A Parameter Estimation Method for Multiscale Models of Hepatitis C Virus Dynamics

Dynamics of a stochastic hepatitis B virus transmission model with media coverage and a case study of China

Hepatitis B virus (HBV) infection is a global public health problem and there are 257 million people living with chronic HBV infection throughout the world. In this paper, we investigate the dynamics of a stochastic HBV transmission model with media coverage and saturated incidence rate. Firstly, we prove the existence and uniqueness of positive solution for the stochastic model. Then the condition on the extinction of HBV infection is obtained, which implies that media coverage helps to control the disease spread and the noise intensities on the acute and chronic HBV infection play a key role in disease eradication. Furthermore, we verify that the system has a unique stationary distribution under certain conditions, and the disease will prevail from the biological perspective. Numerical simulations are conducted to illustrate our theoretical results intuitively. As a case study, we fit our model to the available hepatitis B data of mainland China from 2005 to 2021.

Advances in Parameter Estimation and Learning from Data for Mathematical Models of Hepatitis C Viral Kinetics

Mathematical models, some of which incorporate both intracellular and extracellular hepatitis C viral kinetics, have been advanced in recent years for studying HCV–host dynamics, antivirals mode of action, and their efficacy. The standard ordinary differential equation (ODE) hepatitis C virus (HCV) kinetic model keeps track of uninfected cells, infected cells, and free virus. In multiscale models, a fourth partial differential equation (PDE) accounts for the intracellular viral RNA (vRNA) kinetics in an infected cell. The PDE multiscale model is substantially more difficult to solve compared to the standard ODE model, with governing differential equations that are stiff. In previous contributions, we developed and implemented stable and efficient numerical methods for the multiscale model for both the solution of the model equations and parameter estimation. In this contribution, we perform sensitivity analysis on model parameters to gain insight into important properties and to ensure our numerical methods can be safely used for HCV viral dynamic simulations. Furthermore, we generate in-silico patients using the multiscale models to perform machine learning from the data, which enables us to remove HCV measurements on certain days and still be able to estimate meaningful observations with a sufficiently small error.

Machine learning for mathematical models of HCV kinetics during antiviral therapy

Mathematical models for hepatitis C virus (HCV) dynamics have provided a means for evaluating the antiviral effectiveness of therapy and estimating treatment outcomes such as the time to cure. Recently, a mathematical modeling approach was used in the first proof-of-concept clinical trial assessing in real-time the utility of response-guided therapy with direct-acting antivirals (DAAs) in chronic HCV-infected patients. Several retrospective studies have shown that mathematical modeling of viral kinetics predicts time to cure of less than 12 weeks in the majority of individuals treated with sofosbuvir-based as well as other DAA regimens. A database of these studies was built, and machine learning methods were evaluated for their ability to estimate the time to cure for each patient to facilitate real-time modeling studies. Data from these studies exploring mathematical modeling of HCV kinetics under DAAs in 266 chronic HCV-infected patients were gathered. Different learning methods were applied and trained on part of the dataset ('train' set), to predict time to cure on the untrained part ('test' set). Our results show that this machine learning approach provides a means for establishing an accurate time to cure prediction that will support the implementation of individualized treatment.

Modeling-Based Response-Guided Glecaprevir-Pibrentasvir Therapy for Chronic Hepatitis C to Identify Patients for Ultrashort Treatment Duration

We recently showed in a proof-of-concept study that real-time modeling-based response-guided therapy can shorten hepatitis C virus treatment duration with sofosbuvir-velpatasvir, elbasvir-grazoprevir, and sofosbuvir-ledipasvir without compromising efficacy, confirming our retrospective modeling reports in >200 patients. However, retrospective modeling of pibrentasvir-glecaprevir (P/G) treatment has yet to be evaluated. In the current study, modeling hepatitis C virus kinetics in 44 cirrhotic and noncirrhotic patients predicts that P/G treatment might have been reduced to 4, 6, and 7 weeks in 16%, 34%, and 14% of patients, respectively. These results support the further evaluation of a modeling-based response-guided therapy approach using P/G.

Efficient Methods for Parameter Estimation of Ordinary and Partial Differential Equation Models of Viral Hepatitis Kinetics

Parameter estimation in mathematical models that are based on differential equations is known to be of fundamental importance. For sophisticated models such as age-structured models that simulate biological agents, parameter estimation that addresses all cases of data points available presents a formidable challenge and efficiency considerations need to be employed in order for the method to become practical. In the case of age-structured models of viral hepatitis dynamics under antiviral treatment that deal with partial differential equations, a fully numerical parameter estimation method was developed that does not require an analytical approximation of the solution to the multiscale model equations, avoiding the necessity to derive the long-term approximation for each model. However, the method is considerably slow because of precision problems in estimating derivatives with respect to the parameters near their boundary values, making it almost impractical for general use. In order to overcome this limitation, two steps have been taken that significantly reduce the running time by orders of magnitude and thereby lead to a practical method. First, constrained optimization is used, letting the user add constraints relating to the boundary values of each parameter before the method is executed. Second, optimization is performed by derivative-free methods, eliminating the need to evaluate expensive numerical derivative approximations. The newly efficient methods that were developed as a result of the above approach are described for hepatitis C virus kinetic models during antiviral therapy. Illustrations are provided using a user-friendly simulator that incorporates the efficient methods for both the ordinary and partial differential equation models.

Modeling based response guided therapy in subjects with recent hepatitis C infection

BACKGROUND & AIMS

Mathematical modeling of viral kinetics has been shown to identify patients with chronic hepatitis C virus (HCV) infection who could be cured with a shorter duration of direct-acting antiviral (DAA) treatment. However, modeling therapy duration has yet to be evaluated in recently infected individuals. The aim of this study was to retrospectively examine whether modeling can predict outcomes of six-week sofosbuvir (SOF) and weight-based ribavirin (R) therapy in individuals with recent HCV infection.

METHODS

Modeling was used to estimate viral host parameters and to predict time to cure for 12 adults with recent HCV infection (<12 months of infection) who received six weeks of treatment with SOF + R.

RESULTS

Modeling results yielded a 100% negative predictive value for SOF + R treatment response in nine participants and suggested that a median of 13 [interquartile range: 8-16] weeks of therapy would be required for these patients to achieve cure. Modeling predicted cure after 5 weeks of therapy in the only modeled participant who achieved a sustained virological response. However, cure was also predicted for two participants who relapsed following treatment.

CONCLUSIONS

The modeling results confirm that longer than 6 weeks of SOF + R is needed to reach cure in individuals with recent HCV infection. Prospective real-time modeling under current potent DAA regimens is needed to validate the potential of response-guided therapy in the management of recent HCV infection.