Investigation of the Stochastic Modeling of COVID-19 with Environmental Noise from the Analytical and Numerical Point of View

Hussain, S. Satham; Madi, Elissa Nadia; Khan, Hasib; Etemad, Sina; Rezapour, Shahram; Sitthiwirattham, Thanin; Patanarapeelert, Nichaphat

doi:10.3390/math9233122

Cited by 27 publications

(11 citation statements)

References 52 publications

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“…Mathematical models are variedly used as a significant tool in understanding natural phenomena (Hussain, Madi, Iqbal, et al, 2021). Namely, the stochastic epidemic model was utilized to predict the COVID-19 spread (Hussain, Madi, Khan, et al, 2021).…”

Section: Agglomerative Hierarchical Clusteringmentioning

confidence: 99%

Rhythms Synchronization Effects on Cognition during Listening to Quranic Recitation

Ismail

Reza²,

Jusoh³

et al. 2022

Mal. J. Fund. Appl. Sci.

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Sound has rhythms that can interact with human brain rhythms. The interaction may improve human cognition through neuronal synchronization. However, research on the synchronization effects of listening to the Holy Quran remains elusive. This study aimed to learn the potential synchronous effects of Quranic listening in beta frequency through electroencephalographic oscillatory dataset. Subjects were listening to Fatihah Chapter, Arabic News and Rest in random sequence. Data were pre-processed followed by neuroimaging analysis using BESA Research 6.1. Repeated Measures ANOVA and Agglomerative Hierarchical Clustering (AHC) algorithm were applied to elucidate the significantly different EEG electrode channels compared to Rest and their clusters. Results showed that Beta rhythms synchronization with the Fatihah Chapter is associated with verbal fluency, academic performance, social interaction, inhibitory function, movement planning, self-motivation, self-management and reactivation of sensory features of memory trace as highly activated cluster, followed by working memory, language processing and decision making as medially activated cluster; and tune recognition and visual mental imagery as low activated neural circuits cluster during listening to the Fatihah Chapter.

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Section: Agglomerative Hierarchical Clusteringmentioning

confidence: 99%

Rhythms Synchronization Effects on Cognition during Listening to Quranic Recitation

Ismail

Reza²,

Jusoh³

et al. 2022

Mal. J. Fund. Appl. Sci.

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“…They have considered the CTMC stochastic model and found that disease may not persist even for basic reproduction number ( ) greater than one. Hussain et al [ 28 ] have proposed the deterministic model along with stochastic differential equation model involving environmental white noise. They analyzed the deterministic model and compared the results of stochastic and deterministic models for the future prediction of the spread of COVID-19.…”

Section: Introductionmentioning

confidence: 99%

A mathematical model for transmission dynamics of COVID-19 infection

Mishra

2023

Eur. Phys. J. Plus

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In this paper, a mathematical model of COVID-19 has been proposed to study the transmission dynamics of infection by taking into account the role of symptomatic and asymptomatic infected individuals. The model has also considered the effect of non-pharmaceutical interventions (NPIs) in controlling the spread of virus. The basic reproduction number ( ) has been computed and the analysis shows that for , the disease-free state becomes globally stable. The conditions of existence and stability for two other equilibrium states have been obtained. Transcritical bifurcation occurs when basic reproduction number is one (i.e. ). It is found that when asymptomatic cases get increased, infection will persist in the population. However, when symptomatic cases get increased as compared to asymptomatic ones, the endemic state will become unstable and infection may eradicate from the population. Increasing NPIs decrease the basic reproduction number and hence, the epidemic can be controlled. As the COVID-19 transmission is subject to environmental fluctuations, the effect of white noise has been considered in the deterministic model. The stochastic differential equation model has been solved numerically by using the Euler-Maruyama method. The stochastic model gives large fluctuations around the respective deterministic solutions. The model has been fitted by using the COVID-19 data of three waves of India. A good match is obtained between the actual data and the predicted trajectories of the model in all three waves of COVID-19. The findings of this model may assist policymakers and healthcare professionals in implementing the most effective measures to prevent the transmission of COVID-19 in different settings.

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“…In the recent years, the Ulam-Hyers stability (UHS) has attracted the attention of many authors according to their applications in mechanic, automatic, biology, and fluid flow, where identifying the explicit solutions is a hard task. Many research articles have been appeared in this field; like for qualitative study of fractional stochastic systems, see earlier studies [9][10][11][12][13][14][15], and for applications to Stochastic Epidemic SIR Model, the COVID-19, Volterra integro-differential system, and tobacco smoking model, see other research [16][17][18][19]. Guo et al [13] have investigated the EU and UHS of solutions for almost periodic stochastic differential equations with fBm.…”

Section: Introductionmentioning

confidence: 99%

Ulam–Hyers stability of fractional Itô–Doob stochastic differential equations

Mchiri

2023

Math Methods in App Sciences

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This article is devoted to prove the existence and uniqueness (EU) of solution of fractional Itô–Doob stochastic differential equations (FIDSDE) with order by using the fixed point technique (FPT). We analyze the Ulam–Hyers stability (UHS) of FIDSDE by using the Gronwall inequality (GI) and the stochastic analysis techniques. We present an application of our results by two theoretical examples.

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Investigation of the Stochastic Modeling of COVID-19 with Environmental Noise from the Analytical and Numerical Point of View

Cited by 27 publications

References 52 publications

Rhythms Synchronization Effects on Cognition during Listening to Quranic Recitation

Rhythms Synchronization Effects on Cognition during Listening to Quranic Recitation

A mathematical model for transmission dynamics of COVID-19 infection

Ulam–Hyers stability of fractional Itô–Doob stochastic differential equations

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