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Mathematical Analysis of a Tuberculosis Transmission Model with Vaccination in an Age Structured Population

机译:年龄结构化人群接种疫苗接种的结核传输模型的数学分析

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This article presents a mathematical model of Tuberculosis (TB) transmission considering BCG vaccination in an age-structured population. We used several strategies to simulate the TB dynamic and evaluate the potential impact on active TB. We developed a deterministic compartmental model where the population was distributed into seven compartments, i.e., susceptible individuals that can be vaccinated (Si) and can't be vaccinated (S_2), vaccinated (V), slow (L) and fast (E) exposed, infectious (I), and recovery (R). The mathematical model analysis was done by determining the equilibrium points, the Basic Reproduction Number (R_0) of the model, and analysing the stability of the equilibrium point. Some numeric interpretations were given by sensitivity vaccination parameters and percentage vaccine protection to the value of R_0 and autonomous model simulations. We find that to reach TB free condition is not enough by maximising one of the vaccination parameters for newborn, adults or percentage vaccine protection. We also find that vaccination into the adult population is more effective to suppress TB spread rather than newborn.
机译:本文介绍了考虑到年龄结构群体的BCG疫苗的结核病(TB)传播的数学模型。我们使用了几种策略来模拟TB动态,并评估对活性TB的潜在影响。我们开发了一种确定性的隔间模型,其中人口被分配到七个隔间,即可以接种疫苗(Si)并且不能接种疫苗(S_2),接种疫苗(V),缓慢(L)和快速(e)的敏感个体暴露,传染(i)和恢复(r)。通过确定模型的平衡点,基本再现数(R_0),分析平衡点的稳定性来完成数学模型分析。通过敏感性疫苗接种参数和疫苗保护百分比对R_0和自主模型模拟的百分比进行一些数字解释。我们发现,通过最大化新生儿,成人或疫苗保护百分比的疫苗接种参数之一来达到自由条件是不够的。我们还发现,进入成年人口的疫苗更有效地抑制TB扩散而不是新生儿。

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