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Creators/Authors contains: "Shi, Junping"

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  1. ; (, 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. 
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    Free, publicly-accessible full text available April 30, 2026
  2. ; ; ; ; (, Physica D: Nonlinear Phenomena)
    Free, publicly-accessible full text available June 1, 2026
  3. ; ; (, Journal of Mathematical Biology)
    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. 
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  4. ; (, Journal of Differential Equations)
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  5. ; (, Annales Henri Poincaré)
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  6. ; ; ; (, Journal of Nonlinear Science)
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  7. ; ; (, Bulletin of Mathematical Biology)
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  8. ; ; (, Journal of Differential Equations)
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  9. ; ; (, Journal of Dynamics and Differential Equations)
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  10. ; (, Discrete and Continuous Dynamical Systems - B)
    The bistable dynamics of a modified Nicholson's blowflies delay differential equation with Allee effect is analyzed. The stability and basins of attraction of multiple equilibria are studied by using Lyapunov-LaSalle invariance principle. The existence of multiple periodic solutions are shown using local and global Hopf bifurcations near positive equilibria, and these solutions generate long transient oscillatory patterns and asymptotic stable oscillatory patterns. 
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