Existence, Uniqueness and Stability of Periodic Solution for Nonlinear System of Integro-Differential Equations

In this paper, we investigate the existence, uniqueness, and stability of the periodic solution for the system of nonlinear integro-differential equations by using the numerical-analytic methods for investigating the solutions and the periodic solutions of ordinary differential equations, which are given by A. Samoilenko

Tuberculosis incidence in country of origin is a key determinant of the risk of active tuberculosis in people living with HIV: Data from a 30-year observational cohort study

Introduction: People living with HIV (PLWH) are at high risk of active tuberculosis (TB) but this risk in the era of antiretroviral treatment (ART) remains unclear. It is critical to identify the groups who should be prioritised for latent TB (LTBI) screening. In this study we identified the risk factors associated with developing incident TB disease, by analysing a 30-year observational cohort. // Methods: We evaluated PLWH in Leicester, UK, between 1983 and 2017 to ascertain those who developed active TB and the timing of this in relation to HIV diagnosis; whether before, concurrently with, or more than 3 months after the diagnosis of HIV (incident TB). Predictors of incident TB were ascertained using Cox proportional hazards models. // Results: In all, 325 out of 2158 (15.1%) PLWH under care had had active TB; 64/325 (19.7%) prior to HIV diagnosis, 161/325 (49.5%) concurrently with/within 3 months of HIV diagnosis and 100/325 (30.8%) had incident TB. Incident TB risk was 4.57/1000 person-years. Increased TB incidence in the country of birth was associated with an increased risk of developing incident TB [50–149/100 000 population, adjusted hazard ratio (AHR) = 3.10, 95% CI: 0.94–10.20; 150–249/100 000 population, AHR = 7.14, 95% CI: 3.46–14.74; 250–349/100 000 population, AHR = 5.90, 95% CI: 2.32–14.99; ≥ 350/100 000 population, AHR = 3.96, 95% CI: 1.39–11.26]. // Conclusions: Tuberculosis risk remains high among PLWH and is related to TB incidence in the country of birth. Further work is required to determine whether specific groups of PLWH should be targeted for programmatic LTBI screening, and whether it will result in high uptake and completion of chemoprophylaxis and is cost-effective for widespread implementation