/*
* Modelling the Population Dynamics of Virus Infected Cells
*
* Model Status
*
* This CellML model runs in OpenCell and COR to replicate the
* published results (figure 3 - 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 2 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 ql first_order_rate_constant;
ql=0.001;
real qa first_order_rate_constant;
qa=0.001;
real E(time) dimensionless;
when(time=time.min) E=1.0;
real Il(time) dimensionless;
when(time=time.min) Il=1.0;
real al first_order_rate_constant;
al=0.01;
real c first_order_rate_constant;
c=0.3;
real dE first_order_rate_constant;
dE=0.1;
real K dimensionless;
K=0.1;
real dE_ first_order_rate_constant;
dE_=0.25;
real K_ dimensionless;
K_=05.0;
//
//
T:time=(s-(dT*T+b*T*I));
//
I:time=(b*T*I-(dI*I+p*E*I+ql*I)+qa*I);
//
Il:time=(ql*I-(al*Il+qa*Il));
//
E:time=(c*E*I/(I+K)-(dE*E+dE_*E*I/(K_+I)));
//
}