/*
 * Modeling defective interfering virus therapy for AIDS: conditions
 * for DIV survival
 * 
 * Model Status
 * 
 * This CellML model has been built from the differential expressions
 * in Nelson and Perelson's 1995 paper for the initial model without
 * DIV interference (equations 1-10). This file is known to run
 * in OpenCell and COR, and uses the parameters values in Tables
 * 1, 2, and 3 of the paper. One of the units (for the variable
 * theta) has been changed from micro_L (in the paper), to per_micro_L,
 * to be dimensionally consistent. Parameters in years are represented
 * in day equivalents. The CellML model simulation will replicate
 * the graph traces in figure 2 of the paper. Note that in the
 * paper, some figures are scaled logarithmically.
 * 
 * Model Structure
 * 
 * ABSTRACT: The administration of a genetically engineered defective
 * interfering virus (DIV) that interferes with HIV-1 replication
 * has been proposed as a therapy for HIV-1 infection and AIDS.
 * The proposed interfering virus, which is designed to superinfect
 * HIV-1 infected cells, carries ribozymes that cleave conserved
 * regions in HIV-1 RNA that code for the viral envelope protein.
 * Thus DIV infection of HIV-1 infected cells should reduce or
 * eliminate viral production by these cells. The success of this
 * therapeutic strategy will depend both on the intercellular interaction
 * of DIV and HIV-1, and on the overall dynamics of virus and T
 * cells in the body. To study these dynamical issues, we have
 * constructed a mathematical model of the interaction of HIV-1,
 * DIV, and CD4+ cells in vivo. The results of both mathematical
 * analysis and numerical simulation indicate that survival of
 * the engineered DIV purely on a peripheral blood HIV-1 infection
 * is unlikely. However, analytical results indicate that DIV might
 * well survive on HIV-1 infected CD4+ cells in lymphoid organs
 * such as lymph nodes and spleen, or on other HIV-1 infected cells
 * in these organs.
 * 
 * model diagram
 * 
 * [[Image file: nelson_1995.png]]
 * 
 * Schematic illustration of the main features of the model.
 * 
 * The original paper reference is cited below:
 * 
 * Modeling defective interfering virus therapy for AIDS: conditions
 * for DIV survival, Nelson G, Perelson A, 1995, Mathematical Biosciences,
 * 125, 127-153. PubMed ID: 7881191
 */

import nsrunit;
unit conversion on;
unit day=86400 second^1;
unit per_day=1.1574074E-5 second^(-1);
unit micro_L=1E-9 meter^3;
unit per_micro_L=1E9 meter^(-3);
unit micro_L_per_day=1.1574074E-14 meter^3*second^(-1);
unit per_micro_L_day=1.1574074E4 meter^(-3)*second^(-1);

math main {
	realDomain time day;
	time.min=0;
	extern time.max;
	extern time.delta;
	real mu_T per_day;
	mu_T=0.02;
	real r per_day;
	r=0.03;
	real T_max per_micro_L;
	T_max=1500;
	real s_0 per_micro_L_day;
	s_0=10;
	real theta per_micro_L;
	theta=1;
	real k_1 micro_L_per_day;
	k_1=2.4E-5;
	real k_1_ micro_L_per_day;
	k_1_=2.4E-6;
	real T_1(time) per_micro_L;
	when(time=time.min) T_1=0;
	real V(time) per_micro_L;
	when(time=time.min) V=1E-3;
	real V_(time) per_micro_L;
	when(time=time.min) V_=0;
	real s_V(time) per_micro_L_day;
	real T(time) per_micro_L;
	when(time=time.min) T=1000;
	real k_2 per_day;
	k_2=0.017;
	real k_1D micro_L_per_day;
	k_1D=2.4E-6;
	real mu_b per_day;
	mu_b=0.24;
	real D(time) per_micro_L;
	when(time=time.min) D=0;
	real T_2(time) per_micro_L;
	when(time=time.min) T_2=0;
	real k_s per_day;
	k_s=0.24;
	real mu_bD per_day;
	mu_bD=0.17;
	real T_D2(time) per_micro_L;
	when(time=time.min) T_D2=0;
	real mu_TD per_day;
	mu_TD=0.02;
	real T_D1(time) per_micro_L;
	when(time=time.min) T_D1=0;
	real mu_D per_day;
	mu_D=2.4;
	real N_t(time) dimensionless;
	real N_D_t(time) dimensionless;
	real pi_D_t(time) per_day;
	real mu_V per_day;
	mu_V=2.4;
	real N_2_t(time) dimensionless;
	real N_t_(time) dimensionless;
	real pi_t_(time) per_day;
	real N_0 dimensionless;
	N_0=300;
	real gamma dimensionless;
	gamma=25;
	real t_c day;
	t_c=7305;
	real T_tot(time) per_micro_L;

	// <component name="environment">

	// <component name="uninfected_CD4">
	T:time=(s_V-mu_T*T+r*T*(1-(T+T_1)/T_max)-k_1*V*T-k_1_*V_*T);
	s_V=(s_0*theta/(theta+V));

	// <component name="latently_infected_CD4">
	T_1:time=(k_1*V*T+k_1_*V_*T-mu_T*T_1-k_2*T_1);

	// <component name="actively_infected_CD4">
	T_2:time=(k_2*T_1-k_1D*D*T_2-mu_b*T_2);

	// <component name="actively_coinfected_CD4">
	T_D2:time=(k_1D*D*T_2-k_s*T_D2-mu_bD*T_D2);

	// <component name="stably_coinfected_CD4">
	T_D1:time=(k_s*T_D2-mu_TD*T_D1);

	// <component name="DIV">
	D:time=(N_D_t*mu_bD*T_D2+pi_D_t*T_D1-mu_D*D);
	N_D_t=(.2*N_t);
	pi_D_t=(.3*mu_b*N_t);

	// <component name="HIV1">
	V:time=(N_t*mu_b*T_2+N_2_t*mu_bD*T_D2-k_1*V*T-mu_V*V);
	N_2_t=(.6*N_t);

	// <component name="hybrid_HIV1">
	V_:time=(N_t_*mu_bD*T_D2+pi_t_*T_D1-mu_V*V_-k_1_*T*V_);
	N_t_=(.2*N_t);
	pi_t_=(.1*mu_b*N_t);

	// <component name="production_function">
	N_t=(N_0*(1+gamma*(time^2/(time^2+t_c^2))));

	// <component name="cell_population">
	T_tot=(T+T_1+T_2);
}