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- W2910646745 abstract "This paper investigates a three-patch Rift Valley fever virus transmission model with periodic coefficients. The basic reproduction number <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mfenced open=( close=)><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1,2,3</mml:mn></mml:mrow></mml:mfenced></mml:math> is calculated for the model by using the next infection operator method. The threshold conditions on the extinction and permanence in the mean of the disease with probability one. The Rift Valley fever disease will be permanent in the <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mi>j</mml:mi></mml:math>-th <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mfenced open=( close=)><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1,2,3</mml:mn></mml:mrow></mml:mfenced></mml:math> patch if <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mi>j</mml:mi><mml:mo>≥</mml:mo><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>></mml:mo><mml:mn>1</mml:mn></mml:math> and dies out in the <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mi>j</mml:mi></mml:math>-th patch if <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mi>j</mml:mi><mml:mo><</mml:mo><mml:mi>i</mml:mi></mml:math>. The numerical simulations are given to confirm the theoretical results." @default.
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- W2910646745 date "2019-01-09" @default.
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- W2910646745 title "Threshold Dynamics in a Periodic Three-Patch Rift Valley Fever Virus Transmission Model" @default.
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- W2910646745 doi "https://doi.org/10.1155/2019/7896946" @default.
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