用非正统观测数据用scipy最小化估计参数

Question

我希望最小化这个模型中的参数beta和gamma。然而，我观察到的数据不是时间序列的形式。我想要估计的值是当两个轨迹有平衡值时的值。即当I(患病率)和J_diff(发病率)的平衡值分别达到0.4和0.3时。我的代码如下:

def peak_infections(x):
# Total population, N.
N = 1
# Initial number of infected and recovered individuals, I0 and R0.
I0, R0 = 0.001, 0
# Everyone else, S0, is susceptible to infection initially.
beta = x[0]
gamma = x[1]
U0 = N - I0 - R0
J0 = I0
Lf0, Ls0 = 0, 0
# Contact rate, beta, and mean recovery rate, gamma, (in 1/years).
beta, gamma = 15, 2/5
mu, muTB, sigma, rho = 1/80, 1/6, 1/6, 0.03
u, v, w = 0.083, 0.88, 0.0006
# A grid of time points 
times = np.arange(0,20,2.5)
def deriv(y, times, N, beta, gamma, mu, muTB, sigma, rho, u, v, w):
U, Lf, Ls, I, R, cInc = y
b = (mu * (U + Lf + Ls + R)) + (muTB * I)
lamda = beta * I
clamda = 0.2 * lamda
dU = b - ((lamda + mu) * U)
dLf = (lamda*U) + ((clamda)*(Ls + R)) - ((u + v + mu) * Lf)
dLs = (u * Lf) - ((w + clamda + mu) * Ls)
dI = w*Ls + v*Lf - ((gamma + muTB + sigma) * I) + (rho * R)
dR = ((gamma + sigma) * I) - ((rho + clamda + mu) * R)
cI = w*Ls + v*Lf + (rho * R)
return dU, dLf, dLs, dI, dR, cI
# Initial conditions are S0, I0, R0
# Integrate the SIR equations over the time grid, t.
solve = odeint(deriv, (U0, Lf0, Ls0, I0, R0, J0), times, args=(N, beta, gamma, mu, muTB, sigma, rho, u, v, w))
U, Lf, Ls, I, R, cInc = solve.T
return I
def residual(x):
# Total population,  N.
StartingPop = 1
prev= 0.4/StartingPop
return np.sum((peak_infections(x) - prev) ** 2)

x0 = [12, 0.4] #estimates for beta and gamma starting point
res = minimize(residual, x0, method="Nelder-Mead", options={'fatol':1e-04}).x
print(res)

然而，当我尝试最小化res时，它只是返回我给它的x0中的初始估计值。我如何纠正这段代码，包括在残差函数，这必须优化，当I和J_diff达到他们的平衡状态为0.4和0.3?

Answer 1

您正在将输入参数覆盖到函数'peak_infections'。和分别被赋值为x[0]和x[1]。但几行之后，它们被重新分配为15又2/5。无论你向函数传递什么，结果都是一样的。只需删除将这些值赋给15和2/5的行，就可以得到结果。