currymj/diffeqbayes_delay.jl

## diffeqbayes_delay.jl
using DifferentialEquations
using DiffEqBayes
using Distributions

const p0 = 0.2; const q0 = 0.3; const v0 = 1; const d0 = 5
const p1 = 0.2; const q1 = 0.3; const v1 = 1; const d1 = 1
const d2 = 1; const beta0 = 1; const beta1 = 1; #const tau = 1
function bc_model(du,u,h,p,t)
  du[1] = (v0/(1+beta0*(h(p, t-p[1])[3]^2))) * (p0 - q0)*u[1] - d0*u[1]
  du[2] = (v0/(1+beta0*(h(p, t-p[1])[3]^2))) * (1 - p0 + q0)*u[1] +
          (v1/(1+beta1*(h(p, t-p[1])[3]^2))) * (p1 - q1)*u[2] - d1*u[2]
  du[3] = (v1/(1+beta1*(h(p, t-p[1])[3]^2))) * (1 - p1 + q1)*u[2] - d2*u[3]
end

h(p, t) = ones(3)
tspan = (0.0,10.0)
u0 = [1.0,1.0,1.0]
prob = DDEProblem(bc_model,u0,h,tspan, [1.0])
alg = MethodOfSteps(RK4())
sol = solve(prob,alg)

t_obs = linspace(0.0, 10.0, 1000)
randomized = VectorOfArray([sol(t_obs[i]) + 0.01*randn(3) for i=1:length(t_obs)])
data = convert(Array, randomized)

turing_result = turing_inference(prob, MethodOfSteps(RK4()), t_obs, data, [Gamma(1.0, 1.0)]; num_samples=500)
	using DifferentialEquations
	using DiffEqBayes
	using Distributions

	const p0 = 0.2; const q0 = 0.3; const v0 = 1; const d0 = 5
	const p1 = 0.2; const q1 = 0.3; const v1 = 1; const d1 = 1
	const d2 = 1; const beta0 = 1; const beta1 = 1; #const tau = 1
	function bc_model(du,u,h,p,t)
	du[1] = (v0/(1+beta0(h(p, t-p[1])[3]^2))) (p0 - q0)u[1] - d0u[1]
	du[2] = (v0/(1+beta0(h(p, t-p[1])[3]^2))) (1 - p0 + q0)*u[1] +
	(v1/(1+beta1(h(p, t-p[1])[3]^2))) (p1 - q1)u[2] - d1u[2]
	du[3] = (v1/(1+beta1(h(p, t-p[1])[3]^2))) (1 - p1 + q1)u[2] - d2u[3]
	end

	h(p, t) = ones(3)
	tspan = (0.0,10.0)
	u0 = [1.0,1.0,1.0]
	prob = DDEProblem(bc_model,u0,h,tspan, [1.0])
	alg = MethodOfSteps(RK4())
	sol = solve(prob,alg)

	t_obs = linspace(0.0, 10.0, 1000)
	randomized = VectorOfArray([sol(t_obs[i]) + 0.01*randn(3) for i=1:length(t_obs)])
	data = convert(Array, randomized)

	turing_result = turing_inference(prob, MethodOfSteps(RK4()), t_obs, data, [Gamma(1.0, 1.0)]; num_samples=500)