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A Mathematical Model for the Transmission Dynamics of Lymphatic Filariasis with Intervention Strategies
Acta Biotheoretica ( IF 1.3 ) Pub Date : 2019-11-22 , DOI: 10.1007/s10441-019-09370-y
S M Simelane 1 , P M Mwamtobe 2 , S Abelman 3 , J M Tchuenche 3
Affiliation  

This manuscript considers the transmission dynamics of lymphatic filariasis with some intervention strategies in place. Unlike previously developed models, our model takes into account both the exposed and infected classes in both the human and mosquito populations, respectively. We also consider vaccinated, treated and recovered humans in the presented model. The global dynamics of the proposed model are completely determined by the basic ([Formula: see text]) and effective reproduction numbers ([Formula: see text]). We then use Lyapunov function theory to find the sufficient conditions for global stability of both the disease-free equilibrium and endemic equilibrium. The Lyapunov functions show that when the basic reproduction number is less than or equal to unity, the disease-free equilibrium is globally asymptotically stable, and when it is greater than unity then the endemic equilibrium is also globally asymptotically stable. Finally, numerical simulations are carried out to investigate the effects of the intervention strategies and key parameters to the spread of lymphatic filariasis. The numerical simulations support the analytical results and illustrate possible model behavioral scenarios.

中文翻译:

具有干预策略的淋巴丝虫病传播动力学的数学模型

这份手稿考虑了淋巴丝虫病的传播动态,并制定了一些干预策略。与之前开发的模型不同,我们的模型分别考虑了人类和蚊子种群中的暴露类和感染类。我们还在所呈现的模型中考虑了接种疫苗、治疗和康复的人。所提出模型的全局动态完全由基本([公式:见正文])和有效再生数([公式:见正文])决定。然后我们使用李雅普诺夫函数理论来寻找无病平衡和地方病平衡的全局稳定的充分条件。Lyapunov 函数表明,当基本再生数小于等于 1 时,无病平衡是全局渐近稳定的,当它大于 1 时,地方性均衡也是全局渐近稳定的。最后,进行数值模拟以研究干预策略和关键参数对淋巴丝虫病传播的影响。数值模拟支持分析结果并说明可能的模型行为场景。
更新日期:2019-11-22
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