Sun, Gui-Quan
Bai, Zhenguo
Zhang, Zi-Ke
Zhou, Tao
Jin, Zhen
<jats:p>An SEI autonomous model with logistic growth rate and its corresponding nonautonomous model are investigated. For the autonomous case, we give the attractive regions of equilibria and perform some numerical simulations. Basic demographic reproduction number<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>is obtained. Moreover, only the basic reproduction number<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>cannot ensure the existence of the positive equilibrium, which needs additional condition<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo>></mml:mo><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math>. For the nonautonomous case, by introducing the basic reproduction number defined by the spectral radius, we study the uniform persistence and extinction of the disease. The results show that for the periodic system the basic reproduction number is more accurate than the average reproduction number.</jats:p>
application/pdf
https://sonar.ch/global/documents/28331
eng
info:eu-repo/semantics/altIdentifier/doi/10.1155/2013/470646
info:eu-repo/semantics/altIdentifier/issn/1537-744X
info:eu-repo/semantics/openAccess
The Scientific World Journal. - Hindawi Limited. - 2013, vol. 2013, p. 1-10
General Biochemistry, Genetics and Molecular Biology
General Environmental Science
General Medicine
Positive Periodic Solutions of an Epidemic Model with Seasonality
http://purl.org/coar/resource_type/c_6501