Code for Figure 4.34

hbv_common.m

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 % Hepatitis B model, stochastic simulation. Data and functions defined % in this file are used in both hbv_stoch.m and hbv_binary.m global k k = [1; 0.025; 1000; 0.25; 2; 7.5e-6]; stoi = [0, 1, 0; 1, -1, 0; 0, 0, 1; -1, 0, 0; 0, 0, -1; 0, -1, -1]; x0 = [1; 0; 0]; stoiT = stoi'; tfin = 200; nts = 200; tout = linspace(0,tfin,nts)'; % % steady state analysis % cas = ( k(1)-k(4) ) / ... ( k(6) *k(4)/k(2)*( (-k(1)+k(4) +k(3)) / (k(5))) ); cbs = k(4)/k(2)* cas; ccs = ( k(1)-k(4) ) / ( k(6) *k(4)/k(2) ); Jac = [-k(4), k(2), 0; k(1), -k(2)-k(6)*ccs, -k(6)*cbs; k(3), -k(6)*ccs, -k(5)-k(6)*cbs]; eig(Jac); function rhs = hbv_deriv(t,x); global k rhs = zeros (3, 1); rhs(1) = k(2)*x(2) - k(4)*x(1); rhs(2) = k(1)*x(1) - k(2)*x(2) - k(6)*x(2)*x(3); rhs(3) = k(3)*x(1) - k(5)*x(3) - k(6)*x(2)*x(3); end%function % % deterministic dynamics % opts = odeset ('AbsTol', sqrt (eps), 'RelTol', sqrt (eps)); [tsolver, x] = ode15s(@hbv_deriv, tout, x0, opts); % function xout = stochsim(x0, k, stoiT, tout) % nts = length(tout); % tfin = tout(nts); % time = tout(1); % x = x0; % iout = 1; % while (time < tfin) % r(1) = k(1)*x(1); % r(2) = k(2)*x(2); % r(3) = k(3)*x(1); % r(4) = k(4)*x(1); % r(5) = k(5)*x(3); % r(6) = k(6)*x(2)*x(3); % rtot = sum(r); % p=rand(2,1); % % choose likely time of next reaction % tau = -log(p(1))/rtot; % timenew = time + tau; % % choose which reaction (mth) is likely to occur % rcum = 0; % m = 0; % while ( rcum <= p(2)*rtot) % m = m + 1; % rcum = rcum + r(m); % end % xnew = x + stoiT(:,m); % % check if passing time of requested output % while( tout(iout) <= timenew ) % xout(:,iout) = x; % iout = iout + 1; % if (iout > nts) break; end % end % time = timenew; % x = xnew; % end % end%function %xplot1 = stochsim(x0, k, stoiT, tplot); % % check the deterministic steady state and eigenvalues % % check parameters for hbv_det simulations %k(1) = 2; %k(5) = 1.9985

stochsim.c (Matlab mex file source)

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 /* Copyright (C) 2001, James B. Rawlings This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; see the file COPYING. If not, write to the Free Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ #include #include #include static double get_rand (void) { double rnd; mxArray *plhs[1]; mexCallMATLAB (1, plhs, 0, 0, "rand"); rnd = (mxGetPr (plhs[0]))[0]; mxDestroyArray (plhs[0]); return rnd; } void mexFunction (int nlhs, mxArray* plhs[], int nrhs, const mxArray* prhs[]) { int nargin = nrhs; const mxArray *xin; double *pxin; const mxArray *k; double *pk; const mxArray *stoiT; double *pstoiT; int stoiT_nr; const mxArray *tout; double *ptout; mxArray *xout; double *pxout; int nts, nx; double tfin, time; int iout = 0; double x0, x1, x2; double k0, k1, k2, k3, k4, k5; int pxout_offset = 0; if (nargin < 4 || nargin > 4) mexErrMsgTxt ("usage: stochsim (x0, k, stoiT, tout)"); /* Maybe we should check that these are numeric, to avoid crashing Matlab if someone passes something else? */ xin = prhs[0]; k = prhs[1]; stoiT = prhs[2]; tout = prhs[3]; pxin = mxGetPr (xin); pk = mxGetPr (k); pstoiT = mxGetPr (stoiT); ptout = mxGetPr (tout); stoiT_nr = mxGetM (stoiT); nts = mxGetNumberOfElements (tout); tfin = ptout[nts-1]; time = ptout[0]; nx = mxGetNumberOfElements (xin); if (nx != 3) mexErrMsgTxt ("stochsim: expecting X to be a 3-element vector"); x0 = pxin[0]; x1 = pxin[1]; x2 = pxin[2]; xout = mxCreateDoubleMatrix (nx, nts, mxREAL); pxout = mxGetPr (xout); k0 = pk[0]; k1 = pk[1]; k2 = pk[2]; k3 = pk[3]; k4 = pk[4]; k5 = pk[5]; while (time < tfin) { double r0 = k0 * x0; double r1 = k1 * x1; double r2 = k2 * x0; double r3 = k3 * x0; double r4 = k4 * x2; double r5 = k5 * x1 * x2; double rtot = r0 + r1 + r2 + r3 + r4 + r5; double timenew, rnd, rcum, tmp; int m = 0; double xnew0, xnew1, xnew2; /* return if system has extinguished */ if (rtot == 0.0) { while (iout < nts) { pxout[pxout_offset++] = x0; pxout[pxout_offset++] = x1; pxout[pxout_offset++] = x2; iout++; } break; } /* choose likely time of next reaction */ timenew = time - log (get_rand ()) / rtot; /* choose which reaction (mth) is likely to occur */ rnd = get_rand (); rcum = r0; m = 0; tmp = rnd*rtot; if (rcum <= tmp) { ++m; rcum += r1; if (rcum <= tmp) { ++m; rcum += r2; if (rcum <= tmp) { ++m; rcum += r3; if (rcum <= tmp) { ++m; rcum += r4; if (rcum <= tmp) ++m; rcum += r5; } } } } xnew0 = x0 + pstoiT[stoiT_nr*m]; xnew1 = x1 + pstoiT[stoiT_nr*m+1]; xnew2 = x2 + pstoiT[stoiT_nr*m+2]; /* check if passing time of requested output */ while (ptout[iout] <= timenew) { pxout[pxout_offset++] = x0; pxout[pxout_offset++] = x1; pxout[pxout_offset++] = x2; iout++; if (iout >= nts) break; } time = timenew; x0 = xnew0; x1 = xnew1; x2 = xnew2; } plhs[0] = xout; }

stochsim.cc (Octave oct file source)

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 /* Copyright (C) 2001, James B. Rawlings This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; see the file COPYING. If not, write to the Free Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ #include #include #include #include #include #include DEFUN_DLD (stochsim, args, , "stochsim(x0, k, stoiT, tout)") { octave_value retval; int nargin (args.length ()); if (nargin < 4 || nargin > 4) { print_usage ("stochsim"); return retval; } const ColumnVector xin (args(0) . vector_value ()); const ColumnVector k (args(1) . vector_value ()); const Matrix stoiT (args(2) . matrix_value ()); const ColumnVector tout (args(3) . vector_value ()); if (error_state) { error ("stochsim: invalid arguments"); return retval; } const int nts = tout.numel (); const double tfin = tout(nts-1); double time = tout(0); int iout = 0; const int nx = xin.numel (); if (nx != 3) { error ("stochsim: expecting X to be a 3-element vector"); return retval; } double x0 = xin(0); double x1 = xin(1); double x2 = xin(2); Matrix xout (nx, nts, 0.0); double *pxout = xout.fortran_vec (); int pxout_offset = 0; double k0 = k(0); double k1 = k(1); double k2 = k(2); double k3 = k(3); double k4 = k(4); double k5 = k(5); while (time < tfin) { // Allow this loop to be interrupted. OCTAVE_QUIT; double r0 = k0 * x0; double r1 = k1 * x1; double r2 = k2 * x0; double r3 = k3 * x0; double r4 = k4 * x2; double r5 = k5 * x1 * x2; double rtot = r0 + r1 + r2 + r3 + r4 + r5; // return if system has extinguished if (rtot == 0.0) { while (iout < nts) { pxout[pxout_offset++] = x0; pxout[pxout_offset++] = x1; pxout[pxout_offset++] = x2; iout++; } break; } // choose likely time of next reaction double timenew = time - log (octave_rand::scalar ()) / rtot; // choose which reaction (mth) is likely to occur double rnd = octave_rand::scalar (); double rcum = r0; int m = 0; double tmp = rnd*rtot; if (rcum <= tmp) { ++m; rcum += r1; if (rcum <= tmp) { ++m; rcum += r2; if (rcum <= tmp) { ++m; rcum += r3; if (rcum <= tmp) { ++m; rcum += r4; if (rcum <= tmp) ++m; rcum += r5; } } } } double xnew0 = x0 + stoiT(0,m); double xnew1 = x1 + stoiT(1,m); double xnew2 = x2 + stoiT(2,m); // check if passing time of requested output while (tout(iout) <= timenew) { pxout[pxout_offset++] = x0; pxout[pxout_offset++] = x1; pxout[pxout_offset++] = x2; iout++; if (iout >= nts) break; } time = timenew; x0 = xnew0; x1 = xnew1; x2 = xnew2; } retval = xout; return retval; }