# SIR model in Julia using DifferentialEquations

Author: Simon Frost @sdwfrost Editor: Chris Rackauckas @ChrisRackauckas

Date: 2018-07-12

### Using the Macro DSL

using DifferentialEquations

sir_ode = @ode_def SIRModel begin
dS = -β*S*I
dI = β*S*I-γ*I
dR = γ*I
end β γ

(::SIRModel{getfield(Main, Symbol("##3#4")),Nothing,Nothing,Nothing,Nothing,Nothing,Any,Any}) (generic function with 2 methods)

parms = [0.1,0.05]
init = [0.99,0.01,0.0]
tspan = (0.0,200.0)

(0.0, 200.0)

sir_prob = ODEProblem(sir_ode,init,tspan,parms)

[36mODEProblem[0m with uType [36mArray{Float64,1}[0m and tType [36mFloat64[0m. In-place: [36mtrue[0m
timespan: (0.0, 200.0)
u0: [0.99, 0.01, 0.0]

sir_sol = solve(sir_prob,saveat = 0.1);


### Visualisation

using Plots

plot(sir_sol,xlabel="Time",ylabel="Number")


### Using the Function Interface

function sir_ode2(du,u,p,t)
S,I,R = u
b,g = p
du[1] = -b*S*I
du[2] = b*S*I-g*I
du[3] = g*I
end
parms = [0.1,0.05]
init = [0.99,0.01,0.0]
tspan = (0.0,200.0)
sir_prob2 = ODEProblem(sir_ode2,init,tspan,parms)
sir_sol = solve(sir_prob2,saveat = 0.1)

retcode: Success
Interpolation: 1st order linear
t: 2001-element Array{Float64,1}:
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
⋮
198.9
199.0
199.1
199.2
199.3
199.4
199.5
199.6
199.7
199.8
199.9
200.0
u: 2001-element Array{Array{Float64,1},1}:
[0.99, 0.01, 0.0]
[0.989901, 0.0100491, 5.01227e-5]
[0.989801, 0.0100985, 0.000100492]
[0.989701, 0.010148, 0.000151108]
[0.9896, 0.0101979, 0.000201972]
[0.989499, 0.0102479, 0.000253087]
[0.989397, 0.0102982, 0.000304452]
[0.989295, 0.0103487, 0.000356069]
[0.989193, 0.0103995, 0.000407939]
[0.989089, 0.0104504, 0.000460064]
[0.988986, 0.0105017, 0.000512444]
[0.988882, 0.0105531, 0.000565081]
[0.988777, 0.0106049, 0.000617976]
⋮
[0.21018, 0.0149422, 0.774878]
[0.210148, 0.014899, 0.774953]
[0.210117, 0.0148558, 0.775027]
[0.210086, 0.0148128, 0.775101]
[0.210055, 0.01477, 0.775175]
[0.210024, 0.0147272, 0.775249]
[0.209993, 0.0146845, 0.775322]
[0.209962, 0.014642, 0.775396]
[0.209932, 0.0145996, 0.775469]
[0.209901, 0.0145573, 0.775542]
[0.209871, 0.0145151, 0.775614]
[0.20984, 0.0144731, 0.775687]