Open AccessMathematical analysis for an age-structured SIRS epidemic model
Author(s) -
Kento Okuwa,
Hisashi Inaba,
Toshikazu Kuniya
Publication year - 2019
Publication title -
mathematical biosciences and engineering
Language(s) - Uncategorized
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2019304
Subject(s) - mathematics , operator (biology) , bifurcation , epidemic model , stability (learning theory) , population , attractor , basic reproduction number , steady state (chemistry) , simple (philosophy) , age structure , computer science , mathematical analysis , demography , physics , biology , sociology , nonlinear system , philosophy , chemistry , repressor , biochemistry , epistemology , quantum mechanics , machine learning , transcription factor , gene
In this paper, we investigate an SIRS epidemic model with chronological age structure in a demographic steady state. Although the age-structured SIRS model is a simple extension of the well-known age-structured SIR epidemic model, we have to develop new technique to deal with problems due to the reversion of susceptibility for recovered individuals. First we give a standard proof for the well-posedness of the normalized age-structured SIRS model. Next we examine existence of endemic steady states by fixed point arguments and bifurcation method, where we introduce the next generation operator and the basic reproduction number R 0 to formulate endemic threshold results. Thirdly we investigate stability of steady states by the bifurcation calculation and the comparison method, and we show existence of a compact attractor and discuss the global behavior based on the population persistence theory. Finally we give some numerical examples and discuss the effect of mass-vaccination on R 0 and the critical coverage of immunization based on the reinfection threshold.