
Numerical approximation of the basic reproduction number for a class of agestructured epidemic modelsNumerical approximation of the basic reproduction number for a class of agestructured epidemic models 
"/Kuniya, Toshikazu/"Kuniya, Toshikazu
73pp.106

112 , 201711 , Elsevier
ISSN:08939659
Description
We are concerned with the numerical approximation of the basic reproduction number Ro, which is the wellknown epidemiological threshold value defined by the spectral radius of the next generation operator. For a class of agestructured epidemic models in infinitedimensional spaces, R0 has the abstract form and cannot be explicitly calculated in general. We discretize the linearized equation for the infective population into a system of ordinary differential equations in a finite n dimensional space and obtain a corresponding threshold value R0,Rn,R, which can be explicitly calculated as the positive dominant eigenvalue of the next generation matrix. Under the compactness of the next generation operator, we show that Ro,Rn > R0 as n > +infinity in terms of the spectral approximation theory.
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