University of Malaya, Institute of Mathematical Sciences, Kuala Lumpur, Malaysia.
University of Ilorin, Ilorin, Nigeria.
Acta Biotheor. 2021 Sep;69(3):225-255. doi: 10.1007/s10441-020-09406-8. Epub 2021 Apr 20.
Tuberculosis has continued to retain its title as "the captain among these men of death". This is evident as it is the leading cause of death globally from a single infectious agent. TB as it is fondly called has become a major threat to the achievement of the sustainable development goals (SDG) and hence require inputs from different research disciplines. This work presents a mathematical model of tuberculosis. A compartmental model of seven classes was used in the model formulation comprising of the susceptible S, vaccinated V, exposed E, undiagnosed infectious I, diagnosed infectious I, treated T and recovered R. The stability analysis of the model was established as well as the condition for the model to undergo backward bifurcation. With the existence of backward bifurcation, keeping the basic reproduction number less than unity [Formula: see text] is no more sufficient to keep TB out of the community. Hence, it is shown by the analysis that vaccination program, diagnosis and treatment helps to control the TB dynamics. In furtherance to that, it is shown that preference should be given to diagnosis over treatment as diagnosis precedes treatment. It is as well shown that at lower vaccination rate (0-20%), TB would still be endemic in the population. As such, high vaccination rate is required to send TB out of the community.
结核病仍然保持着“死亡之主”的称号。这是因为它是全球范围内由单一传染病原体导致的主要死亡原因。人们亲切地称之为结核病，它已成为实现可持续发展目标 (SDG) 的主要威胁，因此需要来自不同研究学科的投入。这项工作提出了一个结核病的数学模型。在模型的公式化中使用了一个包含七个类别的隔室模型，包括易感 S、接种 V、暴露 E、未确诊的传染性 I、确诊的传染性 I、治疗 T 和恢复 R。对模型的稳定性分析以及模型发生反向分歧的条件进行了建立。由于反向分歧的存在，保持基本再生数小于 1 [公式：见文本]不再足以使结核病远离社区。因此，分析表明，疫苗接种计划、诊断和治疗有助于控制结核病的动态。此外，分析表明，应该优先考虑诊断而不是治疗，因为诊断先于治疗。分析还表明，在较低的疫苗接种率（0-20%）下，结核病仍将在人群中流行。因此，需要高疫苗接种率才能使结核病远离社区。
