Endemic threshold results for an age-structured SIS epidemic model with periodic parameters

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:402

Article

Kuniya, Toshikazu¹  Inaba, Hisashi¹ 

[1] Univ Tokyo, Grad Sch Math Sci, Tokyo 1538914, Japan

关键词: SIS epidemic model;    Age structure;    Periodicity;    Basic reproduction number;    Malthusian parameter;   

DOI  :  10.1016/j.jmaa.2013.01.044

来源: Elsevier

【 摘 要 】

The main contribution of this paper is to obtain a threshold value for the existence and uniqueness of a nontrivial endemic periodic solution of an age-structured SIS epidemic model with periodic parameters. Under the assumption of the weak ergodicity of a non-autonomous Lotka-McKendrick system, we formulate a normalized system for an infected population as an initial boundary value problem of a partial differential equation. The existence problem for endemic periodic solutions is reduced to a fixed point problem of a nonlinear integral operator acting on a Banach space of locally integrable periodic L-1-valued functions. We prove that the spectral radius of the Frechet derivative of the integral operator at zero plays the role of a threshold for the existence and uniqueness of a nontrivial fixed point of the operator corresponding to a nontrivial periodic solution of the original differential equation in a weak sense. If the Malthusian parameter of the host population is equal to zero, our threshold value is equal to the well-known epidemiological threshold value, the basic reproduction number R-0. However, if it is not the case, then two threshold values are different from each other and we have to pay attention on their actual biological implications. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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