Stochastic SIRC epidemic model with time-delay for COVID-19.

IF 4.1 3区数学 Q1 Mathematics

Advances in Difference Equations Pub Date : 2020-01-01 Epub Date: 2020-09-18 DOI:10.1186/s13662-020-02964-8

F A Rihan, H J Alsakaji, C Rajivganthi

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Abstract

Environmental factors, such as humidity, precipitation, and temperature, have significant impacts on the spread of the new strain coronavirus COVID-19 to humans. In this paper, we use a stochastic epidemic SIRC model, with cross-immune class and time-delay in transmission terms, for the spread of COVID-19. We analyze the model and prove the existence and uniqueness of positive global solution. We deduce the basic reproduction number $R_{0}^{s}$ for the stochastic model which is smaller than $R_{0}$ of the corresponding deterministic model. Sufficient conditions that guarantee the existence of a unique ergodic stationary distribution, using the stochastic Lyapunov function, and conditions for the extinction of the disease are obtained. Our findings show that white noise plays an important part in controlling the spread of the disease; When the white noise is relatively large, the infectious diseases will become extinct; Re-infection and periodic outbreaks can occur due to the existence of feedback time-delay (or memory) in the transmission terms.

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针对 COVID-19 的带有时间延迟的随机 SIRC 流行病模型。

湿度、降水和温度等环境因素对新型冠状病毒 COVID-19 在人类中的传播有重要影响。本文使用随机流行病 SIRC 模型来研究 COVID-19 的传播，该模型具有交叉免疫类和传播时间延迟项。我们对模型进行了分析，并证明了正全局解的存在性和唯一性。我们推导出随机模型的基本繁殖数 R 0 s，它小于相应确定性模型的 R 0。利用随机 Lyapunov 函数，我们得到了保证唯一遍历静态分布存在的充分条件，以及疾病消亡的条件。我们的研究结果表明，白噪声在控制疾病传播中起着重要作用；当白噪声相对较大时，传染病会灭绝；由于传播项中存在反馈时延（或记忆），会出现再感染和周期性爆发。

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来源期刊

Advances in Difference Equations 数学-数学

自引率

0.00%

发文量

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.