seirs_pomp.c File Reference

#include "pomplink.h"
#include "internal.h"

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Macros
#define	Exposed   1
#define	Infected   2
#define	Beta   (__p[__parindex[0]])
#define	sigma   (__p[__parindex[1]])
#define	gamma   (__p[__parindex[2]])
#define	psi   (__p[__parindex[3]])
#define	chi   (__p[__parindex[4]])
#define	omega   (__p[__parindex[5]])
#define	S0   (__p[__parindex[6]])
#define	E0   (__p[__parindex[7]])
#define	I0   (__p[__parindex[8]])
#define	R0   (__p[__parindex[9]])
#define	POP   (__p[__parindex[10]])
#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
#define	lik   (__lik[0])

Functions
static int	random_choice (double n)
static void	change_color (double *color, int nsample, int n, int from, int to)
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)
void	seirs_rinit (double *__x, const double *__p, double t0, const int *__stateindex, const int *__parindex, const int *__covindex, const double *__covars)
void	seirs_gill (double *__x, const double *__p, const int *__stateindex, const int *__parindex, const int *__covindex, const double *__covars, double t, double dt)
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)
	Measurement model likelihood (dmeasure).

Variables
static const int	nrate = 6

Macro Definition Documentation

Beta

#define Beta   (__p[__parindex[0]])

Definition at line 27 of file seirs_pomp.c.

chi

#define chi   (__p[__parindex[4]])

Definition at line 31 of file seirs_pomp.c.

COLOR

#define COLOR   (__x[__stateindex[8]])

Definition at line 46 of file seirs_pomp.c.

E

#define E   (__x[__stateindex[1]])

Definition at line 39 of file seirs_pomp.c.

E0

#define E0   (__p[__parindex[7]])

Definition at line 34 of file seirs_pomp.c.

ellE

#define ellE   (__x[__stateindex[6]])

Definition at line 44 of file seirs_pomp.c.

ellI

#define ellI   (__x[__stateindex[7]])

Definition at line 45 of file seirs_pomp.c.

EVENT_RATES

#define EVENT_RATES

Value:

  event_rates(__x,__p,t,                                \
              __stateindex,__parindex,__covindex,       \
              __covars,rate,logpi,&penalty)             \

Definition at line 48 of file seirs_pomp.c.

#define EVENT_RATES                                     \
  event_rates(__x,__p,t,                                \
              __stateindex,__parindex,__covindex,       \
              __covars,rate,logpi,&penalty)             \
 

Exposed

#define Exposed   1

Definition at line 4 of file seirs_pomp.c.

gamma

#define gamma   (__p[__parindex[2]])

Definition at line 29 of file seirs_pomp.c.

I

#define I   (__x[__stateindex[2]])

Definition at line 40 of file seirs_pomp.c.

I0

#define I0   (__p[__parindex[8]])

Definition at line 35 of file seirs_pomp.c.

Infected

#define Infected   2

Definition at line 5 of file seirs_pomp.c.

lik

#define lik   (__lik[0])

Definition at line 344 of file seirs_pomp.c.

ll

#define ll   (__x[__stateindex[4]])

Definition at line 42 of file seirs_pomp.c.

node

#define node   (__x[__stateindex[5]])

Definition at line 43 of file seirs_pomp.c.

omega

#define omega   (__p[__parindex[5]])

Definition at line 32 of file seirs_pomp.c.

POP

#define POP   (__p[__parindex[10]])

Definition at line 37 of file seirs_pomp.c.

psi

#define psi   (__p[__parindex[3]])

Definition at line 30 of file seirs_pomp.c.

R

#define R   (__x[__stateindex[3]])

Definition at line 41 of file seirs_pomp.c.

R0

#define R0   (__p[__parindex[9]])

Definition at line 36 of file seirs_pomp.c.

S

#define S   (__x[__stateindex[0]])

Definition at line 38 of file seirs_pomp.c.

S0

#define S0   (__p[__parindex[6]])

Definition at line 33 of file seirs_pomp.c.

sigma

#define sigma   (__p[__parindex[1]])

Definition at line 28 of file seirs_pomp.c.

Function Documentation

change_color()

static void change_color ( double * color, int nsample, int n, int from, int to )

static

Definition at line 13 of file seirs_pomp.c.

                                                   {
  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;
}

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event_rates()

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 )

static

Definition at line 53 of file seirs_pomp.c.

   {
  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): non-destructive (psi) + destructive (chi)
  *penalty += (psi+chi)*I;
  assert(R_FINITE(event_rate));
  return event_rate;
}

random_choice()

static int random_choice ( double n )

inlinestatic

Definition at line 9 of file seirs_pomp.c.

                                           {
  return floor(R_unif_index(n));
}

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seirs_dmeas()

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 )

Measurement model likelihood (dmeasure).

Definition at line 347 of file seirs_pomp.c.

   {
  assert(!ISNAN(ll));
  lik = (give_log) ? ll : exp(ll);
}

seirs_gill()

void seirs_gill	(	double *	__x,
		const double *	__p,
		const int *	__stateindex,
		const int *	__parindex,
		const int *	__covindex,
		const double *	__covars,
		double	t,
		double	dt )

Simulator for the latent-state process (rprocess).

This is the Gillespie algorithm applied to the solution of the filter equation for the SEIRS process.

Definition at line 142 of file seirs_pomp.c.

  {
  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+chi);
      if (unif_rand() < psi/(psi+chi)) { // non-destructive sample
    ll += log(I-ellI);
      } else {          // destructive sample
    ll += log(I);
    I -= 1;
      }
    } 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 && R_FINITE(ll)) {
 
    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;
}

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seirs_rinit()

void seirs_rinit	(	double *	__x,
		const double *	__p,
		double	t0,
		const int *	__stateindex,
		const int *	__parindex,
		const int *	__covindex,
		const double *	__covars )

Latent-state initializer (rinit component).

The state variables include S, E, I, R plus 'ellE' and 'ellI' (numbers of E- and I-deme lineages), the accumulated weight ('ll'), the current node number ('node'), and the coloring of each lineage ('COLOR').

Definition at line 117 of file seirs_pomp.c.

  {
  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;
}

Variable Documentation

nrate

const int nrate = 6

static

Definition at line 7 of file seirs_pomp.c.