Make documentation intro and readme more succinct

README.md

@@ -1,55 +1,53 @@
 ## pySODM
 *Simulating and Optimising Dynamical Models in Python 3*
 
+Resources: [documentation](https://twallema.github.io/pySODM), [peer-reviewed paper](https://www.sciencedirect.com/science/article/pii/S1877750323002089), [pyPI](https://pypi.org/project/pySODM/)
+
 ![build](https://github.com/twallema/pySODM/actions/workflows/tests.yml/badge.svg) ![docs](https://github.com/twallema/pySODM/actions/workflows/deploy.yml/badge.svg) [![HitCount](https://hits.dwyl.com/twallema/pySODM.svg)](https://hits.dwyl.com/twallema/pySODM)
 
 ### Quick installation 
 ```
 pip install pySODM
 ```
-### Resources
-
-Documentation: https://twallema.github.io/pySODM
-
-Manuscript: https://www.sciencedirect.com/science/article/pii/S1877750323002089
-
-pyPI: https://pypi.org/project/pySODM/ 
 
 ### Aim & Scope
 
-A modeling and simulation workflow will typically constitute the following steps (see [Villaverde et. al](https://doi.org/10.1093/bib/bbab387)),
-1. Build a system dynamical model to describe some real-world phenomenon. Assess structural identifiability.
-2. Calibrate the model to a set of experimental data.
-3. Extract knowledge from the calibrated parameter values (assess practical identifiability).
-4. Use the model to make projections outside the calibrated range.
+All the simulation projects I've undertaken over the past six years required me to do most of the following,
+1. Integrate a system dynamical model
+2. Its states may be represented by n-dimensional numpy arrays, labeled using coordinates
+3. Its parameters may have time-dependencies 
+4. Its parameters may have to be sampled from distributions
+5. It may have to be calibrate to a dataset(s) by defining and optimising a cost function
 
-The aim of pySODM is to reduce the time it takes to step through this workflow. pySODM provides a *template* to construct, simulate and calibrate dynamical systems governed by differential equations. Models can have n-dimensional labeled states of different sizes and can be simulated deterministically and stochastically. Model parameters can be time-dependent by means of complex functions
-with arbitrary inputs. The labeled n-dimensional model states can be aligned with n-dimensional
-data to compute the posterior probability function, which can subsequently be optimised.
+all these features required me to wrap code around an ODE solver, typically `scipy.solve_ivp`, and I got tired of recycling the same code over and over again, so I packaged it into pySODM.
+
+Does other simulation software exist in Python? Sure, but most of them hold your hand by having you define symbolic transitions, which places a limit on the attainable complexity of a model, making it unfit for academic research. I wanted a piece a software that nicely does all the nasty bookkeeping like keeping track of state sizes, time dependencies on parameters, aligning simulations with datasets etc. and does so in a **generically applicable** way so that I'd never hit a software wall mid-project.
 
 ### Overview of features
 
 | Workflow                     | Features                                                                                                                        |
 |------------------------------|---------------------------------------------------------------------------------------------------------------------------------|
-| Construct a dynamical model     | Implement coupled systems of differential equations            |
-|                                 | States can be n-dimensional and of different sizes, allowing users to build models with subprocesses                                       |
-|                                 | Allows n-dimensional model states to be labelled with coordinates and dimensions by using `xarray.Dataset}` to store simulation output |
-|                                 | Easy indexing, manipulating, saving, and piping to third-party software of model output by formatting simulation output as `xarray.Dataset` |
-| Simulating the model            | Continuous and discrete deterministic simulation or discrete stochastic simulation (Jump processes, Gillespie's Stochastic Simulation Algorithm or Tau-Leaping) |
-|                                 | Vary model parameters during the simulation generically using a complex function |
-|                                 | Use *draw functions* to perform repeated simulations for sensitivity analysis. With multiprocessing support |
+| Construct a dynamical model     | Implement systems of coupled differential equations            |
+|                                 | Labeled n-dimensional model states, states can have different sizes                                     |
+|                                 | Leverages `xarray.Dataset` to store labeled n-dimensional simulation output |
+| Simulating the model            | Deterministic (ODE) or stochastic simulation (Jump process) |
+|                                 | *Time-dependent model parameter functions* to vary parameters during the course of a simulation |
+|                                 | *Draw functions* to vary model parameters during consecutive simulations. |
 | Calibrate the model             | Construct and maximize a posterior probability function  |
-|                                 | Automatic alignment of data and model forecast over timesteps and coordinates  |
-|                                 | Nelder-Mead Simplex and Particle Swarm Optimization for point estimation of model parameters |
-|                                 | Pipeline to and backend for `emcee.EnsembleSampler` to perform Bayesian inference of model parameters                           |
+|                                 | Automatically aligns data and model forecast  |
+|                                 | Nelder-Mead Simplex and Particle Swarm Optimization |
+|                                 | Bayesian inference with `emcee.EnsembleSampler`                  |
+
 
 ### Getting started
 
-The [quistart tutorial](quickstart.md) will teach you the basics of building and simulating models with n-dimensional labeled states in pySODM. It will demonstrate how to vary model parameters over the course of a simulation and how to perform repeated simulations with sampling of model parameters.
+- Detailed [installation instructions](installation.md).
+
+- The [quistart tutorial](quickstart.md) teaches the basics of building and simulating models with n-dimensional labeled states in pySODM. It demonstrates the use of *time-dependent parameter functions* (TDPFs) to vary model parameters over the course of a simulation and *draw functions* to vary model parameters during consecutive simulations.
 
-The [workflow](worfklow.md) tutorial provides a step-by-step introduction to a modeling and simulation workflow by inferring the distributions of the model parameters of a simple compartmental disease model using a synthetic dataset. 
+- The [workflow](worfklow.md) tutorial provides a step-by-step introduction to building a mathematical model and calibrating its parameters to a dataset. An SIR disease model is built and the basic reproduction number during an outbreak is determined by calibrating the model to the outbreak data. 
 
-The [enzyme kinetics](enzyme_kinetics.md) and [influenza 17-18](influenza_1718.md) case studies apply the modeling and simulation workflow to more advanced, real-world problems. In the enzyme kinetics case study, a 1D packed-bed reactor model is implemented in pySODM by reducing the two PDEs to a set of coupled ODEs by using the method-of-lines. In the Influenza 17-18 case study, a stochastic, age-structured model for influenza is developped and calibrated to the Influenza incidence data reported by the Belgian Federal Institute of Public Health. These case studies mainly serve to demonstrate pySODM's capabilities across scientific disciplines and highlight the arbitrarily complex nature of the models that can be built with pySODM. For an academic description of pySODM and on the Enzyme Kinetics and Influenza 17-18 case studies, checkout our [manuscript](https://arxiv.org/abs/2301.10664).
+- The [enzyme kinetics](enzyme_kinetics.md) and [influenza 17-18](influenza_1718.md) case studies apply the [workflow](workflow.md) to more advanced, real-world problems. In the enzyme kinetics case study, a 1D packed-bed reactor model is implemented in pySODM by reducing the PDEs to a set of coupled ODEs by using the method-of-lines. In the Influenza 17-18 case study, a stochastic, age-structured model for influenza is developped and calibrated to the Influenza incidence data reported by the Belgian Federal Institute of Public Health. These case studies mainly serve to demonstrate pySODM's capabilities across scientific disciplines and highlight the arbitrarily complex nature of the models that can be built with pySODM. For an academic exposee of pySODM, the Enzyme Kinetics and Influenza 17-18 case studies, checkout our [peer-reviewed paper](https://www.sciencedirect.com/science/article/pii/S1877750323002089).
 
 ### Versions