A deterministic model for the transmission dynamics of melioidosis disease in human population is designed and analyzed. The model is shown to exhibit the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium when the basic reproduction number [Formula: see text] is less than one. It is further shown that the backward bifurcation dynamics is caused by the reinfection of individuals who recovered from the disease and relapse. The existence of backward bifurcation implies that bringing down [Formula: see text] to less than unity is not enough for disease eradication. In the absence of backward bifurcation, the global asymptotic stability of the disease-free equilibrium is shown whenever [Formula: see text]. For [Formula: see text], the existence of at least one locally asymptotically stable endemic equilibrium is shown. Sensitivity analysis of the model, using the parameters relevant to the transmission dynamics of the melioidosis disease, is discussed. Numerical experiments are presented to support the theoretical analysis of the model. In the numerical experimentations, it has been observed that screening and treating individuals in the exposed class has a significant impact on the disease dynamics.

中文翻译：

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人类类鼻疽传播动力学的数学模型分析

设计和分析了人类类鼻疽病传播动力学的确定性模型。该模型显示出后向分​​叉现象，其中当基本繁殖数 [公式：见文本] 小于 1 时，稳定的无病平衡与稳定的地方性平衡共存。进一步表明，后向分叉动力学是由从疾病中康复和复发的个体的再感染引起的。后向分叉的存在意味着将[公式：见正文]降低到小于统一是不足以根除疾病的。在没有后向分叉的情况下，无病平衡的全局渐近稳定性在任何时候都会显示[公式：见文本]。对于 [公式：见正文]，表明存在至少一个局部渐近稳定的地方性平衡。讨论了模型的敏感性分析，使用与类鼻疽病传播动力学相关的参数。数值实验被提出来支持模型的理论分析。在数值实验中，已经观察到筛查和治疗暴露类中的个体对疾病动态有显着影响。