Study of a nonlinear delayed parabolic model for prion disease dynamics with the unfolded protein response

Authors

• Gangadhara Boregowda, The University of Texas Rio Grande Valley
• Laurent Pujo-Menjouet
• Zhaosheng Feng, The University of Texas Rio Grande Valley
• Michael R. Lindstrom, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

10-2026

Abstract

Prion diseases are neurodegenerative disorders characterized by the dynamic spread of misfolded toxic proteins in the brain. In this process, the normal cellular prion protein (PrPC) produced by neurons misfolds into a toxic form known as scrapie prion protein (PrPSc). These misfolded proteins propagate through the brain by converting healthy prions into their toxic form. This biological mechanism can be modeled by a system of nonlinear parabolic partial differential equations, accompanied by a nonlinear delayed integral boundary condition. Our primary objective is to establish the existence of nonnegative classical solutions to this system. Furthermore, we derive a priori estimates for the total concentrations of PrPC and PrPSc in the brain. Finally, we present numerical simulations to illustrate the spatiotemporal evolution of PrPC and PrPSc and to capture oscillations in their concentrations.

Comments

Pending ArXiv.

Recommended Citation

Boregowda, Gangadhara, Laurent Pujo-Menjouet, Zhaosheng Feng, and Michael R. Lindstrom. "Study of a Nonlinear Delayed Parabolic Model for Prion Disease Dynamics with the Unfolded Protein Response." Communications in Nonlinear Science and Numerical Simulation (2026): 110013. https://doi.org/10.1016/j.cnsns.2026.110013

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Publication Title

Communications in Nonlinear Science and Numerical Simulation

DOI

10.1016/j.cnsns.2026.110013