/*
 * Modelling the Population Dynamics of Virus Infected Cells
 * 
 * Model Status
 * 
 * This CellML model runs in OpenCell and COR to replicate the
 * published results (figure 4 - up until the introduction of the
 * drug, which is not described in this set of equations). The
 * units have been checked and they are consistent. This particular
 * CellML model represents model 3 from the published paper.
 * 
 * Model Structure
 * 
 * ABSTRACT: BACKGROUND: Structured interruptions of antiretroviral
 * therapy of HIV-1 infected individuals are currently being tested
 * in clinical trials to study the effect interruptions have on
 * the immune responses and control of virus replication. OBJECTIVE:
 * To investigate the potential risks and benefits of interrupted
 * therapy using standard population dynamical models of HIV replication
 * kinetics. METHODS: Standard population dynamical models were
 * used to study the effect of structured therapy interruptions
 * on the immune effector cells, the latent cell compartment and
 * the emergence of drug resistance. CONCLUSIONS: The models suggest
 * that structured therapy interruption only leads to transient
 * or sustained virus control if the immune effector cells increase
 * during therapy. This increase must more than counterbalance
 * the increase in susceptible target cells induced by therapy.
 * The risk of inducing drug resistance by therapy interruptions
 * or the risk of repopulating the pool of latent cells during
 * drug-free periods may be small if the virus population remains
 * at levels considerably below baseline. However, if the virus
 * load increases during drug-free periods to levels similar to
 * or higher than baseline before therapy, both these risks increase
 * dramatically.
 * 
 * The original paper reference is cited below:
 * 
 * Risks and benefits of structured antiretroviral drug therapy
 * interruptions in HIV-1 infection, Sebastian Bonhoeffer, Michal
 * Rembiszewski, Gabriel M. Ortiz, and Douglas F. Nixon, 2000,
 * AIDS, 14, 2313-2322. PubMed ID: 11089619
 * 
 * cell diagram
 * 
 * [[Image file: bonhoeffer_rembiszewski_ortiz_nixon_2000.png]]
 * 
 * Schematic diagram of a mathematical model of the interaction
 * between HIV and the immune system.
 */

import nsrunit;
unit conversion on;
unit day=86400 second^1;
unit first_order_rate_constant=1.1574074E-5 second^(-1);

math main {
	realDomain time day;
	time.min=0;
	extern time.max;
	extern time.delta;
	real T(time) dimensionless;
	when(time=time.min) T=1.0;
	real s first_order_rate_constant;
	s=10.0;
	real dT first_order_rate_constant;
	dT=0.01;
	real b first_order_rate_constant;
	b=0.001;
	real I(time) dimensionless;
	when(time=time.min) I=1.0;
	real p first_order_rate_constant;
	p=0.05;
	real dI first_order_rate_constant;
	dI=0.3;
	real E(time) dimensionless;
	when(time=time.min) E=1.0;
	real c first_order_rate_constant;
	c=0.3;
	real dE first_order_rate_constant;
	dE=0.1;

	// <component name="environment">

	// <component name="T">
	T:time=(s-(dT*T+b*T*I));

	// <component name="I">
	I:time=(b*T*I-(dI*I+p*I*E));

	// <component name="E">
	E:time=(c*I-dE*E);

	// <component name="kinetic_parameters">
}