io/static/v1?label=Zulip&message=chat&color=9558b2&labelColor=389826)](https://julialang.zulipchat.com/#narrow/stream/279055-sciml-bridged)
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[![Stable](https://img.shields.io/badge/docs-stable-blue.svg)](http://jump.sciml.ai/stable/)
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[![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](http://jump.sciml.ai/dev/)
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[![Global Docs](https://img.shields.io/badge/docs-SciML-blue.svg)](https://docs.sciml.ai/dev/modules/JumpProcesses/)
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[![Global Docs](https://img.shields.io/badge/docs-SciML-blue.svg)](https://docs.sciml.ai/JumpProcesses/stable/)
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[![Coverage Status](https://coveralls.io/repos/github/SciML/JumpProcesses.jl/badge.svg?branch=master)](https://coveralls.io/github/SciML/JumpProcesses.jl?branch=master)
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[![codecov](https://codecov.io/gh/SciML/JumpProcesses.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/SciML/JumpProcesses.jl)
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[DifferentialEquations.jl](https://github.com/JuliaDiffEq/DifferentialEquations.jl).
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For information on using the package,
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[see the stable documentation](http://jump.sciml.ai/stable/). Use the
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[in-development documentation](http://jump.sciml.ai/dev/) for the version of
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[see the stable documentation](https://docs.sciml.ai/JumpProcesses/stable/). Use the
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[in-development documentation](https://docs.sciml.ai/JumpProcesses/dev/) for the version of
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the documentation, which contains the unreleased features.
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The documentation includes
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- [a tutorial on simulating basic Poisson processes](https://jump.sciml.ai/stable/tutorials/simple_poisson_process/)
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- [a tutorial and details on using JumpProcesses to simulate jump processes via SSAs (i.e. Gillespie methods)](https://jump.sciml.ai/stable/tutorials/discrete_stochastic_example/),
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- [a tutorial on simulating jump-diffusion processes](https://jump.sciml.ai/stable/tutorials/jump_diffusion/),
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- [a reference on the types of jumps and available simulation methods](https://jump.sciml.ai/stable/jump_types/),
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- [a reference on jump time stepping methods](https://jump.sciml.ai/stable/jump_solve/),
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- [a FAQ](https://jump.sciml.ai/stable/faq) with information on changing parameters between simulations and using callbacks,
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- [the JumpProcesses.jl API documentation](https://jump.sciml.ai/stable/api/).
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- [a tutorial on simulating basic Poisson processes](https://docs.sciml.ai/JumpProcesses/stable/tutorials/simple_poisson_process/)
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- [a tutorial and details on using JumpProcesses to simulate jump processes via SSAs (i.e. Gillespie methods)](https://docs.sciml.ai/JumpProcesses/stable/tutorials/discrete_stochastic_example/),
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- [a tutorial on simulating jump-diffusion processes](https://docs.sciml.ai/JumpProcesses/stable/tutorials/jump_diffusion/),
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- [a reference on the types of jumps and available simulation methods](https://docs.sciml.ai/JumpProcesses/stable/jump_types/),
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- [a reference on jump time stepping methods](https://docs.sciml.ai/JumpProcesses/stable/jump_solve/),
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- [a FAQ](https://docs.sciml.ai/JumpProcesses/stable/faq) with information on changing parameters between simulations and using callbacks,
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- [the JumpProcesses.jl API documentation](https://docs.sciml.ai/JumpProcesses/stable/api/).
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## Installation
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There are two ways to install `JumpProcesses.jl`. First, users may install the meta
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To install the `DifferentialEquations.jl` package, refer to the following link
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for complete [installation
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details](https://docs.sciml.ai/dev/modules/DiffEqDocs/).
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details](https://docs.sciml.ai/DiffEqDocs/stable/).
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If the user wishes to separately install the `JumpProcesses.jl` library, which is a
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lighter dependency than `DifferentialEquations.jl`, then the following code will

docs/make.jl

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doctest = false,
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format = Documenter.HTML(; analytics = "UA-90474609-3",
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assets = ["assets/favicon.ico"],
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canonical = "https://jump.sciml.ai/stable/",
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canonical = "https://docs.sciml.ai/JumpProcesses/",
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prettyurls = (get(ENV, "CI", nothing) == "true"),
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mathengine),
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pages = pages)

docs/src/faq.md

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## How can I access earlier solution values in callbacks?
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When using an ODE or SDE time-stepper that conforms to the [integrator
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interface](https://docs.sciml.ai/dev/modules/DiffEqDocs/basics/integrator/) one
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interface](https://docs.sciml.ai/DiffEqDocs/stable/basics/integrator/) one
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can simply use `integrator.uprev`. For efficiency reasons, the pure jump
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[`SSAStepper`](@ref) integrator does not have such a field. If one needs
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solution components at earlier times one can save them within the callback

docs/src/index.md

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JumpProcesses is a component package in the [SciML](https://sciml.ai/) ecosystem,
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and one of the core solver libraries included in
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[DifferentialEquations.jl](https://github.com/JuliaDiffEq/DifferentialEquations.jl).
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[DifferentialEquations.jl](https://docs.sciml.ai/DiffEqDocs/stable/).
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The documentation includes
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- [a tutorial on simulating basic Poisson processes](@ref poisson_proc_tutorial)
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To install the `DifferentialEquations.jl` package, refer to the following link
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for complete [installation
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details](https://docs.sciml.ai/dev/modules/DiffEqDocs/).
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details](https://docs.sciml.ai/DiffEqDocs/stable).
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If the user wishes to separately install the `JumpProcesses.jl` library, which is a
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lighter dependency than `DifferentialEquations.jl`, then the following code will

docs/src/jump_types.md

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```
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is preferred over
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```julia
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reactant_stoich = [[3 => 1, 1 => 2, 4 = > 2], [3 => 2, 2 => 2]]
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reactant_stoich = [[3 => 1, 1 => 2, 4 => 2], [3 => 2, 2 => 2]]
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```
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JumpProblem(prob,DirectCR(),jump1,jump2; dep_graph=your_dependency_graph)
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```
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For systems with only `MassActionJump`s, or those generated from a
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[Catalyst](https://github.com/SciML/Catalyst.jl) `reaction_network`, this graph
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[Catalyst](https://docs.sciml.ai/Catalyst/stable/) `reaction_network`, this graph
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will be auto-generated. Otherwise you must construct the dependency graph
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manually. Dependency graphs are represented as a `Vector{Vector{Int}}`, with the
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`i`th vector containing the indices of the jumps for which rates must be
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of variable indices. The corresponding variables are those that have their
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value, `u[i]`, altered when the jump occurs.
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For systems generated from a [Catalyst](https://github.com/SciML/Catalyst.jl)
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For systems generated from a [Catalyst](https://docs.sciml.ai/Catalyst/stable/)
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`reaction_network` these will be auto-generated. Otherwise you must explicitly
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construct and pass in these mappings.
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In general, for systems with sparse dependency graphs if `Direct` is slow, one
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of `SortingDirect`, `RSSA` or `RSSACR` will usually offer substantially better
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performance. See
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[DiffEqBenchmarks.jl](https://github.com/JuliaDiffEq/DiffEqBenchmarks.jl) for
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[DiffEqBenchmarks.jl](https://docs.sciml.ai/SciMLBenchmarksOutput/stable/) for
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benchmarks on several example networks.
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## Remaking `JumpProblem`s

docs/src/tutorials/discrete_stochastic_example.md

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!!! note
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This tutorial assumes you have read the [Ordinary Differential Equations tutorial](https://docs.sciml.ai/dev/modules/DiffEqDocs/tutorials/ode_example/) in [`DifferentialEquations.jl`](https://docs.sciml.ai/dev/modules/DiffEqDocs/).
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This tutorial assumes you have read the [Ordinary Differential Equations tutorial](https://docs.sciml.ai/DiffEqDocs/stable/tutorials/ode_example/) in [`DifferentialEquations.jl`](https://docs.sciml.ai/DiffEqDocs/stable).
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We begin by demonstrating how to build jump processes using
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[JumpProcesses.jl](https://github.com/SciML/JumpProcesses.jl)'s different jump types,
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[JumpProcesses.jl](https://docs.sciml.ai/JumpProcesses/stable/)'s different jump types,
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which encode the rate functions (i.e. transition rates, intensities, or
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propensities) and state changes when a given jump occurs.
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Note, the SIR model considered here is a type of stochastic chemical kinetics
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jump process model, and as such the biological modeling functionality of
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[Catalyst.jl](https://github.com/SciML/Catalyst.jl) can be used to easily
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[Catalyst.jl](https://docs.sciml.ai/Catalyst/stable/) can be used to easily
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specify the model and automatically calculate inputs needed for JumpProcesses's
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optimized simulation algorithms. We summarize this alternative approach at the
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beginning for users who may be interested in modeling chemical systems, but note
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dependency graphs, are automatically calculated.
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We'll make use of the
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[DifferentialEquations.jl](https://github.com/SciML/DifferentialEquations.jl)
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[DifferentialEquations.jl](https://docs.sciml.ai/DiffEqDocs/stable/)
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meta package, which includes JumpProcesses and ODE/SDE solvers, Plots.jl, and
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(optionally) Catalyst.jl in this tutorial. If not already installed they can be
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added as follows
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For those less-familiar with the time-change representation, we next give a more
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intuitive explanation of the model as a collection of chemical reactions, and
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then demonstrate how these reactions can be written in
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[Catalyst.jl](https://github.com/SciML/Catalyst.jl) and seamlessly converted
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[Catalyst.jl](https://docs.sciml.ai/Catalyst/stable/) and seamlessly converted
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into a form that can be used with the
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[JumpProcesses.jl](https://github.com/SciML/JumpProcesses.jl) solvers. Users
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[JumpProcesses.jl](https://docs.sciml.ai/JumpProcesses/stable/) solvers. Users
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interested in how to directly define jumps using the lower-level JumpProcesses
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interface can skip to [Building and Simulating the Jump Process Using the
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JumpProcesses Low-Level Interface](@ref).
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## Building and Simulating the Jump Processes from Catalyst Models
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Using [Catalyst.jl](https://github.com/SciML/Catalyst.jl) we can input our full
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Using [Catalyst.jl](https://docs.sciml.ai/Catalyst/stable/) we can input our full
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reaction network in a form that can be easily used with JumpProcesses's solvers
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```@example tut2
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using Catalyst
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```
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To build a pure jump process model of the reaction system, where the state is
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constant between jumps, we will use a
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[`DiscreteProblem`](https://docs.sciml.ai/dev/modules/DiffEqDocs/types/discrete_types/).
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[`DiscreteProblem`](https://docs.sciml.ai/DiffEqDocs/stable/types/discrete_types/).
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This encodes that the state only changes at the jump times. We do this by giving
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integrator `affect!(integrator)` (for details on the integrator, see the
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[integrator interface
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docs](https://docs.sciml.ai/dev/modules/DiffEqDocs/basics/integrator/)). Here
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docs](https://docs.sciml.ai/DiffEqDocs/stable/basics/integrator/)). Here
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`u` corresponds to the current state vector of the system; for our SIR model
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`u[1] = S(t)`, `u[2] = I(t)` and `u[3] = R(t)`. `p` corresponds to the parameters of
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the model, just as used for passing parameters to derivative functions in ODE
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Since we want the system state to change only at the discrete jump times, we
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will build a
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[`DiscreteProblem`](https://docs.sciml.ai/dev/modules/DiffEqDocs/types/discrete_types/)
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[`DiscreteProblem`](https://docs.sciml.ai/DiffEqDocs/stable/types/discrete_types/)
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```@example tut2
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prob = DiscreteProblem(u₀, tspan, p)
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```
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## [Reducing Memory Use: Controlling Saving Behavior](@id save_positions_docs)
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Note that jumps act via DifferentialEquations.jl's [callback
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interface](https://docs.sciml.ai/dev/modules/DiffEqDocs/features/callback_functions/),
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interface](https://docs.sciml.ai/DiffEqDocs/stable/features/callback_functions/),
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which defaults to saving at each event. This is required in order to accurately
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resolve every discontinuity exactly (and this is what allows for perfectly
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vertical lines in plots!). However, in many cases when using jump problems you
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may wish to decrease the saving pressure given by large numbers of jumps. To do
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this, you set the `save_positions` keyword argument to `JumpProblem`. Just like
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for other
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[callbacks](https://docs.sciml.ai/dev/modules/DiffEqDocs/features/callback_functions/),
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[callbacks](https://docs.sciml.ai/DiffEqDocs/stable/features/callback_functions/),
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this is a tuple `(bool1, bool2)` which sets whether to save before or after a
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jump. If we do not want to save at every jump, we would thus pass:
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```@example tut2
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jump_prob = JumpProblem(prob, Direct(), jump, jump2; save_positions = (false, false))
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```
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Now the saving controls associated with the integrator should specified, see the
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main [SciML
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Docs](https://docs.sciml.ai/dev/modules/DiffEqDocs/basics/common_solver_opts/)
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Docs](https://docs.sciml.ai/DiffEqDocs/stable/basics/common_solver_opts/)
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for saving options. For example, we can use `saveat = 10.0` to save at an evenly
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```@example tut2

docs/src/tutorials/jump_diffusion.md

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!!! note
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This tutorial assumes you have read the [Ordinary Differential Equations tutorial](https://docs.sciml.ai/dev/modules/DiffEqDocs/tutorials/ode_example/) in [`DifferentialEquations.jl`](https://docs.sciml.ai/dev/modules/DiffEqDocs/).
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This tutorial assumes you have read the [Ordinary Differential Equations tutorial](https://docs.sciml.ai/DiffEqDocs/stable/tutorials/ode_example/) in [`DifferentialEquations.jl`](https://docs.sciml.ai/DiffEqDocs/stable).
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Jump Diffusion equations are stochastic differential equations with discontinuous
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jumps. These can be written as:
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rate(u, p, t) = 2
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```
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Now we define the `affect!` of the jump. This is the same as an `affect!` from a
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[`DiscreteCallback`](https://docs.sciml.ai/dev/modules/DiffEqDocs/features/callback_functions/),
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[`DiscreteCallback`](https://docs.sciml.ai/DiffEqDocs/stable/features/callback_functions/),
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and thus acts directly on the
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[integrator](https://docs.sciml.ai/dev/modules/DiffEqDocs/basics/integrator/).
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[integrator](https://docs.sciml.ai/DiffEqDocs/stable/basics/integrator/).
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Therefore, to make it halve the current value of `u`, we do:
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```@example tut3
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function affect!(integrator)

docs/src/tutorials/simple_poisson_process.md

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`p` and `t`. Likewise, when a jump occurs any
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DifferentialEquations.jl-compatible change to the current system state, as
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encoded by a [DifferentialEquations.jl
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integrator](https://docs.sciml.ai/dev/modules/DiffEqDocs/basics/integrator/), is
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integrator](https://docs.sciml.ai/DiffEqDocs/stable/basics/integrator/), is
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allowed. This includes changes to the current state or to parameter values.
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This tutorial requires several packages, which can be added if not already
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affect!(integrator) = (integrator.u[1] += 1)
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```
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Here the convention is to take a [DifferentialEquations.jl
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integrator](https://docs.sciml.ai/dev/modules/DiffEqDocs/basics/integrator/),
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integrator](https://docs.sciml.ai/DiffEqDocs/stable/basics/integrator/),
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and directly modify the current solution value it stores. i.e. `integrator.u` is
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the current solution vector, with `integrator.u[1]` the first component of this
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vector. In our case we will only have one unknown, so this will be the current

src/SSA_stepper.jl

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sol = solve(jump_prob, SSAStepper())
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```
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see the
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[tutorial](https://jump.sciml.ai/stable/tutorials/discrete_stochastic_example/)
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[tutorial](https://docs.sciml.ai/JumpProcesses/stable/tutorials/discrete_stochastic_example/)
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for details.
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"""
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struct SSAStepper <: DiffEqBase.DEAlgorithm end

src/extended_jump_array.jl

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Extended state definition used within integrators when there are
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`VariableRateJump`s in a system. For detailed examples and usage information see
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the
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- [Tutorial](https://jump.sciml.ai/stable/tutorials/discrete_stochastic_example/)
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- [Tutorial](https://docs.sciml.ai/JumpProcesses/stable/tutorials/discrete_stochastic_example/)
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### Fields
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