juliaepi / mathepiamodels.jl

Epidemic spatial and temporal model setup and simulation. Focusing on state of the art epidemiology models such as universal differential equations, epidemiology-informed deep learning models. Part of Mathepia.jl

MathepiaModels

MathepiaModels.jl is part of Mathepia.jl: Spatial and temporal epidemiology data mining flow tools including data processing and analysis, model setup and simulation, inference and evaluation.

It focuses on models setup, simulation and analysis. It is at very beginning stage. The followings are features will be included in the future.

Models will be designed to include

• classical epidemic compartment models such as SIS, SIR, SEIR, SEIAR models and so on.
• Network epidemic models
• Agent based epidemic models
• epidemic models with spatial and temporal heterogeneity, such as delayed, periodic, reaction diffusion epidemic models
• models with neural networks embeded
• models in some state-of-the-art references
• users defined models

The ways to define epidemic models will include determinstic, stochastic methods.

Simulation will be designed to include

• determinstic
• stochastic

Analysis will be designed to include

• Stability of disease free equilibria (DFE) and endemic equilibria (EE)
• Calculation of basic reproduction number
• Calculation of the peak of epidemic
• Calculation of final epidemic size
• Calculation of epidemicity
• Calculation of herd immunity level
• Calculation of time to extinction

Installation

The package can be installed with the Julia package manager. From the Julia REPL, type ] to enter the Pkg REPL mode and run:

pkg> add MathepiaModels

Or, equivalently, via the Pkg API:

julia> import Pkg; Pkg.add("MathepiaModels")

Documentation

• STABLE
• DEVEL

Related Packages and Works

The other parts of Mathepia.jl: Spatial and temporal epidemiology data mining flow tools is as follows:

• MathepiaData.jl: Spatial and temporal data preprocessing and analysis
• MathepiaInference.jl: Bayesian inference tools.
• MathepiaOptimal.jl: Optimization, optimal control and optimal transport tools

MathepiaModels.jl is dependent on many packages from SciML Open Source Scientific Machine Learning. They do a lot of excellent works and packages. Because of them, I find my idol ChrisRackauckas, become to love julia and decide to do some contributions.

Other packages or works on epidemic models:

• jangevaare/Pathogen.jl
• epirecipes/sir-julia: Various implementations of the classical SIR model in Julia

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