Threshold Dynamics for Compartmental Epidemic Models in Periodic Environments |
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Authors: | Wendi Wang Xiao-Qiang Zhao |
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Institution: | (1) Department of Mathematics, Southwest University, Chongqing, 400715, People’s Republic of China;(2) Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, Canada, A1C 5S7 |
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Abstract: | The basic reproduction ratio and its computation formulae are established for a large class of compartmental epidemic models
in periodic environments. It is proved that a disease cannot invade the disease-free state if the ratio is less than unity
and can invade if it is greater than unity. It is also shown that the basic reproduction number of the time-averaged autonomous
system is applicable in the case where both the matrix of new infection rate and the matrix of transition and dissipation
within infectious compartments are diagonal, but it may underestimate and overestimate infection risks in other cases. The
global dynamics of a periodic epidemic model with patch structure is analyzed in order to study the impact of periodic contacts
or periodic migrations on the disease transmission.
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Keywords: | Compartmental models Reproduction ratio Periodicity Threshold dynamics |
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