Impulsive SUI epidemic model for HIV/AIDS with chronological age and infection age |
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Authors: | Ping Yan |
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Affiliation: | a School of Science, Anhui Agricultural University, Hefei 230036, PR China b College of Mathematics and System Science, Xinjiang University, Urumqi 830046, PR China |
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Abstract: | This paper develops an impulsive SUI model of human immunodeficiency virus/acquired immunodeficiency syndrome(HIV/AIDS) epidemic for the first time to study the dynamic behavior of this model. The SUI model is described by impulsive partial differential equations. First, the well-posedness of the model is attained by the method of characteristic lines and iterative method. Secondly, the basic reproduction number R0(q,T) of the epidemic which depends on the impulsive HIV-finding period T and the HIV-finding proportion q is obtained by mathematical analysis. Our result shows that HIV/AIDS epidemic can be theoretically eradicated if we can have the suitable HIV-finding proportion q and the impulsive HIV-finding period T such that R0(q,T)<1. We also conjecture that the infection-free periodic solution of the SUI model is unstable when R0(q,T)>1. |
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Keywords: | HIV/AIDS epidemic Basic reproduction number Infection-age-structure |
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