Journal of Applied Mathematics and Computing

, Volume 59, Issue 1–2, pp 631–660

# Global stability of an age-structured model for pathogen–immune interaction

• Tsuyoshi Kajiwara
• Toru Sasaki
• Yoji Otani
Original Research

## Abstract

In this paper, we present an age-structured mathematical model for infectious disease in vivo with infection age of cells. The model contains an immune variable and the effect of absorption of pathogens into uninfected cells. We construct Lyapunov functionals for the model and prove that the time derivative of the functionals are nonpositive. Using this, we prove the global stability results for the model. Especially, we present the full mathematical detail of the proof of the global stability.

## Keywords

Lyapunov functionals Age-structured equations Immunity Persistence

## Mathematics Subject Classification

35B15 45D05 92B05

## Notes

### Acknowledgements

The authors would like to thank the anonymous referees for very helpful suggestions and comments which led to improvement of our original manuscripts. This work is partly supported by Grand-in-Aid Scientific Research (C) No. 17K05365 from Japan Society for the Promotion of Science.

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