/* * Modelling the Kinetics of Plasma Virus Following the Initiation * of Therapy * * Model Status * * This is the original unchecked version of the model imported * from the previous CellML model repository, 24-Jan-2006. * * Model Structure * * Highly active anti-retroviral therapy (HAART) significantly * reduces the viral load in most HIV infected patients. Most believe * that this is due to the drug's ability to act as an efficient * blockade of the de novo infection of target cells. However, * HAART is not 100 percent effective, usually because some long-lived * infected cells persist, which then convert to short-lived HIV * producers when activated. The extent to which virus production * from infected to uninfected cells is blocked is of great importance. * The answer will help to determine whether or not HAART is capable * of eradicating HIV infection. * * The concept that drug treatment is an efficient blockade of * viral replication has derived much of its credibility from being * incorporated into a model that successfully fits the kinetic * data. This model of HIV dynamics was published by Perelson et * al. in 1996. Their main observation was that viral load decline * following drug application occurred in two discrete phases: * an initial rapid decline (phase I) followed by a more gradual * decline (phase II). They explained this observation by the fact * that the drugs decreased viral load by inhibiting the de novo * infection of susceptible cells. Phase I reflected the decline * of the originally infected cells, and phase II reflected the * decline of those infected cells which had a slightly longer * half-life. * * However, the authors of the current model, Grossman et al. argue * that the idea of a cell having a half-life is biologically implausible. * They suggest instead that it is more plausible to think of the * infected lymphocytes undergoing an aging-like process. That * is, the death of an infected, HIV-producing cell follows productive * infection after a time delay (see below). The observed exponential * decline in viral load then requires an alternative explanation. * This is provided by assuming that de novo infection is not blocked * completely by HAART, but only reduced. * * The complete original paper reference is cited below: * * HIV infection: how effective is drug combination treatment?, * Zvi Grossman, Mark Feinberg, Vladimir Kuznetsov, Dimiter Dimitrov, * and William Paul, 1998,Immunology Today, 19, 528-532. PubMed * ID: 9818549 * * cell diagram * * [[Image file: grossman_1998.png]] * * Schematic diagram of the conceptual model representing the cycles * of infection of activated, susceptible cells (S), with delay-type * kinetics of infected cell death. V represents the ambient virus, * and Ij represents the infected cells in the various different * stages of infection. * * Model simulations revealed that the half-life of the infected * cells can be calculated with reasonable accuracy from clinical * data. However, the remaining parameters can not be accurately * predicted from the current model, more data is needed. * * A variable delay from productive cell infection to cell death * can be modelled by dividing the process into several sequential * stages. These stages may represent real stages in the infection * process, or they may be regarded as a modelling convenience. * Another method of modelling a variable delay is to introduce * a distribution of delay times around a fixed average. This is * the approach chosen by the authors of the current model. */ import nsrunit; // Warning: unit conversion turned off due to unit errors in 4 equation(s) unit conversion off; unit per_ml=1E6 meter^(-3); unit day=86400 second^(-1); unit first_order_rate_constant=1.1574074E-5 second^1; math main { //Warning: the following variables were set 'extern' or given // an initial value of '0' because the model would otherwise be // underdetermined: c, p, a, S, V, I1, I2, I3, I4, I5 realDomain time day; time.min=0; extern time.max; extern time.delta; real k first_order_rate_constant; k=2.76; extern real c first_order_rate_constant; extern real p first_order_rate_constant; real q first_order_rate_constant; q=3.0; real b first_order_rate_constant; b=1.0; extern real a first_order_rate_constant; real S(time) per_ml; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) S=0; real V(time) per_ml; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) V=0; real I1(time) per_ml; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) I1=0; real I2(time) per_ml; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) I2=0; real I3(time) per_ml; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) I3=0; real I4(time) per_ml; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) I4=0; real I5(time) per_ml; //Warning: Assuming zero initial condition; nothing provided in original CellML model. when(time=time.min) I5=0; real Se per_ml; real Ve per_ml; real R0 dimensionless; real I1e per_ml; real I2e per_ml; real I3e per_ml; real I4e per_ml; real I5e per_ml; // // // S:time=(a-(b*S+c*S*V)); // I1:time=(c*S*V-k*I1); // I2:time=(k*(I1-I2)); // I3:time=(k*(I2-I3)); // I4:time=(k*(I3-I4)); // I5:time=(k*(I4-I5)); // V:time=(p*I5-q*V); // Se=(q*k/(p*c)); // Ve=(b/c*(R0-1)); R0=(a*p*c/(b*q*k)); // I1e=(q/p*Ve); // I2e=(q/p*Ve); // I3e=(q/p*Ve); // I4e=(q/p*Ve); // I5e=(q/p*Ve); }