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            Abstract A dynamic reaction–diffusion model of four variables is proposed to describe the spread of lytic viruses among phytoplankton in a poorly mixed aquatic environment. The basic ecological reproductive index for phytoplankton invasion and the basic reproduction number for virus transmission are derived to characterize the phytoplankton growth and virus transmission dynamics. The theoretical and numerical results from the model show that the spread of lytic viruses effectively controls phytoplankton blooms. This validates the observations and experimental results of Emiliana huxleyi-lytic virus interactions. The studies also indicate that the lytic virus transmission cannot occur in a low-light or oligotrophic aquatic environment.more » « less
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            Liu, Di; Potts, Jonathan R; Salmaniw, Yurij; Shi, Junping; Wang, Hao (, Physica D: Nonlinear Phenomena)Free, publicly-accessible full text available June 1, 2026
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            Tao, Yiwen; Shi, Junping (, SIAM Journal on Applied Mathematics)A reaction-diffusion-advection glucose metabolism model is proposed to describe the spatiotemporal behaviors of glucose in the pancreatic islet. The global existence and boundedness of the solution to the model are proved, and the existence and uniqueness of the positive steady state are established. Spatiotemporal sensitivity index and correlation index are proposed to identify high-impact physiological factors and illustrate parameter interdependency. Additionally, different stages of glucose metabolism such as hyperinsulinemia, hypoglycemia, euglycemia, and diabetes are simulated to demonstrate the system’s dynamics under varying physiological conditions. These findings provide valuable guidance in the therapeutic process, aiding in the development of effective interventions.more » « lessFree, publicly-accessible full text available April 30, 2026
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            Chen, Xuqing; Reece, Kimberly S.; Shields, Jeffrey D. (, Journal of Invertebrate Pathology)
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