In this paper, we have considered an SIS epidemic model with arbitrary disease transmission function and arbitrary treatment control function. We have analyzed the model considering the disease transmission function as an increasing and decreasing function separately. To introduce heterogeneity in the system we have taken both the disease transmission function and treatment function as fuzzy numbers. Fuzzy expected value of the infected individual is defined and determined. Then fuzzy basic reproduction number is computed. At last, a threshold value is determined in both the cases where the system undergoes a transcritical and backward bifurcation.

中文翻译：

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具有模糊传输和模糊治疗控制的流行病模型的动力学行为

在本文中，我们考虑了具有任意疾病传播函数和任意治疗控制函数的SIS流行病模型。我们分别分析了将疾病传播函数作为递增函数和递减函数的模型。为了在系统中引入异质性，我们将疾病传播函数和治疗函数都作为模糊数。定义和确定受感染个体的模糊期望值。然后计算模糊基本再现数。最后，在系统经历跨临界和后向分叉的情况下确定阈值。