Impact of awareness and time-delayed saturated treatment on the transmission of infectious diseases

Q3 Mathematics Results in Control and Optimization Pub Date : 2024-09-11 DOI:10.1016/j.rico.2024.100463

Aditya Pandey, Archana Singh Bhadauria, Vijai Shanker Verma

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Abstract

We have proposed a mathematical model with saturated incidence and treatment rates along with awareness and delay in treatment. We analyze the model and find the equilibrium points and their stability. We also find the basic reproduction number

R_{0}

to understand the disease dynamics. We performed the sensitivity analysis and found that treatment along with awareness plays a significant role in controlling infectious disease. We deduce that awareness about the disease affects the transmission rate of infection. As people become aware of aspects of the infectious disease, they amend their behavior so that they fend themselves from catching the disease. We have introduced a time lag in treatment and found the threshold value of the time delay. It is observed that when the value of the time delay crosses the threshold value, we get a Hopf bifurcation i.e. endemic steady state becomes unstable above the threshold value and it may become difficult to control the disease beyond the threshold value of delay in treatment.

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提高认识和延时饱和治疗对传染病传播的影响

我们提出了一个数学模型，其中包含饱和的发病率和治疗率，以及治疗意识和治疗延迟。我们对模型进行了分析，找到了平衡点及其稳定性。我们还找到了基本繁殖数 R0，以了解疾病的动态变化。我们进行了敏感性分析，发现治疗和认识在控制传染病方面发挥着重要作用。我们推断，对疾病的认识会影响传染病的传播率。当人们意识到传染病的方方面面时，他们就会修正自己的行为，从而避免感染这种疾病。我们在治疗中引入了时滞，并找到了时滞的临界值。据观察，当时间延迟的值超过临界值时，我们就会出现霍普夫分岔，即在临界值以上，地方病的稳定状态变得不稳定，超过治疗延迟的临界值后，可能就很难控制疾病了。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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