help with Algorithm to route unsplittable flows on a single primary path

What I have done is taken the network from paper 1 (all network specifications are from there and implemented the optimization from paper 2 in the network from 1 and I am trying to measure the effect on link utilization. How would you change the given Algorithm to route unsplittable flows on the specified single primary path only

% delta_edp : if link e on path p used for demand d % x_dp : if path used for demand % y_e : if link e used in any primary path % l_dp : the fraction of traffic via path p %link

      global hd ce Ye delta_edp X_dp;
      link(1,:)=[1 2];
      link(2,:)=[1 3];
      link(3,:)=[1 4];
      link(4,:)=[2 6];
     link(5,:)=[3 6];
     link(6,:)=[3 7];
     link(7,:)=[4 8];
     link(8,:)=[4 9];
     link(9,:)=[6 10];
     link(10,:)=[7 10];
     link(11,:)=[8 11];
     link(12,:)=[8 12];
     link(13,:)=[9 12];
     link(14,:)=[9 13];
     link(15,:)=[1 5];
     link(16,:)=[5 13];

     %primary path    
      Pd_pr(1,:)=[2, 6, 10];
      Pd_pr(2,:)=[3,7,11];
      Pd_pr(3,:)=[3,7,12];
      Pd_pr(4,:)=[15, 16,0];

      %sencondary path
      Pd_s(1,:)=[1,4,9];
      Pd_s(2,:)=[2,5,9];
      Pd_s(3,:)=[3,8,13];
      Pd_s(4,:)=[3,8,14];

      path=[Pd_pr;Pd_s];

      %link capacity
      ce=[50 50 200 50 50 50 150 50 50 50 50 50 50 50 50 50];

      %demand
      demand=[1 10;1 11;1 12;1 13];

      %associated flow values for demand
      hd=[45 45 50 40];

      %value of X_dp
      X_dp=zeros(4,8);

%Algorithm

      for jj=1:4 %4 demands
          for kk=1:8  %8Paths
              demandStart=demand(jj,1);
              demandEnd=demand(jj,2);
              pathStart=path(kk,1);
              linkStart=link(pathStart,1);
              pathEnd=path(kk,3);
              if pathEnd==0
                  pathEnd=path(kk,2);
              end

              linkEnd=link(pathEnd,2);
              if pathEnd==0
                  pathEnd=path(kk,2);
              end
              if demandStart==linkStart && demandEnd==linkEnd
                  X_dp(jj,kk)=1;
              end
          end
      end