Spatial dynamics of a viral infection model with nonlinear incidence rate

Yan Geng; Jinhu Xu; Yan Geng; Jinhu Xu

doi:10.3934/era.2026077

Electronic Research Archive

2026, Volume 34, Issue 3: 1691-1719. doi: 10.3934/era.2026077

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Research article

Spatial dynamics of a viral infection model with nonlinear incidence rate

Yan Geng ¹,
Jinhu Xu ^{2
,
,}

1.
School of Science, Xi'an Polytechnic University, Xi'an 710048, Shaanxi, China
2.
School of Mathematics, Xi'an University of Technology, Xi'an 710048, Shaanxi, China

Received: 30 December 2025 Revised: 21 January 2026 Accepted: 05 February 2026 Published: 27 February 2026

This work investigates the dynamics of a diffusive viral infection model that incorporates a nonlinear incidence and follicular dendritic cells (FDCs). First, the well-posedness is established. Then, We show that the basic reproduction number serves as a critical threshold for global stabilities: the infection-free steady state is globally asymptotically stable when the basic reproduction number is less than one, while the model exhibits a uniform persistence when the basic reproduction number is greater than one. Under the condition that the basic reproduction number equals to one, the infection-free steady state is shown to be globally asymptotically stable given certain additional assumptions. Furthermore, the global stability of the infected steady state is established for the homogeneous case. We find that ignoring the spatial heterogeneity in the infection capacity of viruses and infected cells may lead to an underestimation of the transmission risk. Although the spatial heterogeneity of a FDC does not affect the basic reproduction number, neglecting the infection originating from a FDC may lead to an underestimation of the infection risk.
- spatial heterogeneity,
- nonlinear incidence,
- basic reproduction number,
- global asymptotic stability,
- uniform persistence
Citation: Yan Geng, Jinhu Xu. Spatial dynamics of a viral infection model with nonlinear incidence rate[J]. Electronic Research Archive, 2026, 34(3): 1691-1719. doi: 10.3934/era.2026077

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Abstract

This work investigates the dynamics of a diffusive viral infection model that incorporates a nonlinear incidence and follicular dendritic cells (FDCs). First, the well-posedness is established. Then, We show that the basic reproduction number serves as a critical threshold for global stabilities: the infection-free steady state is globally asymptotically stable when the basic reproduction number is less than one, while the model exhibits a uniform persistence when the basic reproduction number is greater than one. Under the condition that the basic reproduction number equals to one, the infection-free steady state is shown to be globally asymptotically stable given certain additional assumptions. Furthermore, the global stability of the infected steady state is established for the homogeneous case. We find that ignoring the spatial heterogeneity in the infection capacity of viruses and infected cells may lead to an underestimation of the transmission risk. Although the spatial heterogeneity of a FDC does not affect the basic reproduction number, neglecting the infection originating from a FDC may lead to an underestimation of the infection risk.

References

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