/*
 * Modelling Immunotherapy of the Tumour-Immune Interaction
 * 
 * Model Status
 * 
 * This model has been recoded using the nondimensionalized equations.
 * This was suggested by the author to help with solving the problem,
 * due to its very stiff nature. Some but not all output from the
 * paper can be reproduced by this model. Values of s1 and s2 have
 * been set to zero to represent a non-treatment situation. A value
 * of 0.02 has been given to the variable c, which defines the
 * antigenicity of the tumour, to represent the middle of the range
 * given for this parameter. The model may be re-parameterised
 * to give other relevant outputs, for example, if s1 is greater
 * than 0 while s2 equals 0, the model can simulate adoptive cellular
 * immunotherapy. The model will not run in COR due to time being
 * defined as dimensionless.
 * 
 * Model Structure
 * 
 * ABSTRACT: A number of lines of evidence suggest that immunotherapy
 * with the cytokine interleukin-2 (IL-2) may boost the immune
 * system to fight tumors. CD4+ T cells, the cells that orchestrate
 * the immune response, use these cytokines as signaling mechanisms
 * for immune-response stimulation as well as lymphocyte stimulation,
 * growth, and differentiation. Because tumor cells begin as 'self',
 * the immune system may not respond in an effective way to eradicate
 * them. Adoptive cellular immunotherapy can potentially restore
 * or enhance these effects. We illustrate through mathematical
 * modeling the dynamics between tumor cells, immune-effector cells,
 * and IL-2. These efforts are able to explain both short tumor
 * oscillations in tumor sizes as well as long-term tumor relapse.
 * We then explore the effects of adoptive cellular immunotherapy
 * on the model and describe under what circumstances the tumor
 * can be eliminated.
 * 
 * The original paper reference is cited below:
 * 
 * Modeling immunotherapy of the tumor-immune interaction, Denise
 * Kirschner and John Carl Panetta, 1998, Journal of Mathematical
 * Biology, 37, 235-252. PubMed ID: 9785481
 * 
 * reaction diagram
 * 
 * [[Image file: kirschner_1998.png]]
 * 
 * A schematic diagram of the interactions between the effector
 * T cells, the tumour cells, and the cytokine interleukin-2 (IL-2).
 */

import nsrunit;
unit conversion on;
unit day=86400 second^1;
unit first_order_rate_constant=1.1574074E-5 second^(-1);
unit cells = fundamental;
unit cells_per_microlitre=1E9 meter^(-3)*cells^1;
unit flux=1.1574074E4 meter^(-3)*second^(-1)*cells^1;
// unit micromolar predefined

math main {
	realDomain tau dimensionless;
	tau.min=0;
	extern tau.max;
	extern tau.delta;
	real mu2 dimensionless;
	mu2=0.03;
	real c dimensionless;
	c=0.02;
	real p1 dimensionless;
	p1=0.1245;
	real g1 dimensionless;
	g1=2.0E-7;
	real s1 dimensionless;
	s1=0;
	real y(tau) dimensionless;
	when(tau=tau.min) y=1.0;
	real x(tau) dimensionless;
	when(tau=tau.min) x=1.0;
	real z(tau) dimensionless;
	when(tau=tau.min) z=1.0;
	real r2 dimensionless;
	r2=0.18;
	real a dimensionless;
	a=1.0;
	real b dimensionless;
	b=1.0E-9;
	real g2 dimensionless;
	g2=1.0E5;
	real mu3 dimensionless;
	mu3=10.0;
	real p2 dimensionless;
	p2=5.0;
	real g3 dimensionless;
	g3=1.0E3;
	real s2 dimensionless;
	s2=0;

	// <component name="environment">

	// <component name="x">
	x:tau=(c*y-mu2*x+p1*x*z/(g1+z)+s1);

	// <component name="y">
	y:tau=(r2*y*(1-b*y)-a*x*y/(g2+y));

	// <component name="z">
	z:tau=(p2*x*y/(g3+y)-mu3*z+s2);
}