Individuals living with HIV/AIDS are significantly at higher risk of infection with Salmonella Typhi. A deterministic nonlinear mathematical model that describes the co-infection dynamics of HIV and typhoid incorporating typhoid vaccine and treatment has been developed. The basic reproduction number for the co-infection model is computed. The co-infection model exhibits four steady states, namely, the disease-free, HIV alone endemic, typhoid alone endemic, and the co-infection endemic states. The local stability of the disease-free state has been investigated. The co-infection endemic state, if it exists, is found to be locally stable. The minimum vaccination rate that eliminates the typhoid infection is determined. Sensitivity analysis has been performed to ascertain model parameters that have a strong impact on the disease dynamics. It is demonstrated that the co-infection basic reproduction number can be reduced to below unity by simultaneous preventive measures, thereby eliminating both diseases. Numerical simulation of the co-infection model is carried out to examine the effects of parameters on disease spread. The study suggests that the two diseases need to be managed simultaneously for effective control of the co-infection.

艾滋病毒/艾滋病感染者极易感染沙门氏菌伤寒 已经开发出一种确定性非线性数学模型，该模型描述了结合了伤寒疫苗和治疗的HIV和伤寒的共同感染动态。计算出共感染模型的基本繁殖数。合并感染模型表现出四个稳定状态，即无疾病，仅HIV流行，伤寒单独流行和共感染流行状态。已经研究了无病状态的局部稳定性。如果存在共感染流行状态，则发现该状态局部稳定。确定消除伤寒感染的最小疫苗接种率。已经进行了敏感性分析，以确定对疾病动力学有很大影响的模型参数。已经证明，通过同时的预防措施，可以将共同感染的基本繁殖数量减少到统一以下，从而消除了两种疾病。进行共感染模型的数值模拟以检查参数对疾病传播的影响。研究表明，为了同时控制合并感染，需要同时控制两种疾病。