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• W2952116897 abstract "We propose and study a viral infection model with two nonlocal effects and a general incidence rate. First, the semigroup theory and the classical renewal process are adopted to compute the basic reproduction number <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=script>R</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant=normal>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> as the spectral radius of the next-generation operator. It is shown that <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=script>R</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant=normal>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> equals the principal eigenvalue of a linear operator associated with a positive eigenfunction. Then we obtain the existence of endemic steady states by Shauder fixed point theorem. A threshold dynamics is established by the approach of Lyapunov functionals. Roughly speaking, if <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:msub><mml:mrow><mml:mi mathvariant=script>R</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant=normal>0</mml:mn></mml:mrow></mml:msub><mml:mo><</mml:mo><mml:mn mathvariant=normal>1</mml:mn></mml:math>, then the virus-free steady state is globally asymptotically stable; if <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:msub><mml:mrow><mml:mi mathvariant=script>R</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant=normal>0</mml:mn></mml:mrow></mml:msub><mml:mo>></mml:mo><mml:mn mathvariant=normal>1</mml:mn></mml:math>, then the endemic steady state is globally attractive under some additional conditions on the incidence rate. Finally, the theoretical results are illustrated by numerical simulations based on a backward Euler method." @default.
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• W2952116897 date "2019-06-16" @default.
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• W2952116897 title "Spatial and Temporal Dynamics of a Viral Infection Model with Two Nonlocal Effects" @default.
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• W2952116897 doi "https://doi.org/10.1155/2019/5842942" @default.
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