ApproximantCoefficientsSEIR
%This computes the A_n coefficients, B_n coefficients, lambda_1, and f_infinity needed for the N-term SEIR approximant
%given as equation (15) in the preprint found at https://www.researchgate.net/publication/342211425_Analytic_solution_of_the_SEIR_epidemic_model_via_asymptotic_approximant
%The inputs correspond to the number of terms N (must be even), SEIR parameters, and initial conditions as
%specified in equation (1) in the preprint. The code uses padeapprox.m [1], which implements the algorithm of [2].
%
%[1] https://github.com/chebfun/chebfun/blob/master/padeapprox.m
%[2] P. Gonnet, S. Guettel, and L. N. Trefethen, "ROBUST PADE APPROXIMATION
% VIA SVD", SIAM Rev., 55:101-117, 2013.
% %%% example, reproducing figure 1b in Weinstein et. al.
% alpha=0.466089; beta=0.2; gamma=0.1; I0=0.05; S0=0.88; E0=0.07; R0=0; %input parameters
% t=0:0.1:100 %time interval 0 to 100 in increments of 0.1
% N=18; %number of terms in the approximant, increase until answer stops changing
% [A0,A,B,lambda_1,f_infinity]=ApproximantCoefficientsSEIR(N,alpha,beta,gamma,S0,E0,I0); %using the code provided to get the stuff needed below
% tv=t;clear t; syms t;
% f1=A0; f2=1;
% for j=1:N/2
% f1=f1+A(j)*t.^j;
% f2=f2+B(j)*t.^j;
% end
% FA=f_infinity+exp(lambda_1*t).*(f1./f2);
% dFA=diff(FA,t); t=tv; FA=eval(FA); dFA=eval(dFA);
% SA=exp(FA);
% IA=-1/beta*dFA;
% RA=R0-gamma/beta*(FA-log(S0));
% EA=gamma/beta*(FA-log(S0))-SA+dFA/beta+E0+I0+S0;
% plot(tv,SA,'r','displayname','S');hold on
% plot(tv,EA,'m','displayname','E')
% plot(tv,IA,'c','displayname','I')
% plot(tv,RA,'b','displayname','R'); legend show
Zitieren als
Nathaniel Barlow (2024). ApproximantCoefficientsSEIR (https://www.mathworks.com/matlabcentral/fileexchange/77007-approximantcoefficientsseir), MATLAB Central File Exchange. Abgerufen .
Kompatibilität der MATLAB-Version
Plattform-Kompatibilität
Windows macOS LinuxTags
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!Live Editor erkunden
Erstellen Sie Skripte mit Code, Ausgabe und formatiertem Text in einem einzigen ausführbaren Dokument.
Version | Veröffentlicht | Versionshinweise | |
---|---|---|---|
1.0.1 | A few things made more efficient and includes an example test-case in the comments. |
||
1.0.0 |