https://scholar.korea.ac.kr/handle/2021.sw.korea/2340 2026-04-05T17:56:27Z https://scholar.korea.ac.kr/handle/2021.sw.korea/270648 Title: A simple yet effective approach for predicting disease spread using mathematically-inspired diffusion-informed neural networks Authors: Jeong, ByeongChang; Lee, Yeon Ju; Han, Cheol E. Abstract: The COVID-19 outbreak has highlighted the importance of mathematical epidemic models like the Susceptible-Infected-Recovered (SIR) model, for understanding disease spread dynamics. However, enhancing their predictive accuracy complicates parameter estimation. To address this, we proposed a novel model that integrates traditional mathematical modeling with deep learning which has shown improved predicted power across diverse fields. The proposed model includes a simple artificial neural network (ANN) for regional disease incidences, and a graph convolutional neural network (GCN) to capture spread to adjacent regions. GCNs are a recent deep learning algorithm designed to learn spatial relationship from graph-structured data. We applied the model to COVID-19 incidences in Spain to evaluate its performance. It achieved a 0.9679 correlation with the test data, outperforming previous models with fewer parameters. By leveraging the efficient training methods of deep learning, the model simplifies parameter estimation while maintaining alignment with the mathematical framework to ensure interpretability. The proposed model may allow the more robust and insightful analyses by leveraging the generalization power of deep learning and theoretical foundations of the mathematical models. 2025-04-29T00:00:00Z https://scholar.korea.ac.kr/handle/2021.sw.korea/198599 Title: A risk-induced dispersal strategy of the infected population for a disease-free state in the SIS epidemic model Authors: Choi, Wonhyung; Ahn, Inkyung Abstract: This article proposes a dispersal strategy for infected individuals in a spatial susceptible-infected-susceptible (SIS) epidemic model. The presence of spatial heterogeneity and the movement of individuals play crucial roles in determining the persistence and eradication of infectious diseases. To capture these dynamics, we introduce a moving strategy called risk-induced dispersal (RID) for infected individuals in a continuous-time patch model of the SIS epidemic. First, we establish a continuous-time n-patch model and verify that the RID strategy is an effective approach for attaining a disease-free state. This is substantiated through simulations conducted on 7-patch models and analytical results derived from 2-patch models. Second, we extend our analysis by adapting the patch model into a diffusive epidemic model. This extension allows us to explore further the impact of the RID movement strategy on disease transmission and control. We validate our results through simulations, which provide the effects of the RID dispersal strategy. 2024-12-31T00:00:00Z https://scholar.korea.ac.kr/handle/2021.sw.korea/199691 Title: Spreading dynamics for an epidemic model of West-Nile virus with shifting environment Authors: Ahn, Inkyung; Choi, Wonhyung; Guo, Jong-Shenq Abstract: We study the disease -spreading dynamics of the West Nile virus (WNv) epidemic model under shifting climatic conditions. A WNv epidemic model is developed incorporating a shifting net growth term to depict the evolving mosquito habitat. First, we comprehensively characterize the spreading dynamics of mosquitoes for any given climate change speed compared with the intrinsic spreading speed of mosquitoes. Utilizing the results from mosquito dynamics, we determine the spreading dynamics of infected birds and mosquitoes, taking into account relationships among the shifting speed and the spreading speeds of mosquito and WNv. Ultimately, we find that infected mosquitoes and birds propagate, and their population densities converge to a stable positive endemic state. This paper provides crucial insights into the impact of climate change on the spread of vector -borne diseases such as WNv. 2024-12-01T00:00:00Z https://scholar.korea.ac.kr/handle/2021.sw.korea/200759 Title: The impulsive vaccination in an SVIS diffusive model Authors: Luo, Zipeng; Ahn, Inkyung; Lin, Zhigui Abstract: This paper examines a reaction-diffusion problem with impulses, which presents a susceptible-vaccinated-infected-susceptible (SVIS) epidemic model with impulsive vaccination. First, the existence and uniqueness of the global solution and the disease-free periodic solution have been established. Second, by considering the principal eigenvalue, the asymptotic behavior of the disease-free periodic solution and the sufficient condition for the persistence of diseases are given, in addition, the mono-tonicity of the principal eigenvalue is investigated. Third, the periodic state of the endemic disease has been explored when vaccination is not completely effective. Finally, the numerical simulations presented reveal the impacts of the infection rate and impulses, and demonstrate that effective vaccination is a reliable way to control the spread of diseases. 2024-09-16T00:00:00Z