RESUMEN
Reconstructing a nonlinear dynamical system from empirical time series is a fundamental task in data-driven analysis. One of the main challenges is the existence of hidden variables; we only have records for some variables, and those for hidden variables are unavailable. In this work, the techniques for Carleman linearization, phase-space embedding, and dynamic mode decomposition are integrated to rebuild an optimal dynamical system from time series for one specific variable. Using the Takens theorem, the embedding dimension is determined, which is adopted as the dynamical system's dimension. The Carleman linearization is then used to transform this finite nonlinear system into an infinite linear system, which is further truncated into a finite linear system using the dynamic mode decomposition technique. We illustrate the performance of this integrated technique using data generated by the well-known Lorenz model, the Duffing oscillator, and empirical records of electrocardiogram, electroencephalogram, and measles outbreaks. The results show that this solution accurately estimates the operators of the nonlinear dynamical systems. This work provides a new data-driven method to estimate the Carleman operator of nonlinear dynamical systems.
RESUMEN
Background: Hepatitis C virus (HCV) genotype 1 is the most prevalent HCV infection in China. Sofosbuvir-based direct antiviral agent (DAA) regimens are the current mainstays of treatment. Sofosbuvir/velpatasvir (SOF/VEL) and sofosbuvir/ledipasvir (SOF/LDV) regimens became reimbursable in China in 2020. Thus, this study aimed to identify the optimal SOF-based regimen and to inform efficient use of healthcare resources by optimizing DAA use in treating HCV genotype 1. Methods and Models: A modeling-based cost-utility analysis was conducted from the payer's perspective targeting adult Chinese patients with chronic HCV genotype 1 infection. Direct medical costs and health utilities were inputted into a Markov model to simulate lifetime experiences of chronically infected HCV patients after receiving SOF/LDV, SOF/VEL or the traditional strategy of pegylated interferon (pegIFN) + ribavirin (RBV). Discounted lifetime cost and quality adjusted life years (QALYs) were computed and compared to generate the incremental cost utility ratio (ICUR). An ICUR below the threshold of 31,500 $/QALY suggests cost-effectiveness. Deterministic and probabilistic sensitivity analyses were performed to examine the robustness of model findings. Results: Both SOF/LDV and SOF/VEL regimens were dominant to the pegIFN + RBV regimen by creating more QALYs and incurring less cost. SOF/LDV produced 0.542 more QALYs but cost $10,390 less than pegIFN + RBV. Relative to SOF/LDV, SOF/VEL had an ICUR of 168,239 $/QALY which did not meet the cost-effectiveness standard. Therefore SOF/LDV was the optimal strategy. These findings were robust to linear and random variations of model parameters. However, reducing the SOF/VEL price by 40% would make this regimen the most cost-effective option. Conclusions: SOF/LDV was found to be the most cost-effective treatment, and SOF/VEL was also economically dominant to pegIFN + RBV. These findings indicated that replacing pegIFN + RBV with DAA regimens could be a promising strategy.