Xue Ling, Jing Shuanglin, Wang Hao
College of Mathematical Sciences, Harbin Engineering University, Harbin, 150001, Heilongjiang, China.
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, AB, T6G 2R3, Canada.
Bull Math Biol. 2022 Apr 29;84(6):61. doi: 10.1007/s11538-022-01019-1.
Although great progress has been made in the prevention and mitigation of TB in the past 20 years, China is still the third largest contributor to the global burden of new TB cases, accounting for 833,000 new cases in 2019. Improved mitigation strategies, such as vaccines, diagnostics, and treatment, are needed to meet goals of WHO. Given the huge variability in the prevalence of TB across age-groups in China, the vaccination, diagnostic techniques, and treatment for different age-groups may have different effects. Moreover, the statistics data of TB cases show significant seasonal fluctuations in China. In view of the above facts, we propose a non-autonomous differential equation model with age structure and seasonal transmission rate. We derive the basic reproduction number, [Formula: see text], and prove that the unique disease-free periodic solution, [Formula: see text] is globally asymptotically stable when [Formula: see text], while the disease is uniformly persistent and at least one positive periodic solution exists when [Formula: see text]. We estimate that the basic reproduction number [Formula: see text] ([Formula: see text]), which means that TB is uniformly persistent. Our results demonstrate that vaccinating susceptible individuals whose ages are over 65 and between 20 and 24 is much more effective in reducing the prevalence of TB, and each of the improved vaccination strategy, diagnostic strategy, and treatment strategy leads to substantial reductions in the prevalence of TB per 100,000 individuals compared with current approaches, and the combination of the three strategies is more effective. Scenario A (i.e., coverage rate [Formula: see text], diagnosis rate [Formula: see text], relapse rate [Formula: see text]) is the best and can reduce the prevalence of TB per 100,000 individuals by [Formula: see text] and [Formula: see text] in 2035 and 2050, respectively. Although the improved strategies will significantly reduce the incidence rate of TB, it is challenging to achieve the goal of WHO in 2050. Our findings can provide guidance for public health authorities in projecting effective mitigation strategies of TB.
尽管在过去20年里结核病的预防和缓解工作取得了巨大进展，但中国仍是全球新增结核病病例负担的第三大贡献国，2019年新增病例达83.3万例。需要改进缓解策略，如疫苗、诊断和治疗方法，以实现世界卫生组织的目标。鉴于中国不同年龄组结核病患病率差异巨大，不同年龄组的疫苗接种、诊断技术和治疗效果可能不同。此外，中国结核病病例的统计数据显示出明显的季节性波动。鉴于上述事实，我们提出了一个具有年龄结构和季节性传播率的非自治微分方程模型。我们推导了基本再生数[公式：见正文]，并证明当[公式：见正文]时，唯一的无病周期解[公式：见正文]是全局渐近稳定的，而当[公式：见正文]时，疾病是一致持续存在的，并且至少存在一个正周期解。我们估计基本再生数公式：见正文，这意味着结核病是一致持续存在的。我们的结果表明，对65岁以上以及20至24岁的易感个体进行疫苗接种在降低结核病患病率方面更为有效，与当前方法相比，每一种改进的疫苗接种策略、诊断策略和治疗策略都能使每10万人中的结核病患病率大幅降低，并且三种策略的组合效果更佳。情景A（即覆盖率[公式：见正文]、诊断率[公式：见正文]、复发率[公式：见正文]）是最佳方案，分别可在2035年和2050年使每10万人中的结核病患病率降低[公式：见正文]和[公式：见正文]。尽管改进后的策略将显著降低结核病发病率，但要在2050年实现世界卫生组织的目标仍具有挑战性。我们的研究结果可为公共卫生当局制定有效的结核病缓解策略提供指导。
