Creating functionality for time and age varying model.

[sumalibajaj]

We will consider a simplified case where the age and time specific FOI $\lambda=\lambda(a, t)$ is a product of an age-specific pattern and one that varies by time, $\lambda(a, t)=u(a) v(t)$.

[ekamau]

draft of time and age model in stan

// without seroreversion assumption!
// with estimated age and time rates

functions {
  real prob_seropos_calculate(vector time_rate, vector age_rate, int age){
    
    real prob_infected;
    vector[age] v_vector = tail(time_rate, age);
    for(i in 1:age){
      real sum_foi = 0;
      for(j in 1:i){
        real foi = (age_rate[j] * v_vector[j]);
        sum_foi += foi;
      }
      prob_infected = 1-exp(-sum_foi);
    }

    return prob_infected;
  }
   
  vector probability_seropos(vector time_rate, vector age_rate, int N) {
    
    vector[N] prob_seropos;
    
    for(n in 1:N) {
      prob_seropos[n] = prob_seropos_calculate(time_rate, age_rate, n);
    }
    
    return prob_seropos;
  }
  
}
      
data {
  int<lower=0> N;
  int<lower=0> age_max;
  int ages[N];
  int n_pos[N];
  int total[N];
 
}

parameters {
  vector<lower=0>[age_max] age_rate;
  vector<lower=0>[age_max] time_rate;
  
}

transformed parameters {
  vector[N] probability_age;
  vector[N] probability_age2;
  
  for(n in 1:N) {
    probability_age2[n] = prob_seropos_calculate(time_rate, age_rate, n);
  }
  
  probability_age = probability_seropos(time_rate, age_rate, N);
    
}


model {
  // priors
  age_rate ~ beta(2,5); // cauchy(0,1);
  time_rate ~ beta(2,5); // cauchy(0,1);
  
  // likelihood
  n_pos ~ binomial(total, probability_age);
}

generated quantities {
  int pos_pred[N];
  
  pos_pred = binomial_rng(total, probability_age);
  
}