Abstract

Awareness programs by the media play a pivotal role in the control of infectious diseases. In this paper, we formulate and analyse a mathematical model for listeriosis incorporating aware individuals. Mathematical analyses of the model are done and equilibrium points determined. The model has three equilibria; namely; the disease-free, the bacteria-free, and the endemic equilibria. Local asymptotic stability of the equilibria is established based on the food contamination threshold \({{\mathcal{R}}_{f}}.\) Numerical simulations are carried out and the effects of various parameters on the model state variables investigated. The results from numerical simulations reveal that an increase in the efficacy of awareness programs, the rate of implementation of awareness programs, and the rate at which unaware susceptible become aware result in the reduction of listeriosis in the human population. The results have important implications in the control and management of listeriosis.

中文翻译：

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结合意识计划影响的李斯特菌病数学模型

摘要

媒体宣传计划在控制传染病方面发挥着关键作用。在本文中，我们制定并分析了一个包含有意识个体的李斯特菌病数学模型。完成模型的数学分析并确定平衡点。该模型具有三个均衡；即；无病、无细菌和地方病平衡。基于食物污染阈值\({{\mathcal{R}}_{f}}.\)建立平衡的局部渐近稳定性进行了数值模拟并研究了各种参数对模型状态变量的影响。数值模拟的结果表明，提高意识计划的效力、提高意识计划的实施率以及未意识到的易感者意识到的速度会导致人群中李斯特菌病的减少。结果对李斯特菌病的控制和管理具有重要意义。