<?xml version="1.0" encoding="ISO-8859-1" standalone="no"?>
<!DOCTYPE MAN SYSTEM "file://D:\PROGRA~1\scilab-4.0\man/manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>sirs</TITLE>
  <TYPE>Scilab Function  </TYPE>
  <DATE>4-Sep-2006</DATE>
  <SHORT_DESCRIPTION name="sirs">the susceptible-infected-rescued-susceptible (SIRS) model</SHORT_DESCRIPTION>

  <CALLING_SEQUENCE>
  <CALLING_SEQUENCE_ITEM>inf = sirs(a,b,N,T,N0,Ti,Tr,P)</CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>

  <PARAM>
  <PARAM_INDENT>

    <PARAM_ITEM>
    <PARAM_NAME>a</PARAM_NAME>
    <PARAM_DESCRIPTION>
	    <SP>
		    : row vector of the numbers of the tail nodes of the graph (its size is the number of edges of the graph)
	    </SP>
    </PARAM_DESCRIPTION>
    </PARAM_ITEM>

    <PARAM_ITEM>
    <PARAM_NAME>b</PARAM_NAME>
    <PARAM_DESCRIPTION>
	    <SP>
		    : row vector of the numbers of the head nodes of the graph (its size is the number of edges of the graph)
      	    </SP>
    </PARAM_DESCRIPTION>
    </PARAM_ITEM>

    <PARAM_ITEM>
    <PARAM_NAME>N</PARAM_NAME>
    <PARAM_DESCRIPTION>
	    <SP>
		    : the node number of the SIRS model
      	    </SP>
    </PARAM_DESCRIPTION>
    </PARAM_ITEM>

    <PARAM_ITEM>
    <PARAM_NAME>T</PARAM_NAME>
    <PARAM_DESCRIPTION>
	    <SP>
		    : the epidemic time step
      	    </SP>
    </PARAM_DESCRIPTION>
    </PARAM_ITEM>

    <PARAM_ITEM>
    <PARAM_NAME>N0</PARAM_NAME>
    <PARAM_DESCRIPTION>
	    <SP>
		    : the initial infected node
      	    </SP>
    </PARAM_DESCRIPTION>
    </PARAM_ITEM>

    <PARAM_ITEM>
    <PARAM_NAME>Ti</PARAM_NAME>
    <PARAM_DESCRIPTION>
	    <SP>
		    : the infected state holding time, then the node will change its status to refractory state
      	    </SP>
    </PARAM_DESCRIPTION>
    </PARAM_ITEM>

    <PARAM_ITEM>
    <PARAM_NAME>Tr</PARAM_NAME>
    <PARAM_DESCRIPTION>
	    <SP>
		    : the refractory state holding time, then the node will change its status to suspectible state
     	    </SP>
    </PARAM_DESCRIPTION>
    </PARAM_ITEM>

    <PARAM_ITEM>
    <PARAM_NAME>P</PARAM_NAME>
    <PARAM_DESCRIPTION>
	    <SP>
		    : the infected probability
      	    </SP>
    </PARAM_DESCRIPTION>
    </PARAM_ITEM>

    <PARAM_ITEM>
    <PARAM_NAME>inf</PARAM_NAME>
    <PARAM_DESCRIPTION>
	    <SP>
		    : row vector of the infected fraction of the graph(its size is the time step)
      	    </SP>
    </PARAM_DESCRIPTION>
    </PARAM_ITEM>
  </PARAM_INDENT>
  </PARAM>
 
  <DESCRIPTION>
     <DESCRIPTION_INDENT>
     <DESCRIPTION_ITEM>
	     <P>
		     sirs calculates the infected fraction every time step for the SIRS epidemic process. Note when the TR is large enough, SIRS is the SIR epidemic process.
	     </P>
     </DESCRIPTION_ITEM>
     </DESCRIPTION_INDENT>
  </DESCRIPTION>

  <EXAMPLE><![CDATA[
	  [a b]=ba(6,4,9994);
	  inf=sirs(a,b,10000,1000,1000,5,3,1);
	  t=[1:1000];
	  plot2d(t,inf(t));   
  ]]></EXAMPLE>

  <SEE_ALSO>
    <SEE_ALSO_ITEM> <LINK>sis</LINK> </SEE_ALSO_ITEM>
  </SEE_ALSO>

  <AUTHORS>
    <AUTHORS_ITEM label='Wubo'>
    </AUTHORS_ITEM>
  </AUTHORS>
</MAN>
