Hepatitis C remains a major global health burden, causing chronic liver disease and progressing to life-threatening outcomes when untreated. The highest burdens occur in resource-limited populations, with countries such as Pakistan, Egypt, and China cited as having particularly large case numbers. Public health strategies emphasize mass screening, early diagnosis, and effective antiviral treatment, but behavioral comorbidities influence outcomes and complicate control efforts.
Chronic alcohol consumption is biologically associated with accelerated liver injury among people with hepatitis C, increasing the risk of advanced fibrosis and cirrhosis. Alcohol use may also reduce antiviral treatment effectiveness, particularly with earlier interferon-based regimens, whereas abstinence is associated with improved therapeutic responses. Because alcohol modifies both individual prognosis and potentially population-level transmission dynamics, it is important to incorporate alcohol use into mechanistic models designed to forecast hepatitis C trends and to inform interventions.
The authors adapt compartmental modeling to represent hepatitis C dynamics while explicitly including alcohol-related effects. The formulated model, denoted SFBHCR, comprises six coupled nonlinear ordinary differential equations that partition the population across epidemiologic states relevant to hepatitis C infection and alcohol exposure. The model structure is a modification of existing compartmental frameworks, with assumptions grounded in clinical and biological evidence linking high alcohol consumption to faster progression toward chronic disease.
Because the system is nonlinear and multidimensional, obtaining accurate simulations across the solution domain is computationally challenging using only traditional numerical solvers. The authors therefore explore an alternative computational approach to approximate solutions.
The manuscript reports calculation of the disease transmission threshold, the basic reproduction number (R0), for the proposed SFBHCR model. Stability analyses are performed at the disease-free and endemic equilibria to characterize conditions under which hepatitis C would die out or persist in the modeled population. These analytical steps are used to connect parameter values and structural elements of the model to long-term qualitative behavior.
To address the numerical complexity of solving the six-dimensional, nonlinear ODE system, the authors employ a deep learning technique based on artificial neural networks (ANNs). The approach is motivated by the universal approximation theorem, which establishes that multilayer perceptrons can approximate continuous functions with arbitrary accuracy given suitable architecture and training. The ANN implementation uses gradient-based optimization (backpropagation) to minimize discrepancies between the network output and the differential system constraints and initial conditions. Advantages highlighted include continuous, differentiable network outputs, closed-form approximations once trained, good interpolation properties, and relatively modest memory requirements because only network weights must be stored.
The ANN framework is presented as a feasible and computationally effective method for simulating ODE models under specified initial and boundary conditions, with citations to prior applications of neural networks to ordinary and partial differential equations and to related epidemiological modeling efforts.
To validate and benchmark the ANN-based solver, the authors compare its performance against established numerical methods: the Runge–Kutta family of integrators and the Livermore ODE solver algorithm. Comparison criteria include solution accuracy, convergence behavior, and stability characteristics. The study reports that the proposed ANN approach demonstrates superior convergence and stability in comparison with these standard numerical techniques, suggesting it is an efficient and robust alternative for solving complex epidemiological ODE systems.
Sensitivity analysis is performed on the model to determine which parameters most strongly influence hepatitis C transmission and the model’s predicted dynamics. This analysis supports interpretation of which biological or behavioral factors (including alcohol-related parameters) are likely to be most impactful for disease spread and for achieving disease control objectives. The sensitivity results complement the analytical computation of R0 and inform prioritization of interventions in modeled scenarios.
Overall, the authors find that combining a mechanistic compartmental model with a neural-network–based solver yields a workable, accurate forecasting framework. The ANN produces continuous closed-form approximations of the six-compartment system and, according to the manuscript’s comparisons, offers better convergence and stability than the tested conventional solvers. The study underscores the potential for data-driven machine learning methods to augment traditional epidemiological modeling, particularly when behavioral risk factors such as alcohol consumption materially affect disease progression and treatment outcomes.
The authors state that all data used in the manuscript are included and that the author-generated code underpinning the ANN implementation and model simulations has been made publicly available without restrictions. The code repository is provided in the manuscript for reproducibility and reuse.
This work illustrates an approach that integrates biological insight about alcohol’s role in hepatitis C progression with a six-compartment epidemiological model and a neural network–based solver. The combined analytic, sensitivity, and computational results support the use of ANN techniques as complementary tools to classical numerical methods for forecasting infectious disease dynamics. The authors conclude that deep learning methods can be promising for epidemiological prediction and control planning when behavioral comorbidities are important. Specific numerical results, parameter estimates, and detailed model outputs are reported in the source article and associated figures and tables.