In this paper, a non-linear mathematical model for HIV-TB co-infection has been proposed. A constant time delay parameter is introduced into the model which accounts for the delay in detection and the commencement of appropriate treatment for co-infected individuals. The basic reproduction number along with the location and existence of equilibrium points is computed. Local stability analysis of all the equilibrium points in the presence of delay parameter is performed, which gives certain conditions, under which Hopf-bifurcation takes place. Numerical simulations are performed with different set of parameters for each equilibrium point to explore the effect of delay in detection and treatment of the infected individuals. The numerical results have also been used to describe the rich dynamics generated by the system in the presence of delay.

在本文中，提出了一种针对HIV-TB合并感染的非线性数学模型。将恒定的时间延迟参数引入模型，该参数说明了检测的延迟以及对合并感染个体的适当治疗的开始。计算基本再生数以及平衡点的位置和存在。在存在时延参数的情况下，对所有平衡点进行局部稳定性分析，这给出了某些条件，在该条件下发生了霍普夫分支。对每个平衡点使用不同的参数集进行数值模拟，以探索延迟检测和治疗感染个体的影响。数值结果也已用于描述在存在延迟的情况下系统生成的丰富动态。