Automating the derivation of sensitivity indices

2 次查看（过去 30 天）

Bas123 2022-12-22

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1883437-automating-the-derivation-of-sensitivity-indices

评论： Torsten 2022-12-30

I am currently reviewing some papers on mathematical epidemiology and trying to replicate certain results on those papers. I want to calculate the sensitivity indices of model parameters (of the paper https://pubmed.ncbi.nlm.nih.gov/32834653/) with respect to the basic reproduction number

using the formula

where p is a parameter and

is the sensitivity index of p. I have already calculated the indices manually, but I would like to know how to automate this process using MATLAB. The formula for

and the parameter values are given below. The sensitivity index values given in the paper are

. Thank you in advance!

beta_s = 0.274;
alpha_a = 0.4775;
alpha_u = 0.695;
mu = 0.062;
q_i = 0.078;
gamma_a = 0.29;
eta_i = 0.009;
eta_u = 0.05;
R0 = (beta_s*alpha_a)/(gamma_a+mu) + (beta_s*alpha_u*gamma_a*(1-q_i))/((gamma_a+mu)*(eta_u+mu))

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

Bas123 2022-12-29

Does anyone have any ideas on this question? Thanks!

请先登录，再进行评论。

请先登录，再回答此问题。

回答（1 个）

Torsten 2022-12-29

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1883437-automating-the-derivation-of-sensitivity-indices#answer_1138102

编辑：Torsten 2022-12-29

在 MATLAB Online 中打开

You could use

syms beta_s alpha_a alpha_u mu q_i gamma_a eta_i eta_u

beta_s_num = 0.274;

alpha_a_num = 0.4775;

alpha_u_num = 0.695;

mu_num = 0.062;

q_i_num = 0.078;

gamma_a_num = 0.29;

eta_i_num = 0.009;

eta_u_num = 0.05;

R0 = (beta_s*alpha_a)/(gamma_a+mu) + (beta_s*alpha_u*gamma_a*(1-q_i))/((gamma_a+mu)*(eta_u+mu));

%S_beta_s as an example

dR0dbeta_s = diff(R0,beta_s)

dR0dbeta_s =

S_beta_s = beta_s_num/subs(R0,[beta_s alpha_a alpha_u mu q_i gamma_a eta_i eta_u],[beta_s_num alpha_a_num alpha_u_num mu_num q_i_num gamma_a_num eta_i_num eta_u_num])*subs(dR0dbeta_s,[beta_s alpha_a alpha_u mu q_i gamma_a eta_i eta_u],[beta_s_num alpha_a_num alpha_u_num mu_num q_i_num gamma_a_num eta_i_num eta_u_num])

S_beta_s =

6 个评论
显示 4更早的评论隐藏 4更早的评论

Bas123 2022-12-30

Hey, thank you! Here is the Mathematica code that I used.

f[betas_, alphaa_, alphau_, mu_, qi_, gammaa_, etau_] := (betas*alphaa)/(gammaa+mu) + (betas*alphau*gammaa*(1-qi))/((gammaa+mu)*(etau+mu))

R0 = f[0.274, 0.4775, 0.695, 0.062, 0.078, 0.29, 0.05]

Sbetas = (betas/R0)*D[f[betas, alphaa, alphau, mu, qi, gammaa, etau], betas]

SbetasValue = Sbetas/.{betas->0.274, alphaa->0.4775, alphau->0.695, mu->0.062, qi->0.078, gammaa->0.29, etau->0.05}

Torsten 2022-12-30

I don't see a difference between MATLAB and MATHEMATICA code.

If the results are different, I'd compare intermediate results, e.g. R0 and dR0dbeta_s, in both programs.

请先登录，再进行评论。

请先登录，再回答此问题。

类别

Sciences Geoscience Earth and Planetary Science

在 Help Center 和 File Exchange 中查找有关 Earth and Planetary Science 的更多信息

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by