Nanang Susyanto

Partially observed epidemic systems are difficult to analyze because confirmed cases provide only an indirect view of transmission and hidden infections are usually unobserved. We consider the susceptible–unidentified infected–confirmed (SUC) epidemic model and develop SUC–PINN, a physics-informed neural network framework for estimating hidden epidemic states, transmission and confirmation rates, and the initial unidentified population from confirmed-case time series alone. The method combines confirmed-case observations with SUC residuals and initial-condition constraints, so that the learned trajectories remain tied to the governing dynamics. Experiments with synthetic data and COVID-19 surveillance data from Indonesia, Thailand, India, and the Philippines show that SUC–PINN recovers plausible hidden infection trajectories, yields stable parameter estimates, and provides accurate short-term forecasts. These results support SUC–PINN as a practical computational approach for inverse modeling and prediction in partially observed epidemic dynamics.

This paper studies tabular Q-learning when implemented as a feedback controller in deterministic discrete-time systems, where the learning process interacts with the system dynamics to generate closed-loop trajectories. Unlike classical convergenceresults, which assume infinite visitation as an external sampling condition, this property arises from the interaction between recurrence of the induced state dynamics and persistent exploration under GLIE-compliant ϵ-greedy policies. In particular, we prove that exploration remains sufficiently persistent along recurrent states, implying infinite visitation of all state-action pairs within the recurrent region. The results provide a dynamical-systems characterization of the sampling condition underlying classical Q-learning convergence and establish a formal connection between reinforcement learning and recurrence analysis in discrete-time systems. Numerical experiments on nonlinear epidemic dynamics and linear quadratic control benchmarks illustrate the resulting closed-loop behavior.

Spatial epidemic dynamics are strongly affected by local interactions and by the movement of individuals. This study develops a susceptible–infected–susceptible (SIS) model based on point pattern dynamics with individual movement. The model extends the spatial SIS point pattern framework of Hamada and Takasu by allowing susceptible and infected points to move in continuous space. Disease transmission is represented by a distance-dependent infection kernel, and Gaussian, step-function, and exponential kernels are compared. Heuristic singlet and pair-density equations are derived to describe how infection, recovery, birth, death, and movement affect the spatial distribution of susceptible and infected individuals. Numerical simulations are used to illustrate the effects of kernel shape, infection range, and movement on singlet densities, pair correlations, and the temporal evolution of point patterns. The results show how spatial movement and distance-dependent transmission jointly shape infection spread in a recurrent-infection framework.

In this paper, we deal with a Lévy noise‐driven epidemic model reflecting the dynamics of hepatitis C virus infection subject to the effect of the immune cells. A stochastic model for hepatitis C at the cellular level is developed, considering random fluctuations and the influence of immune cells. After formulating the model, the system's feasibility was examined using the fundamental principles of existence and uniqueness theory. Additionally, the behavior of the solutions near the disease‐free and endemic equilibrium points was analyzed. To evaluate the persistence or elimination of the infection, the threshold parameter a reproduction number ( and ) was computed, revealing that the disease dies out whenever and . Numerical simulations are performed to illustrate the analysis results. Finally, we establish the stochastic stability of the disease‐free equilibrium point. We examine stochastic disease extinction. Furthermore, we have demonstrated that the disease persists with or without immunity under appropriate conditions. Numerical simulations have been performed to confirm the theoretical results and demonstrate the stochastic dynamics of infection.

Accurately estimating aggregate loss distributions is critical in actuarial and financial risk assessment, as it underpins effective risk analysis and the development of mitigation strategies. However, incorrect parametric assumptions can lead to biased risk estimates and underestimated losses. Non-parametric methods, such as Kernel Density Estimation (KDE), offer a flexible alternative by generating smooth empirical probability density functions (PDFs) directly from sample data without assuming a specific distributional form. This study examines the impact of dependence structures on risk measures by applying KDE with a Gaussian kernel to estimate aggregate loss distributions. To quantify the effects of ignoring dependence, we introduce the concept of performance loss, focusing on variance, Value at Risk (VaR), and Tail Value at Risk (TVaR). The results show that performance loss increases with the correlation coefficient, indicating that higher dependency leads to greater underestimation of risk. Additionally, higher confidence levels amplify performance loss for VaR and TVaR, underscoring the sensitivity of these measures to tail behavior. These findings highlight the importance of incorporating dependence structures in risk modeling to avoid misleading evaluations. The implications are particularly relevant for disaster risk management in Central Asia, where overlooking interdependencies in seismic losses could result in inadequate financial and actuarial strategies.