matlab.tex

\documentclass[a4paper,12pt]{article}

\usepackage{upquote}
\usepackage{listings}

% Check
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\usepackage{inconsolata}
\renewcommand{\lstlistingname}{Algorithm}

% Based on https://gist.github.com/eyliu/120689
\lstset{language=Matlab,
  frame=single,
  showspaces=false,
  showtabs=false,
  breaklines=true,
  showstringspaces=false,
  breakatwhitespace=true,
  escapeinside={(*@}{@*)},
  morekeywords={plot, title, xlabel},
  morekeywords=[2]{alpha, beta, theta, kappa, gamma},
  deletekeywords={alpha, beta, gamma},
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}
\begin{document}

\lstinputlisting[caption={Modelo SEIRS},label=lst:seir_model,firstline=14]{seirs.m}
\end{document}

seirs.m

% SEIRS model

% Inputs:
%   t - time variable: not used here because our system
%       is independent of the time (autonomous)
%   x - independent variable: this contains the populations.
% Output:
%   dx - First derivative: The rate of change of the population.

% S = dx_dt(1)
% E = dx_dt(2)
% I = dx_dt(3)
% R = dx_dt(4)
function dx_dt = seirs_model(t, x)
  
    dx_dt = [0; 0; 0; 0];

    alpha = 0.375;
    beta = 0.1;
    gamma = 0.143;
    theta = 0.004;
    kappa = 0.00042;
    
    dx_dt(1) = - alpha * x(1) + theta * x(4);
    dx_dt(2) = alpha * x(1) - beta * x(2);
    dx_dt(3) = beta * x(2) - kappa * x(3) - gamma * x(3);
    dx_dt(4) = gamma * x(3) - theta * x(4);