4.7 Article

Well-posedness results for a new class of stochastic spatio-temporal SIR-type models driven by proportional pure-jump Lévy noise

相关参考文献

注意:仅列出部分参考文献,下载原文获取全部文献信息。
Article Mathematics, Applied

Dynamical analysis of a stochastic non-autonomous SVIR model with multiple stages of vaccination

Mohamed Mehdaoui et al.

Summary: In this paper, the dynamics of a proposed stochastic non-autonomous SVIR model with multiple stages of vaccination due to vaccine ineffectiveness are analyzed. The parameters of the model are allowed to vary with time to incorporate seasonal variation. The study proves the mathematical and biological well-posedness of the model, establishes conditions for disease vanishing or persistence, and provides a condition for the model to have a non-trivial periodic solution. Numerical simulations demonstrate the impact of different vaccination stages and stochastic Gaussian noise on the dynamics of the population being studied.

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING (2023)

Article Mathematics, Applied

Analysis of a stochastic SVIR model with time-delayed stages of vaccination and Levy jumps

Mohamed Mehdaoui et al.

Summary: The paper aims to enhance the existing stochastic epidemic models by incorporating new disease characteristics, such as vaccination validation time, stages of vaccine, deaths linked to the vaccine, and environmental noise caused by sociocultural changes. It extends the standard SVIR epidemic model to a new mathematical model governed by a system of coupled stochastic delay differential equations. The model's mathematical well-posedness, biological feasibility, disease extinction, and persistence are analyzed and supported by numerical simulations.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2023)

Article Automation & Control Systems

Analysis of an optimal control problem for a spatio-temporal SIR model with nonlinear density dependent diffusion terms

Mohamed Mehdaoui et al.

Summary: This paper focuses on the study of an optimal control problem for a new spatio-temporal SIR epidemic model with nonlinear density dependent diffusion terms and a class of nonlinear incidence functions. We consider two types of control variables, vaccination for the susceptible and treatment for the infected. For fixed controls, by means of Schauder fixed point theorem, we prove that the proposed model admits a weak biologically feasible solution, the uniqueness of the latter is also investigated. Furthermore, using the state and adjoint problems, first order necessary optimal conditions are obtained. Finally, numerical simulations are carried out for particular diffusion terms incorporating the heard mentality of individuals, when it comes to the spatial movement, and for particular incidence functions, as well as by varying the parameters of the objective functional, to illustrate the possible optimal control strategies and their effect on the studied population.

OPTIMAL CONTROL APPLICATIONS & METHODS (2023)

Article Automation & Control Systems

Optimal control for a multi-group reaction-diffusion SIR model with heterogeneous incidence rates

Mohamed Mehdaoui et al.

Summary: This paper focuses on the optimal control problem for a generalized multi-group reaction-diffusion SIR epidemic model with heterogeneous nonlinear incidence rates. The study introduces two types of control variables and derives the existence and uniqueness of a biologically feasible solution. Necessary optimality conditions are obtained and numerical simulations show the stability and feasibility of the model.

INTERNATIONAL JOURNAL OF DYNAMICS AND CONTROL (2023)

Article Engineering, Multidisciplinary

Bifurcation and stability of a delayed SIS epidemic model with saturated incidence and treatment rates in heterogeneous networks

Gui Guan et al.

Summary: This paper investigates an epidemic model with a saturated treatment rate, analyzing the boundedness, equilibrium points, and stability of the system, as well as observing bifurcation behavior at R-0 = 1. The stability of the disease-spreading equilibrium point is also proved under certain conditions, with numerical simulations validating the theoretical results.

APPLIED MATHEMATICAL MODELLING (2022)

Article Mathematics, Applied

Analysis of a stochastic reaction-diffusion Alzheimer?s disease system driven by space-time white noise

Jing Hu et al.

Summary: This study introduces a stochastic reaction-diffusion system with space-time white noise for Alzheimer's disease (AD) analysis, describing the positive feedback loop between A beta and Ca2+. The existence and uniqueness of mild solutions for the system are obtained using the truncation method. Furthermore, the long-time behaviors of the system are studied, and an illustrative example is presented to support the analytical results.

APPLIED MATHEMATICS LETTERS (2022)

Article Mathematical & Computational Biology

Stochastic modeling of the Monkeypox 2022 epidemic with cross-infection hypothesis in a highly disturbed environment

Asad Khan et al.

Summary: Monkeypox 2022, caused by the Monkeypox virus, is a re-emerging disease with severe symptoms. A mathematical model is proposed to understand the dynamics of Monkeypox 2022, considering horizontal human dissemination and cross-infection between animals and humans as two modes of transmission. The model is extended to a probabilistic formulation with Levy jumps due to the lack of substantial knowledge about the virus diffusion and external perturbations. The study proves two principal asymptotic properties: eradication and continuation in the mean of Monkeypox 2022. Numerical simulations and real data examples support the theoretical findings and demonstrate the impact of the adopted mathematical techniques on the study.

MATHEMATICAL BIOSCIENCES AND ENGINEERING (2022)

Article Mathematics, Applied

On the existence and uniqueness of an inverse problem in epidemiology

Anibal Coronel et al.

Summary: This paper introduces the functional framework and necessary conditions for the inverse problem arising from mathematical modeling of disease transmission. By formulating the inverse problem as an optimization problem, the existence of solutions is proved, and uniqueness is established.

APPLICABLE ANALYSIS (2021)

Article Engineering, Mechanical

A stochastic SEIHR model for COVID-19 data fluctuations

Ruiwu Niu et al.

Summary: In this research, a stochastic SEIHR (sSEIHR) model was proposed to describe random fluctuations in new infections and hospitalizations, with sufficient conditions for stochastic stability based on estimated basic reproduction number. The study showed strong threshold behavior near the estimated basic reproduction number, with increasing noise levels slightly reducing the final proportion of infected individuals. Additionally, the sSEIHR model accurately depicted trends and fluctuations in COVID-19 data from different regions worldwide using fewer compartments and parameters compared to other stochastic compartmental models.

NONLINEAR DYNAMICS (2021)

Article Biology

Basic Reproduction Numbers for a Class of Reaction-Diffusion Epidemic Models

Chayu Yang et al.

BULLETIN OF MATHEMATICAL BIOLOGY (2020)

Article Statistics & Probability

Analysis of a spatially inhomogeneous stochastic partial differential equation epidemic model

Dang H. Nguyen et al.

JOURNAL OF APPLIED PROBABILITY (2020)

Article Mathematics

A spatial SEIRS reaction-diffusion model in heterogeneous environment

Pengfei Song et al.

JOURNAL OF DIFFERENTIAL EQUATIONS (2019)

Article Biology

Parameter identification for a stochastic SEIRS epidemic model: case study influenza

Anna Mummert et al.

JOURNAL OF MATHEMATICAL BIOLOGY (2019)

Article Mathematics, Applied

Optimal control strategies for a reaction-diffusion epidemic system

Min Zhou et al.

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS (2019)

Article Mathematics, Applied

Global dynamics in a reaction-diffusion multi-group SIR epidemic model with nonlinear incidence

Yantao Luo et al.

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS (2019)

Article Statistics & Probability

Maximal inequalities for stochastic convolutions driven by compensated Poisson random measures in Banach spaces

Jiahui Zhu et al.

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES (2017)

Article Mathematics, Applied

NONLINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS OF HYPERBOLIC TYPE DRIVEN BY LEVY-TYPE NOISES

Jiahui Zhu et al.

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B (2016)

Article Mathematics, Applied

Solving the inverse problem of an SIS epidemic reaction-diffusion model by optimal control methods

Huili Xiang et al.

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2015)

Article Mathematics

Impacts of noise on a class of partial differential equations

Guangying Lv et al.

JOURNAL OF DIFFERENTIAL EQUATIONS (2015)

Article Mathematics, Applied

Strong solutions to stochastic hydrodynamical systems with multiplicative noise of jump type

Hakima Bessaih et al.

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS (2015)

Article Physics, Mathematical

Stochastic nonlinear wave equation with memory driven by compensated Poisson random measures

Fei Liang et al.

JOURNAL OF MATHEMATICAL PHYSICS (2014)

Article Mathematics, Applied

Stochastic SIR model with jumps

Xianghua Zhang et al.

APPLIED MATHEMATICS LETTERS (2013)

Article Mathematics, Applied

Dynamics of positive solutions to SIR and SEIR epidemic models with saturated incidence rates

Zhenjie Liu

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS (2013)

Article Mathematics, Applied

Stochastic wave equation of pure jumps: Existence, uniqueness and invariant measures

Yiming Jiang et al.

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS (2012)

Article Mathematics

Explosive solutions of stochastic reaction-diffusion equations in mean Lp-norm

Pao-Liu Chow

JOURNAL OF DIFFERENTIAL EQUATIONS (2011)

Article Computer Science, Interdisciplinary Applications

Asymptotic behavior of global positive solution to a stochastic SIR model

Daqing Jiang et al.

MATHEMATICAL AND COMPUTER MODELLING (2011)

Article Biology

SVIR epidemic models with vaccination strategies

Xianning Liu et al.

JOURNAL OF THEORETICAL BIOLOGY (2008)

Article Mathematics, Applied

Global properties of a delayed SIR model with temporary immunity and nonlinear incidence rate

YN Kyrychko et al.

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS (2005)

Article Infectious Diseases

A double epidemic model for the SARS propagation

TW Ng et al.

BMC INFECTIOUS DISEASES (2003)

Article Statistics & Probability

Environmental Brownian noise suppresses explosions in population dynamics

XR Mao et al.

STOCHASTIC PROCESSES AND THEIR APPLICATIONS (2002)

Article Mathematics

Homoclinic bifurcation in an SIQR model for childhood diseases

LI Wu et al.

JOURNAL OF DIFFERENTIAL EQUATIONS (2000)