seirs_pomp.c

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#include "pomplink.h"
#include "internal.h"
 
#define Exposed  1
#define Infected 2
 
static const int nrate = 6;
 
static inline int random_choice (double n) {
  return floor(R_unif_index(n));
}
 
static void change_color (double *color, int nsample,
                          int n, int from, int to) {
  int i = -1;
  i = -1;
  while (n >= 0 && i < nsample) {
    i++;
    if (!ISNA(color[i]) && nearbyint(color[i]) == from) n--;
  }
  assert(i < nsample);
  assert(n == -1);
  assert(nearbyint(color[i]) == from);
  color[i] = to;
}
 
#define Beta      (__p[__parindex[0]])
#define sigma     (__p[__parindex[1]])
#define gamma     (__p[__parindex[2]])
#define psi       (__p[__parindex[3]])
#define omega     (__p[__parindex[4]])
#define S0        (__p[__parindex[5]])
#define E0        (__p[__parindex[6]])
#define I0        (__p[__parindex[7]])
#define R0        (__p[__parindex[8]])
#define POP       (__p[__parindex[9]])
#define S         (__x[__stateindex[0]])
#define E         (__x[__stateindex[1]])
#define I         (__x[__stateindex[2]])
#define R         (__x[__stateindex[3]])
#define ll        (__x[__stateindex[4]])
#define node      (__x[__stateindex[5]])
#define ellE      (__x[__stateindex[6]])
#define ellI      (__x[__stateindex[7]])
#define COLOR     (__x[__stateindex[8]])
 
#define EVENT_RATES                                     \
  event_rates(__x,__p,t,                                \
              __stateindex,__parindex,__covindex,       \
              __covars,rate,logpi,&penalty)             \
 
static double event_rates
(
 double *__x,
 const double *__p,
 double t,
 const int *__stateindex,
 const int *__parindex,
 const int *__covindex,
 const double *__covars,
 double *rate,
 double *logpi,
 double *penalty
 ) {
  double event_rate = 0;
  double alpha, pi;
  *penalty = 0;
  // 0: transmission, s=(0,0) or s=(0,1)
  assert(S>=0 && I>=0);
  alpha = (POP > 0) ? Beta*S*I/POP : 0;
  pi = (I > 0) ? 1-ellI/I : 0;
  assert(I >= ellI);
  event_rate += (*rate = alpha*pi); rate++;
  *logpi = log(pi); logpi++;
  // 1: transmission, s=(1,0)
  pi = 1-pi;
  event_rate += (*rate = alpha*pi); rate++;
  *logpi = log(pi)-log(ellI); logpi++;
  // 2: progression, s=(0,0)
  assert(E>=0);
  alpha = sigma*E;
  pi = (E > 0) ? 1-ellE/E : 1;
  assert(E >= ellE);
  event_rate += (*rate = alpha*pi); rate++;
  *logpi = log(pi); logpi++;
  // 3: progression, s=(0,1)
  pi = 1-pi;
  event_rate += (*rate = alpha*pi); rate++;
  *logpi = log(pi)-log(ellE); logpi++;
  // 4: recovery
  assert(I>=0);
  alpha = gamma*I;
  if (I > ellI) {
    event_rate += (*rate = alpha); rate++;
    *logpi = 0; logpi++;
  } else {
    *rate = 0; rate++;
    *logpi = 0; logpi++;
    *penalty += alpha;
  }
  // 5: waning
  event_rate += (*rate = omega*R); rate++;
  *logpi = 0; logpi++;
  // sampling (Q = 0)
  *penalty += psi*I;
  assert(R_FINITE(event_rate));
  return event_rate;
}

void seirs_rinit
(
 double *__x,
 const double *__p,
 double t0,
 const int *__stateindex,
 const int *__parindex,
 const int *__covindex,
 const double *__covars
 ){
  double adj = POP/(S0+E0+I0+R0);
  S = nearbyint(S0*adj);
  E = nearbyint(E0*adj);
  I = nearbyint(I0*adj);
  R = nearbyint(R0*adj);
  ellE = 0;
  ellI = 0;
  ll = 0;
  node = 0;
}

void seirs_gill
(
 double *__x,
 const double *__p,
 const int *__stateindex,
 const int *__parindex,
 const int *__covindex,
 const double *__covars,
 double t,
 double dt
 ){
  double tstep = 0.0, tmax = t + dt;
  double *color = &COLOR;
  const int nsample = *get_userdata_int("nsample");
  const int *nodetype = get_userdata_int("nodetype");
  const int *lineage = get_userdata_int("lineage");
  const int *sat = get_userdata_int("saturation");
  const int *index = get_userdata_int("index");
  const int *child = get_userdata_int("child");
 
  int parent = (int) nearbyint(node);
 
#ifndef NDEBUG
  int nnode = *get_userdata_int("nnode");
  assert(parent>=0);
  assert(parent<=nnode);
#endif
 
  int parlin = lineage[parent];
  int parcol = color[parlin];
  assert(parlin >= 0 && parlin < nsample);
 
  ll = 0;
 
  // singular portion of filter equation
  switch (nodetype[parent]) {
  default:                      // non-genealogical event #nocov
    break;                      // #nocov
  case 0:                       // root
    // color lineages by sampling without replacement
    assert(sat[parent]==1);
    int c = child[index[parent]];
    assert(lineage[parent]==lineage[c]);
    if (E-ellE + I-ellI > 0) {
      double x = (E-ellE)/(E-ellE + I-ellI);
      if (unif_rand() < x) {      // lineage is put into E deme
        color[lineage[c]] = Exposed;
        ellE += 1;
        ll -= log(x);
      } else {                    // lineage is put into I deme
        color[lineage[c]] = Infected;
        ellI += 1;
        ll -= log(1-x);
      }
    } else {                // more roots than infectives
      ll += R_NegInf;       // this is incompatible with the genealogy
      // the following keeps the state valid
      if (unif_rand() < 0.5) {  // lineage is put into E deme
        color[lineage[c]] = Exposed;
        ellE += 1; E += 1;
        //        ll -= log(0.5);
      } else {                  // lineage is put into I deme
        color[lineage[c]] = Infected;
        ellI += 1; I += 1;
        //        ll -= log(0.5);
      }
    }
    break;
  case 1:                       // sample
    // If parent is not in deme I, likelihood = 0.
    if (parcol != Infected) {
      ll += R_NegInf;
      color[parlin] = Infected;
      // the following keeps the state valid
      ellE -= 1; ellI += 1;
      E -= 1; I += 1;
    }
    if (sat[parent] == 1) {     // s=(0,1)
      int c = child[index[parent]];
      color[lineage[c]] = Infected;
      ll += log(psi);
    } else if (sat[parent] == 0) { // s=(0,0)
      ellI -= 1;
      ll += log(psi*(I-ellI));
    } else {
      assert(0);                // #nocov
      ll += R_NegInf;           // #nocov
    }
    color[parlin] = R_NaReal;
    break;
  case 2:                       // branch point s=(1,1)
    // If parent is not in deme I, likelihood = 0.
    if (parcol != Infected) {
      ll += R_NegInf;
      color[parlin] = Infected;
      // the following keeps the state valid
      ellE -= 1; ellI += 1;
      E -= 1; I += 1;
    }
    assert(sat[parent]==2);
    ll += (S > 0 && I > 0) ? log(Beta*S/POP/(E+1)) : R_NegInf;
    S -= 1; E += 1;
    ellE += 1;
    S = (S > 0) ? S : 0;
    int c1 = child[index[parent]];
    int c2 = child[index[parent]+1];
    assert(c1 != c2);
    assert(lineage[c1] != lineage[c2]);
    assert(lineage[c1] != parlin || lineage[c2] != parlin);
    assert(lineage[c1] == parlin || lineage[c2] == parlin);
    if (unif_rand() < 0.5) {
      color[lineage[c1]] = Exposed;
      color[lineage[c2]] = Infected;
    } else {
      color[lineage[c1]] = Infected;
      color[lineage[c2]] = Exposed;
    }
    ll -= log(0.5);
    break;
  }
 
  // continuous portion of filter equation:
  // take Gillespie steps to the end of the interval
  if (tmax > t) {
 
    double rate[nrate], logpi[nrate];
    int event;
    double event_rate = 0;
    double penalty = 0;
 
    event_rate = EVENT_RATES;
    tstep = exp_rand()/event_rate;
 
    while (t + tstep < tmax) {
      event = rcateg(event_rate,rate,nrate);
      assert(event>=0 && event<nrate);
      ll -= penalty*tstep + logpi[event];
      switch (event) {
      case 0:                   // transmission, s=(0,0) or s=(0,1)
        assert(S>=1);
        S -= 1; E += 1;
        ll += log(1-ellE/E);
        assert(!ISNAN(ll));
        break;
      case 1:                   // transmission, s=(1,0)
        assert(S>=1);
        change_color(color,nsample,random_choice(ellI),Infected,Exposed);
        ellE += 1; ellI -= 1;
        S -= 1; E += 1;
        ll += log(1-ellI/I)-log(E);
        assert(!ISNAN(ll));
        break;
      case 2:                   // progression, s=(0,0)
        assert(E>=1);
        E -= 1; I += 1;
        ll += log(1-ellI/I);
        assert(!ISNAN(ll));
        break;
      case 3:                   // progression, s=(0,1)
        assert(E>=1);
        change_color(color,nsample,random_choice(ellE),Exposed,Infected);
        ellE -= 1; ellI += 1;
        E -= 1; I += 1;
        ll -= log(I);
        assert(!ISNAN(ll));
        break;
      case 4:                   // recovery
        assert(I>=1);
        I -= 1; R += 1;
        assert(!ISNAN(ll));
        break;
      case 5:                   // waning
        assert(R>=1);
        R -= 1; S += 1;
        assert(!ISNAN(ll));
        break;
      default:                  // #nocov
        assert(0);              // #nocov
        ll += R_NegInf;         // #nocov
        break;                  // #nocov
      }
 
      ellE = nearbyint(ellE);
      ellI = nearbyint(ellI);
 
      t += tstep;
      event_rate = EVENT_RATES;
      tstep = exp_rand()/event_rate;
 
    }
    tstep = tmax - t;
    ll -= penalty*tstep;
  }
  node += 1;
}
 
# define lik  (__lik[0])

void seirs_dmeas
(
 double *__lik,
 const double *__y,
 const double *__x,
 const double *__p,
 int give_log,
 const int *__obsindex,
 const int *__stateindex,
 const int *__parindex,
 const int *__covindex,
 const double *__covars,
 double t
 ) {
  assert(!ISNAN(ll));
  lik = (give_log) ? ll : exp(ll);
}