Advances in theMathematical ModellingofHepatitisCVirusDynamics

| Mathematical models have provided key insights into the pathogenesis of hepatitis C virus (HCV) in vivo, suggested predominant mechanism(s) of drug action, explained confounding patterns of viral load changes in HCV infected patients undergoing therapy, and presented a framework for therapy optimization. In this article, I present an overview of the major advances in the mathematical modeling of HCV dynamics. Introduction Nearly 170 million people worldwide are infected with hepatitis C virus (HCV) [1]. Chronic HCV infection is a major cause of cirrhosis necessitating liver transplantation and often leading to death. The current treatment for HCV infection involves combination therapy with two drugs, pegylated interferon and ribavirin [2]. Combination therapy induces long-term responses in only ∼50% of the patients treated [2,3]. For patients who do not respond to combination therapy, no effective alternatives exist [3]. It is of importance therefore to identify markers of disease progression and early predictors of therapeutic response that would suggest refinements of therapeutic protocols leading to enhancement of long-term response rates and/or minimization of exposure of patients to drugs, which remain expensive and have toxic side effects. The responses of patients to combination therapy fall into three broad categories [4]. Sustained virological response (SVR) occurs when the concentration of viral particles in the blood, called viral load, falls below the detection limit (∼100 HCV RNA copies per ml) during therapy and remains undetectable for 24 weeks after cessation of therapy. Patients exhibiting SVR are generally cured of the infection. In some patients, the viral load becomes undetectable during therapy, called an end-of-treatment response (ETR), but relapses upon cessation of therapy. Reinstatement of therapy may lead to SVR in such patients. In some patients, called non-responders, the viral load remains detectable throughout. Upon initiation of therapy, such patients experience either an initial drop in the viral load followed by a nearly constant detectable viral load (flat response) or no drop at all (null response). The profiles of viral load decline in patients following the initiation of therapy serve as broad indicators of long-term response [4]. The pretreatment viral load remains approximately constant in chronically infected patients. Following the onset of therapy, the viral load drops in a biphasic or triphasic manner. In responders with a biphasic decay pattern, a sharp drop occurs for the first 1–2 days, followed by a slower second phase decline until viral load becomes undetectable. In patients exhibiting a transient response followed by relapse, the initial drop and/or the second phase decline may be subdued. Non-responders typically do not exhibit a significant second phase decline. When a triphasic response is observed, a shoulder phase of 4–28 days duration, where the viral load is nearly constant, separates the initial sharp drop and the subsequent slow decline [5]. These intriguing patterns of viral load changes in HCV infected patients under therapy hold clues to HCV pathogenesis in vivo and outcomes of therapy. Over the past decade, mathematical models of HCV dynamics have been developed that have Journal of the Indian Institute of Science VOL 88:1 Jan–Mar 2008 journal.library. iisc.ernet. in 37 REVIEW Narendra M. Dixit Figure 1: Decline in viral load following the onset of therapy predicted by Eqs. (2) and (3) with η = 0.8,ε = 0 (green); η = 0,ε = 0.8 (red solid); η=0.8, ε = 0.8 (red dashed). The uninfected cell density is held constant at the pretreatment value T = cδ/pβ. The initial viral load, V0 = 10 copies ml−1, and the infected cell density, I0 = cV0/p. Parameter values employed are β = 2.25×10−7 ml day−1 virions−1, δ = 1 day−1, p = 2.9 virions cell−1 day−1, and c = 6 day−1.