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In this paper, we consider a Hepatitis C model characterized by acute and chronic infections, treatment as a health-protective measure for the chronically infected is proposed, and its effect on the population is further highlighted. The model is perturbed by white noise and we incorporate Lévy jumps as means to depict abrupt fluctuations. We demonstrate the solution’s existence and uniqueness and deduce adequate criteria for the disease’s extinction and persistence. The importance of treatment as a protective strategy is manifested in its ability to eradicate or mitigate the propagation of the disease. We present numerical simulations to demonstrate the theoretical findings we have obtained.
Alternative medicines are being increasingly used and investigated in the management of a variety of disorders. Hepatitis is a common indication for the use of alternative therapies but evidence for the efficacy of many compounds is lacking. We have utilized a well-defined model of liver injury to study the efficacy of three herbal products designed to assist in the management of liver disease. Mice were exposed to carbon tetrachloride (CCL4) given intragastrically after they had been pretreated for five days with either saline or one of four doses of silymarin extract or CH100 (a Chinese herbal medicine comprising of 19 herbs) or one of two doses of CH101 (a Chinese herbal preparation designed to reduce fibrosis). Animals were sacrificed 24 hours after receiving CCL4. Liver enzymes and hepatic histology formed the basis for evaluating efficacy of the treatments. Each of the alternative medicines reduced the alanine amino transferase (ALT) elevation demonstrated after CCL4 injection. The high dose CH100 regimen was most effective in protecting against injury and this was confirmed with hepatic histology. Other doses of CH100, CH101 and silymarin were not shown to provide protection against the histological damage. In conclusion, Silymarin, CH100 and CH101 are able to reduce ALT elevation in animals exposed to CCL4. High dose CH100 provides protection from hepatocyte necrosis in this model. The data add to our understanding of the capacity some herbal medicines have to modify the reaction of the liver to a variety of insults and suggest the value of studying these agents further in human liver diseases.
This study analyzes a model of hepatitis C with acute infectious, chronic infectious and the recovery or immune classes. Stability characters of disease-free and endemic proportionate equilibrium points are discussed. The role of immune system on the long-term survival of the susceptible population is derived. It has been shown that chronic infected populations persist whenever acute infected class persists and conversely. Lastly, the criterion for robustness of the system is established under stochastic perturbations. Numerical simulations are also performed to validate the results obtained.
The main goal of this paper is to determine an optimal treatment strategy using interferon and ribavirin, through mathematical modeling. We formulate a mathematical model using a system of ordinary differential equations, which describes the interaction of target cells (hepatocytes), infected cells, infectious virions, non-infectious virions and the two drugs, namely, interferon and ribavirin. We solve an optimal control problem with an objective functional that minimizes the viral load as well as the side effects of treatment. Finally we derive optimal treatment strategy and then solve it numerically.
A mathematical model for the transmission dynamics of Hepatitis C virus (HCV) have been proposed and investigated. The model presented looks into preferential sexual contacts between intravenous drug users and non-drug users. The threshold parameters of the model are determined and stabilities analysed. Both analytic and numerical simulations show that increase in intravenous drug use in addition to sex results in an increase of HCV cases. Thus, safe sex and treatment of HCV alone are not enough to curtail the transmission of HCV. Effective control of HCV require strategies that are tailor made for intravenous drug users.
Treatment of hepatitis C virus (HCV) is lengthy, expensive and fraught with side-effects, succeeding in only 50% of treated patients. In clinical settings, short-term treatment response (so-called sustained virological response (SVR)) is used to predict prolonged viral suppression. Although ordinary differential equation (ODE) models for within-host HCV infection have illuminated the mechanisms underlying treatment with interferon (IFN) and ribavirin (RBV), they have difficulty producing SVR without the introduction of an external extinction threshold. Here we show that bistability in an existing ODE model of HCV, which occurs when infected hepatocytes proliferate sufficiently faster than uninfected hepatocytes, can produce SVR without an external extinction threshold under biologically relevant conditions. The model can produce all clinically observed patient profiles for realistic parameter values; it can also be used to estimate the efficacy and/or duration of treatment that will ensure permanent cure for a particular patient.
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