Global stability analysis for a generalized delayed SIR model with vaccination and treatment.

IF 4.1 3区数学 Q1 Mathematics

Advances in Difference Equations Pub Date : 2019-01-01 Epub Date: 2019-12-21 DOI:10.1186/s13662-019-2447-z

A Elazzouzi, A Lamrani Alaoui, M Tilioua, A Tridane

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引用次数: 34

Abstract

In this work, we investigate the stability of an SIR epidemic model with a generalized nonlinear incidence rate and distributed delay. The model also includes vaccination term and general treatment function, which are the two principal control measurements to reduce the disease burden. Using the Lyapunov functions, we show that the disease-free equilibrium state is globally asymptotically stable if $R_{0} \leq 1$ , where $R_{0}$ is the basic reproduction number. On the other hand, the disease-endemic equilibrium is globally asymptotically stable when $R_{0} > 1$ . For a specific type of treatment and incidence functions, our analysis shows the success of the vaccination strategy, as well as the treatment depends on the initial size of the susceptible population. Moreover, we discuss, numerically, the behavior of the basic reproduction number with respect to vaccination and treatment parameters.

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具有接种和治疗的广义延迟SIR模型的全局稳定性分析。

本文研究一类具有广义非线性发病率和分布时滞的SIR流行病模型的稳定性问题。该模型还包括疫苗接种期和一般治疗函数，这是减少疾病负担的两个主要控制措施。利用Lyapunov函数证明了当r0≤1时无病平衡状态是全局渐近稳定的，其中r0为基本繁殖数。另一方面，当r0 > 1时，地方病平衡全局渐近稳定。对于特定类型的治疗和发病率函数，我们的分析表明，疫苗接种策略的成功，以及治疗取决于易感人群的初始规模。此外，我们在数值上讨论了基本繁殖数与疫苗接种和治疗参数的关系。

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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来源期刊

Advances in Difference Equations 数学-数学

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0.00%

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审稿时长

4-8 weeks

期刊介绍： The theory of difference equations, the methods used, and their wide applications have advanced beyond their adolescent stage to occupy a central position in applicable analysis. In fact, in the last 15 years, the proliferation of the subject has been witnessed by hundreds of research articles, several monographs, many international conferences, and numerous special sessions. The theory of differential and difference equations forms two extreme representations of real world problems. For example, a simple population model when represented as a differential equation shows the good behavior of solutions whereas the corresponding discrete analogue shows the chaotic behavior. The actual behavior of the population is somewhere in between. The aim of Advances in Difference Equations is to report mainly the new developments in the field of difference equations, and their applications in all fields. We will also consider research articles emphasizing the qualitative behavior of solutions of ordinary, partial, delay, fractional, abstract, stochastic, fuzzy, and set-valued differential equations. Advances in Difference Equations will accept high-quality articles containing original research results and survey articles of exceptional merit.