Fractional Stochastic Differential Equation Approach for Spreading of Diseases

Lima, L.S.

doi:10.3390/e24050719

Cited by 10 publications

(7 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The stochasticity impacts the outcomes of the model. Moreover, even a slight modification in the parameter value can result in chaotic dynamics, potentially leading to the occurrence of a disease outbreak [23].…”

Section: Introductionmentioning

confidence: 99%

Fractional Optimal Control Model and Bifurcation Analysis of Human Syncytial Respiratory Virus Transmission Dynamics

Awadalla,

Alahmadi,

Cheneke

et al. 2024

Fractal Fract

View full text Add to dashboard Cite

In this paper, the Caputo-based fractional derivative optimal control model is looked at to learn more about how the human respiratory syncytial virus (RSV) spreads. Model solution properties such as boundedness and non-negativity are checked and found to be true. The fundamental reproduction number is calculated by using the next-generation matrix’s spectral radius. The fractional optimal control model includes the control functions of vaccination and treatment to illustrate the impact of these interventions on the dynamics of virus transmission. In addition, the order of the derivative in the fractional optimal control problem indicates that encouraging vaccination and treatment early on can slow the spread of RSV. The overall analysis and the simulated behavior of the fractional optimum control model are in good agreement, and this is due in large part to the use of the MATLAB platform.

show abstract

Section: Introductionmentioning

confidence: 99%

Fractional Optimal Control Model and Bifurcation Analysis of Human Syncytial Respiratory Virus Transmission Dynamics

Awadalla,

Alahmadi,

Cheneke

et al. 2024

Fractal Fract

View full text Add to dashboard Cite

show abstract

“…[5]. The modeling based in the fractional stochastic differential equation has been used in [3,[6][7][8]. The stochastic dynamics smoking with non-Gaussian noise was studied in Refs.…”

Section: Introductionmentioning

confidence: 99%

“…Fractional stochastic differential equations (FSDE) can be employed to model the spread of infectious diseases, including the COVID-19. These equations incorporate both fractional calculus and stochastic elements, allowing for the inclusion of long-range dependence and random fluctuations in the modeling process [1][2][3][4][5][6][7][8][9][10][11]. However, the use of fractional calculus in epidemiology is a relatively advanced and specialized approach.…”

Section: Introductionmentioning

confidence: 99%

Fractional stochastic calculus approach for evolution in time of epidemiological systems

Lima

2024

Preprint

Self Cite

View full text Add to dashboard Cite

Fractional stochastic nonlinear differential equation approach is used in the analysis of evolution in time of the infected number by COVID-19 in countries where the number of cases is large. The rises and falls of novel cases are treated as randomness in the model for spreading of novel cases. The rescaled range analysis (RS) is used to determine the Hurst index of the time series of novel cases of epidemiologic week that exhibits a Hurst exponent greater than 1/2, meaning that the time series has a behavior that is distinct from a random walk i.e., that nth value is independent of all the values before this.

show abstract

“…An instance of this can be found in [21], where this approach is combined with linearization, resulting in a closed-form solution for stochastic differential equations (SDEs). The commonly employed Brownian motion process is typically stationary, although some authors have explored the utilization of fractional Brownian motion, as demonstrated in [17]. This concept is crucial in that it disrupts the typical independence of changes within a process and is particularly useful for cyclic growth patterns, notably in disease modeling.…”

Section: Introductionmentioning

confidence: 99%

Enhancing Reliability and Accuracy in Stochastic Growth Modeling: Method of Three Selected Points Approach

Chidzalo,

Abonongo,

Naryongo

2023

Computational Journal of Mathematical and Statistical Sciences

View full text Add to dashboard Cite

Growth models play a pivotal role in diverse fields, such as population dynamics, epidemiology, finance, and ecological systems. Traditionally, deterministic growth models have been extensively employed to capture various aspects of growth phenomena. However, in real-world scenarios, stochasticity is inherent in the data, challenging the suitability of deterministic models. Consequently, there is a growing interest in developing stochastic growth models capable of accommodating inherent uncertainties. This study addresses three fundamental questions within the context of stochastic growth modeling. Firstly, it investigates the continued reliability of the Method of Three Selected Points (MTSP) for estimating parameters in stochastic differential equations (SDEs), given the increasing popularity of stochastic models over deterministic ones. Secondly, it explores the required form of SDEs that maximizes the success and reliability of the MTSP approach. Lastly, it conducts a comparative analysis of the MTSP method against commonly employed techniques in the literature. To address these questions, we propose a novel approach to constructing SDEs that enhance the stability of both bounded and unbounded stochastic growth models. By carefully selecting the form of the diffusion coefficient, we achieve higher accuracy in estimating the parameters of the drift coefficient. Through empirical simulations and a comprehensive reliability analysis using real stock data, we demonstrate the superior performance of the MTSP method when compared to the Pseudo-maximum likelihood method and physics-informed neural networks within the framework of SDEs. Our findings underscore the continued effectiveness of the MTSP method for estimating parameters in stochastic growth models, even in an era where stochastic models dominate. Additionally, we provide insights into the optimal structure of SDEs for maximizing the reliability of the MTSP approach. Thus, the study contributes to the ongoing dialogue surrounding stochastic growth modeling and offers a robust methodology for parameter estimation in this context, with practical applications in fields ranging from epidemiology to finance.

show abstract

Fractional Stochastic Differential Equation Approach for Spreading of Diseases

Cited by 10 publications

References 49 publications

Fractional Optimal Control Model and Bifurcation Analysis of Human Syncytial Respiratory Virus Transmission Dynamics

Fractional Optimal Control Model and Bifurcation Analysis of Human Syncytial Respiratory Virus Transmission Dynamics

Fractional stochastic calculus approach for evolution in time of epidemiological systems

Enhancing Reliability and Accuracy in Stochastic Growth Modeling: Method of Three Selected Points Approach

Contact Info

Product

Resources

About