/*
 * A model of HIV-1 pathogenesis that includes an intracellular
 * delay
 * 
 * Model Status
 * 
 * This CellML model represents the general model from the paper,
 * based on equation 1. The CellML model runs in both COR and OpenCell
 * and the units are consistent. The model simulation output looks
 * reasonable but we are unsure as to whether or not it recreates
 * the results of the published model as there are no obvious figures
 * for simple comparison.
 * 
 * Model Structure
 * 
 * ABSTRACT: Mathematical modeling combined with experimental measurements
 * have yielded important insights into HIV-1 pathogenesis. For
 * example, data from experiments in which HIV-infected patients
 * are given potent antiretroviral drugs that perturb the infection
 * process have been used to estimate kinetic parameters underlying
 * HIV infection. Many of the models used to analyze data have
 * assumed drug treatments to be completely efficacious and that
 * upon infection a cell instantly begins producing virus. We consider
 * a model that allows for less then perfect drug effects and which
 * includes a delay in the initiation of virus production. We present
 * detailed analysis of this delay differential equation model
 * and compare the results to a model without delay. Our analysis
 * shows that when drug efficacy is less than 100%, as may be the
 * case in vivo, the predicted rate of decline in plasma virus
 * concentration depends on three factors: the death rate of virus
 * producing cells, the efficacy of therapy, and the length of
 * the delay. Thus, previous estimates of infected cell loss rates
 * can be improved upon by considering more realistic models of
 * viral infection..
 * 
 * The original paper reference is cited below:
 * 
 * A model of HIV-1 pathogenesis that includes an intracellular
 * delay, Patrick W. Nelson, James D. Murray, and Alan S. Perelson,
 * 2000, Mathematical Biosciences, 163, 201-215. PubMed ID: 10701304
 * 
 * reaction schematic for the model
 * 
 * [[Image file: nelson_2000.png]]
 * 
 * A schematic diagram showing the cascade of events triggered
 * by the binding of a HIV-1 virus particle to a receptor on a
 * target T-cell.
 */

import nsrunit;
unit conversion on;
unit day=86400 second^1;
unit per_day=1.1574074E-5 second^(-1);
unit ml=1E-6 meter^3;
unit cell = fundamental;
unit viron = fundamental;
unit cells_per_day=1.1574074E-5 second^(-1)*cell^1;
unit cells_per_ml=1E6 meter^(-3)*cell^1;
unit virons_per_day=1.1574074E-5 second^(-1)*viron^1;
unit virons_per_cell=1 cell^(-1)*viron^1;
unit virons_per_ml=1E6 meter^(-3)*viron^1;
unit ml_per_virons_per_day=1.1574074E-11 meter^3*second^(-1)*viron^(-1);

math main {
	realDomain time day;
	time.min=0;
	extern time.max;
	extern time.delta;
	real lambda cells_per_ml;
	lambda=5.0;
	real delta_1 cells_per_day;
	delta_1=0.03;
	real delta cells_per_day;
	delta=0.5;
	real np dimensionless;
	np=1.0;
	real c virons_per_day;
	c=3;
	real k ml_per_virons_per_day;
	k=3.43e-5;
	real N virons_per_cell;
	N=480;
	real T(time) cells_per_ml;
	when(time=time.min) T=180.0;
	real VI(time) virons_per_ml;
	when(time=time.min) VI=134e3;
	real T_star(time) cells_per_ml;
	when(time=time.min) T_star=3.6;
	real log_VI(time) dimensionless;
	real VNI(time) virons_per_ml;
	when(time=time.min) VNI=0;
	real virus_total(time) virons_per_ml;
	real log_virus_total(time) dimensionless;

	// <component name="environment">

	// <component name="model_parameters">

	// <component name="uninfected_T_cells">
	T:time=(lambda*(1 per_day)-delta_1*T/(1 cell)-k*VI*T);

	// <component name="infected_T_cells">
	T_star:time=(k*VI*T-delta/(1 cell)*T_star);

	// <component name="infectious_virus">
	VI:time=((1-np)*N*delta*T_star/(1 cell)-c*VI/(1 viron));
	log_VI=log(VI/(1 virons_per_ml));

	// <component name="non_infectious_virus">
	VNI:time=(np*N*delta*T_star/(1 cell)-c*VNI/(1 viron));

	// <component name="total_virus">
	virus_total=(VI+VNI);
	log_virus_total=log(virus_total/(1 virons_per_ml));
}