Role of precautionary measures in HIV epidemics： A mathematical assessment

作     者：N. Bairagi D. Adak 

作者机构：Center for Mathematical Biology and Ecology Department of Mathematics Jadavpur University Kolkata 700032 India 

出 版 物：《International Journal of Biomathematics》 (生物数学学报（英文版）)

年 卷 期：2016年第9卷第6期

页      面：307-331页

核心收录：

学科分类：0710[理学-生物学] 07[理学] 08[工学] 09[农学] 0903[农学-农业资源与环境] 071007[理学-遗传学] 0901[农学-作物学] 0836[工学-生物工程] 090102[农学-作物遗传育种] 

基　　金：University Grants Committee  UGC  (F30-63/2015 (SA-II  P-1/RS/97/14) 

主　　题：HIV epidemic model reproduction number bistability backward bifurcation Dulac criterion. 

摘      要：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.