United Nations Political Declaration 2011 on HIV and AIDS calls to reduce the sexual transmission and the transmission of HIV among people, who inject drugs by 50% by 2015, through different control strategies and pre...United Nations Political Declaration 2011 on HIV and AIDS calls to reduce the sexual transmission and the transmission of HIV among people, who inject drugs by 50% by 2015, through different control strategies and precautionary measures. In this paper, we propose and study a simple SI type model that considers the effect of various precaution- ary measures to control HIV epidemic. We show, unlike conventional epidemic models, that the basic reproduction number which essentially considered as the disease eradica- tion condition is no longer sufficient to eliminate HIV infection. In particular, we show that even when the basic reproduction number is made less than unity, the disease may persist if the initial outbreak is not low. Eradication of disease is however guaranteed if the ensemble control measure exceeds some upper critical value. It is also shown that an epidemic model with mass action incidence may exhibit backward bifurcation and bistability if density-dependent demography is considered. Our theoretical study thus indicates that extra attention should be given in controlling HIV epidemic to achieve the desired result.展开更多
文摘United Nations Political Declaration 2011 on HIV and AIDS calls to reduce the sexual transmission and the transmission of HIV among people, who inject drugs by 50% by 2015, through different control strategies and precautionary measures. In this paper, we propose and study a simple SI type model that considers the effect of various precaution- ary measures to control HIV epidemic. We show, unlike conventional epidemic models, that the basic reproduction number which essentially considered as the disease eradica- tion condition is no longer sufficient to eliminate HIV infection. In particular, we show that even when the basic reproduction number is made less than unity, the disease may persist if the initial outbreak is not low. Eradication of disease is however guaranteed if the ensemble control measure exceeds some upper critical value. It is also shown that an epidemic model with mass action incidence may exhibit backward bifurcation and bistability if density-dependent demography is considered. Our theoretical study thus indicates that extra attention should be given in controlling HIV epidemic to achieve the desired result.
