I’m trying to simulate a Covid model using a delay differential equation in DifferentialEquations.jl but I’m having a bit of difficultly getting it to work. I’m not sure If I’m applying the methods correctly.
The model is as follows.
function covid_model_delay(beta = 0.2,
E_E = 0.3,
E_Q = 0.2,
E_J = 0.36,
mu = 0.000034,
z = 0.06,
gamma_1 = 0.4,
gamma_2 = 0.5,
kappa_1 = 0.1,
kappa_2 = 0.125,
sigma_1 = 0.0337,
sigma_2 = 0.0386,
d_1 = 0.0079,
d_2 = 0.0068)
S_0 = 4000000.0 # Susceptible
E_0 = 6.0 # Asymptomatic
Q_0 = 0.0 # Quarantined
I_0 = 1.0 # Symptomatic
J_0 = 0.0 # Isolated
R_0 = 0.0 # Recovered
N_0 = sum(SA[S_0, E_0, Q_0, I_0, J_0, R_0]) # Population
h(p,t) = ones(7)
tau = 1
lags = [tau]
function F(u, h, p, t)
histI = h(p, t-tau)[4]
S, E, Q, I, J, R, N = u
dS = 136.0 - (S*(beta*histI + E_E*beta*E + E_Q*beta*Q +E_J*beta*J)) / N - mu*S
dE = z + (S*(beta*histI + E_E*beta*E + E_Q*beta*Q +E_J*beta*J)) / N - (gamma_1 + kappa_1 + mu)*E
dQ = gamma_1*E - (kappa_2 + mu)*Q
dI = kappa_1*E - (gamma_2 + sigma_1 + d_1 mu)*histI
dJ = gamma_2*histI + kappa_2*Q - (sigma_2 + d_2 + mu)*J
dR = sigma_1*histI + sigma_2*J - mu*R
dN = dS + dE + dQ + dI + dJ + dR
return SA[dS, dE, dQ, dI, dJ, dR]
end
u0 = SA[S_0, E_0, Q_0, I_0, J_0, R_0]
tspan = (0,700)
prob = DDEproblem(F, u0, h, tspan; constand_lags=lags)
alg = MethodOfSteps(Rodas4(), constrained=true)
solution = solve(prob, alg)
return solution
end
The function runs and generates a sensible solution for tau=1 as specified, but I can’t run the model for tau greater than 1. Ideally, I want a time lag of 20. The interruption states that a larger max_iter may be required but that doesn’t seem to help. I think I’m made a mistake somewhere along the line.
Any advice would be greatly appreciated.