Global dynamics of a PDE in-host viral model

Abstract

We consider an in-host virus dynamics model with spatial heterogeneity on the general bounded domain, and homogenous Neumann boundary condition. Under the assumption that only the free virus diffuse and the host cells (infected and uninfected) are not mobile, the model turns out to be hybrid in the sense that it consists of two point-wise ODEs and an PDE. We explore the virus dynamics by analyzing the model and identifying the basic reproduction number. When all model parameters are constants, the global dynamics of the model are fully determined.

Keywords:

• HBV
• Infection
• threshold
• basic reproduction number
• principle eigenvalue

Acknowledgements

While this work was initiated when FBW was visiting the University of Western Ontario, it was finalized when the authors were visiting the National Center of Theoretical Sciences (NCTS) at the National Tsing Hua University in Taiwan. The authors would like to thank NCTS for its support and hospitality during their visit.

Notes

Dedicated to Professor Wei Lin (Sun Yat-sen University) on the occasion of his 80th birthday.

FBW is partially supported by Ministry of Science and Technology of Taiwan, YH is partially supported by NNSF of China [grant number 11371380] and XZ is partially supported by NSERC of Canada.