samubernard

---
title: "Pharmacokinetics Pharmacodynamics with `DeSolve`"
author: "INSA Lyon - 3BIM EDO Modelling"
date: '2019-01-28'
output: slidy_presentation
---

```{r, message=FALSE, warning=FALSE, include=FALSE}
library(DiagrammeR)
library(deSolve) # need library `deSolve`

samubernard

%% FitzHugh-Nagumo avec diffusion 1D
% 1D FitzHugh-Nagumo with diffusion

% parametre des equations
% equation parameters
epsilon = 0.08;
b = 0.7;
c = 0.8;
D = .01;        % coefficient de diffusion/diffusion coefficient
I = 0.0;

samubernard

% Equation FKPP difference finie 1D implicite Crank-Nicolson
% FKPP equation with finite-difference implicite Crank-Nicolson

% parametre des equations/equation parameters
r = 0.5; % taux de croissance/growth rate
D = 0.1; % coefficient de diffusion/diffusion coefficient

% parametres de simulation, espace/space simulation parameters
% x in domain Omega = [x0,x1]
h = 0.05;  % intervalle de discretisation spatiale/space step

samubernard

#!/usr/bin/python2.6
# -*-coding:Latin-1 -*

from numpy import *

"""
module python pour factorisation QR avec méthodes de Gram-Schmidt et Householder
Algèbre linéaire et matricielle 3BIM INSA Lyon
2014 v20/11/2014
"""

samubernard

%% Turing Patterns in 2D: an example with the FitzHugh-Nagumo equations 

% parametre des equations
% equation parameters
epsilon = 0.08;
b = 0.7;
c = 0.8;
Dv = 0.1;
Dw = 1.6; 
I = 0.35;

samubernard

% Equation FKPP difference finie 2D inplicite Crank-Nicolson avec
% approximation ADI approximation: alternate direction implicit method
% FKPP equation finite-difference explicite 2D

% parametre des equations/equation parameters
r = 0.5; % taux de croissance
D = 0.1; % coefficient de diffusion

% parametres de simulation, espace/space simulation parameters
% x in Omega [0,Sx]x[0,Sy]

samubernard

% Equation FKPP difference finie 2D implicite Crank-Nicolson
% FKPP equation finite-difference implicite Crank-Nicolson 2D

% parametre des equations/equation parameters
r = 0.5; % taux de croissance/growth rate
D = 0.1; % coefficient de diffusion/diffusion coefficient

% parametres de simulation, espace
% x in Omega [0,Sx]x[0,Sy]
h = 0.025;  % intervalle de discretisation spatiale/space step

samubernard

% Equation FKPP difference finie 2D explicite
% FKPP equation finite-difference explicite 2D

% parametre des equations/equation parameters
r = 0.5; % taux de croissance
D = 0.1; % coefficient de diffusion

% parametres de simulation, espace/space simulation parameters
% x in Omega [0,Sx]x[0,Sy]
h = 0.025;  % intervalle de discretisation spatiale/space step

samubernard

# Systems Biology - Université Lyon 1 
# Fall 2021
#
# Inferring parameters from a ODE model 
# --------------------------------------
#
# This script shows how to fit an ODE model to 
# a dataset.
#
# The dataset is the first subject of the Indometh dataset

samubernard

%% 2D reaction-diffusion equation, explicit method

% equation parameters
r = 1.0; % some model parameter
D = 0.1; % diffusion coefficient

% Simulation parameters: space
% Domain: rectangle of size Sx by Sy
h = 0.2; % grid step size
Sx = 10.0;