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

Global stability of an age-structured model for pathogen–immune interaction J. Appl. Math. Comput. https://doi.org/10.1007/s12190-018-1194-8 ORIGINAL RESEARCH Global stability of an age-structured model for pathogen–immune interaction 1 1 1 Tsuyoshi Kajiwara · Toru Sasaki · Yoji Otani Received: 1 August 2017 © Korean Society for Computational and Applied Mathematics 2018 Abstract In this paper, we present an age-structured mathematical model for infec- tious 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 non- positive. 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 1 Introduction Infectious diseases in vivo have been investigated extensively using ordinary differ- ential equations, and differential equations with delay. Anderson et al. [2] and Nowak and Bangham [17] proposed models containing immune variables explicitly. Local stability analyses of the equilibria of such models are often difﬁcult because the sizes of Jacobi matrices are large and a lot of symbolic http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Mathematics and Computing Springer Journals

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

, Volume OnlineFirst – Jun 5, 2018
30 pages

/lp/springer_journal/global-stability-of-an-age-structured-model-for-pathogen-immune-JXM4w0ReFm
Publisher
Springer Berlin Heidelberg
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Theory of Computation; Mathematics of Computing
ISSN
1598-5865
eISSN
1865-2085
D.O.I.
10.1007/s12190-018-1194-8
Publisher site
See Article on Publisher Site

### Abstract

J. Appl. Math. Comput. https://doi.org/10.1007/s12190-018-1194-8 ORIGINAL RESEARCH Global stability of an age-structured model for pathogen–immune interaction 1 1 1 Tsuyoshi Kajiwara · Toru Sasaki · Yoji Otani Received: 1 August 2017 © Korean Society for Computational and Applied Mathematics 2018 Abstract In this paper, we present an age-structured mathematical model for infec- tious 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 non- positive. 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 1 Introduction Infectious diseases in vivo have been investigated extensively using ordinary differ- ential equations, and differential equations with delay. Anderson et al. [2] and Nowak and Bangham [17] proposed models containing immune variables explicitly. Local stability analyses of the equilibria of such models are often difﬁcult because the sizes of Jacobi matrices are large and a lot of symbolic

### Journal

Journal of Applied Mathematics and ComputingSpringer Journals

Published: Jun 5, 2018

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