# American Institute of Mathematical Sciences

2010, 7(1): 123-147. doi: 10.3934/mbe.2010.7.123

## An age-structured two-strain epidemic model with super-infection

 1 Department of Mathematics, Xinyang Normal University, Xinyang 464000, China, China 2 Department of Mathematics, 358 Little Hall, University of Florida, Gainesville, FL 32611, United States

Received  May 2009 Revised  October 2009 Published  January 2010

This article focuses on the study of an age-structured two-strain model with super-infection. The explicit expression of basic reproduction numbers and the invasion reproduction numbers corresponding to strain one and strain two are obtained. It is shown that the infection-free steady state is globally stable if the basic reproductive number $R_0$ is below one. Existence of strain one and strain two exclusive equilibria is established. Conditions for local stability or instability of the exclusive equilibria of the strain one and strain two are established. Existence of coexistence equilibrium is also obtained under the condition that both invasion reproduction numbers are larger than one.
Citation: Xue-Zhi Li, Ji-Xuan Liu, Maia Martcheva. An age-structured two-strain epidemic model with super-infection. Mathematical Biosciences & Engineering, 2010, 7 (1) : 123-147. doi: 10.3934/mbe.2010.7.123
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