This study introduces a novel mathematical model to describe the progression of cholera by integrating fractional derivatives with both singular and non-singular kernels alongside stochastic differential equations ove...This study introduces a novel mathematical model to describe the progression of cholera by integrating fractional derivatives with both singular and non-singular kernels alongside stochastic differential equations over four distinct time intervals.The model incorporates three key fractional derivatives:the Caputo-Fabrizio fractional derivative with a non-singular kernel,the Caputo proportional constant fractional derivative with a singular kernel,and the Atangana-Baleanu fractional derivative with a non-singular kernel.We analyze the stability of the core model and apply various numerical methods to approximate the proposed crossover model.To achieve this,the approximation of Caputo proportional constant fractional derivative with Grünwald-Letnikov nonstandard finite difference method is used for the deterministic model with a singular kernel,while the Toufik-Atangana method is employed for models involving a non-singular Mittag-Leffler kernel.Additionally,the integral Caputo-Fabrizio approximation and a two-step Lagrange polynomial are utilized to approximate the model with a non-singular exponential decay kernel.For the stochastic component,the Milstein method is implemented to approximate the stochastic differential equations.The stability and effectiveness of the proposed model and methodologies are validated through numerical simulations and comparisons with real-world cholera data from Yemen.The results confirm the reliability and practical applicability of the model,providing strong theoretical and empirical support for the approach.展开更多
This paper investigates the stability and bifurcation phenomena of a cholera transmission model in which individuals who have recovered from the disease may become susceptible again.The threshold for determining disea...This paper investigates the stability and bifurcation phenomena of a cholera transmission model in which individuals who have recovered from the disease may become susceptible again.The threshold for determining disease prevalence is established,and the parameter conditions for the existence of equilibria are discussed.The Routh-Hurwitz criterion is applied to demonstrate the local asymptotic stability of equilibria.By utilizing composite matrices and geometric techniques,the global dynamic behavior of the endemic equilibrium is investigated,and the sufficient conditions for its global asymptotic stability are derived.Furthermore,the disease-free equilibrium is a saddle-node when the basic reproductive number is 1,and tthe transcritical bifurcation in this case is discussed.展开更多
We propose,in this paper,a hybrid Cholera transmission model with phage to simulate the interaction between Vibrio cholerae and phages in the host population and environment,which is coupled with some reaction-diffusi...We propose,in this paper,a hybrid Cholera transmission model with phage to simulate the interaction between Vibrio cholerae and phages in the host population and environment,which is coupled with some reaction-diffusion equations and first-order partial differential equations.The precise formulation of basic reproduction number(Ro)is deduced,which characterizes the elimination or prevalence of this disease.Specifically,the disease-free steady state is globally asymptotically stable for R_(0)≤1 but unstable for R_(0)>1.Further,the phage invasion reproduction number Ri is also obtained,which portrays the impact of phages on Vibrio cholerae in the environment.That is,for R_(0)>1,the phage-free endemic steady state is globally asymptotically stable if R_(1)≤1,and the phage-present endemic steady state is globally asymptotically stable if R_(1)>1.Numerical simulations are introduced for the purpose of verifying the main results.展开更多
In this research work, we present a mathematical model for the control of cholera outbreak without natural recovery. This follows a slight modification as compared to previous cholera models for the Nigerian case. Our...In this research work, we present a mathematical model for the control of cholera outbreak without natural recovery. This follows a slight modification as compared to previous cholera models for the Nigerian case. Our model incorporates treatment, water hygiene as well as environmental sanitation. The model employs a system of nonlinear ordinary differential equations, which is analyzed in detail for its stability properties. We compute the basic reproduction ratio R<sub>0</sub> for the various control parameters and discover that with proper combination of control measures, the spread of cholera could be minimized. Numerical simulation of the cholera model is done using MathCAD14, and the graphical profiles of the main variables are depicted. We conclude that improvement in treatment, water hygiene and the environmental sanitation is indeed effective in eradicating the cholera epidemic.展开更多
This paper develops an SIBR cholera transmission model with general incidence rate. Necessary and sufficient conditions for local and global asymptotic stability of the equilibria are established by Routh Hurwitz crit...This paper develops an SIBR cholera transmission model with general incidence rate. Necessary and sufficient conditions for local and global asymptotic stability of the equilibria are established by Routh Hurwitz criterium, Lyapunov function, and the second additive composite matrix theorem. What is more, exploiting the DED is cover simulation tool, the parameter values of the model are estimated with the 1998-2021 cholera case data in China. Finally, we perform sensitivity analysis for the basic reproduction number to seek for effective interventions for cholera control. .展开更多
In this paper, we consider a SVIR-B cholera model with imperfect vaccination. By analyzing the corresponding characteristic equations, the local asymptotically stability of a disease-free equilibrium and an endemic eq...In this paper, we consider a SVIR-B cholera model with imperfect vaccination. By analyzing the corresponding characteristic equations, the local asymptotically stability of a disease-free equilibrium and an endemic equilibrium is established. We calculate the certain threshold known as the basic reproduction number Rv. If Rv the community. By comparison arguments, it is proved that if Rv > 1, the unique endemic equilibrium is local asymptotically stable. We perform sensitivity analysis of Rv on the parameters in order to determine their relative importance to disease control and show that an imperfect vaccine is always beneficial in reducing disease spread within the community.展开更多
The global dynamics of a cholera model with delay is considered. We determine a basic reproduction number R0 which is chosen based on the relative ODE model, and establish that the global dynamics are determined by th...The global dynamics of a cholera model with delay is considered. We determine a basic reproduction number R0 which is chosen based on the relative ODE model, and establish that the global dynamics are determined by the threshold value R0. If R0 〈 1, then the infection-free equilibrium is global asymptotically stable, that is, the cholera dies out; If R0 〉 1, then the unique endemic equilibrium is global asymptotically stable, which means that the infection persists. The results obtained show that the delay does not lead to periodic oscillations. Finally, some numerical simulations support our theoretical results.展开更多
将麦芽糖结合蛋白(maltose-binding protein,MBP)、霍乱毒素B亚基(cholera toxin B subunit,CTB)以及增强型绿色荧光蛋白(enhanced green fluorescent protein,EGFP)基因重组构建MBP-CTB-EGFP并原核表达纯化,利用HEK293T细胞模型探究MBP...将麦芽糖结合蛋白(maltose-binding protein,MBP)、霍乱毒素B亚基(cholera toxin B subunit,CTB)以及增强型绿色荧光蛋白(enhanced green fluorescent protein,EGFP)基因重组构建MBP-CTB-EGFP并原核表达纯化,利用HEK293T细胞模型探究MBP-CTB-EGFP穿透细胞膜的能力,从而开发新型黏膜佐剂.进一步地,利用原肌球蛋白(tropomyosin,TM)重组融合蛋白MBP-CTB-TM,将其应用于Balb/c小鼠致敏实验,探究融合蛋白的致敏性及其对小鼠食物过敏相关免疫反应的影响,以达到降低过敏原剂量提高建模效率的效果.结果表明:MBP-CTB-EGFP具有作为黏膜佐剂的能力,从而促进外源蛋白进入HEK293T细胞内,且与转染方式相比,携带外源蛋白进入细胞的效率更高.另一方面,利用融合蛋白MBP-CTB-TM免疫小鼠,TM特异性IgE的OD450 nm达到0.4,而天然TM致敏组仅为0.05,此外融合蛋白致敏还导致高水平的TM特异性IgG1、IgG2a产生.本研究表明,融合蛋白MBP-CTB-TM致敏效果更好,有可能达到降低过敏原用量的效果,为后续食物过敏研究提供了有力工具.展开更多
文摘This study introduces a novel mathematical model to describe the progression of cholera by integrating fractional derivatives with both singular and non-singular kernels alongside stochastic differential equations over four distinct time intervals.The model incorporates three key fractional derivatives:the Caputo-Fabrizio fractional derivative with a non-singular kernel,the Caputo proportional constant fractional derivative with a singular kernel,and the Atangana-Baleanu fractional derivative with a non-singular kernel.We analyze the stability of the core model and apply various numerical methods to approximate the proposed crossover model.To achieve this,the approximation of Caputo proportional constant fractional derivative with Grünwald-Letnikov nonstandard finite difference method is used for the deterministic model with a singular kernel,while the Toufik-Atangana method is employed for models involving a non-singular Mittag-Leffler kernel.Additionally,the integral Caputo-Fabrizio approximation and a two-step Lagrange polynomial are utilized to approximate the model with a non-singular exponential decay kernel.For the stochastic component,the Milstein method is implemented to approximate the stochastic differential equations.The stability and effectiveness of the proposed model and methodologies are validated through numerical simulations and comparisons with real-world cholera data from Yemen.The results confirm the reliability and practical applicability of the model,providing strong theoretical and empirical support for the approach.
基金supported by the National Natural Science Foundation of China(No.12171337)the Central Government Guided Local Science and Technology Development Projects(No.2024ZYD0059)+1 种基金the Natural Science Foundation of Sichuan Province(No.2022NSFSC0529)the Open Research Fund Program of Data Recovery Key Laboratory of Sichuan Province(No.DRN2405)。
文摘This paper investigates the stability and bifurcation phenomena of a cholera transmission model in which individuals who have recovered from the disease may become susceptible again.The threshold for determining disease prevalence is established,and the parameter conditions for the existence of equilibria are discussed.The Routh-Hurwitz criterion is applied to demonstrate the local asymptotic stability of equilibria.By utilizing composite matrices and geometric techniques,the global dynamic behavior of the endemic equilibrium is investigated,and the sufficient conditions for its global asymptotic stability are derived.Furthermore,the disease-free equilibrium is a saddle-node when the basic reproductive number is 1,and tthe transcritical bifurcation in this case is discussed.
基金supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region(Grant Nos.2022TSYCCX0015 and 2021D01E12)the National Natural Science Foundation of China(Grant No.12361103)the Scientific Research and Innovation Project of Outstanding Doctoral Students in Xinjiang University(Grant No.XJU2022BS022).
文摘We propose,in this paper,a hybrid Cholera transmission model with phage to simulate the interaction between Vibrio cholerae and phages in the host population and environment,which is coupled with some reaction-diffusion equations and first-order partial differential equations.The precise formulation of basic reproduction number(Ro)is deduced,which characterizes the elimination or prevalence of this disease.Specifically,the disease-free steady state is globally asymptotically stable for R_(0)≤1 but unstable for R_(0)>1.Further,the phage invasion reproduction number Ri is also obtained,which portrays the impact of phages on Vibrio cholerae in the environment.That is,for R_(0)>1,the phage-free endemic steady state is globally asymptotically stable if R_(1)≤1,and the phage-present endemic steady state is globally asymptotically stable if R_(1)>1.Numerical simulations are introduced for the purpose of verifying the main results.
文摘In this research work, we present a mathematical model for the control of cholera outbreak without natural recovery. This follows a slight modification as compared to previous cholera models for the Nigerian case. Our model incorporates treatment, water hygiene as well as environmental sanitation. The model employs a system of nonlinear ordinary differential equations, which is analyzed in detail for its stability properties. We compute the basic reproduction ratio R<sub>0</sub> for the various control parameters and discover that with proper combination of control measures, the spread of cholera could be minimized. Numerical simulation of the cholera model is done using MathCAD14, and the graphical profiles of the main variables are depicted. We conclude that improvement in treatment, water hygiene and the environmental sanitation is indeed effective in eradicating the cholera epidemic.
文摘This paper develops an SIBR cholera transmission model with general incidence rate. Necessary and sufficient conditions for local and global asymptotic stability of the equilibria are established by Routh Hurwitz criterium, Lyapunov function, and the second additive composite matrix theorem. What is more, exploiting the DED is cover simulation tool, the parameter values of the model are estimated with the 1998-2021 cholera case data in China. Finally, we perform sensitivity analysis for the basic reproduction number to seek for effective interventions for cholera control. .
文摘In this paper, we consider a SVIR-B cholera model with imperfect vaccination. By analyzing the corresponding characteristic equations, the local asymptotically stability of a disease-free equilibrium and an endemic equilibrium is established. We calculate the certain threshold known as the basic reproduction number Rv. If Rv the community. By comparison arguments, it is proved that if Rv > 1, the unique endemic equilibrium is local asymptotically stable. We perform sensitivity analysis of Rv on the parameters in order to determine their relative importance to disease control and show that an imperfect vaccine is always beneficial in reducing disease spread within the community.
文摘The global dynamics of a cholera model with delay is considered. We determine a basic reproduction number R0 which is chosen based on the relative ODE model, and establish that the global dynamics are determined by the threshold value R0. If R0 〈 1, then the infection-free equilibrium is global asymptotically stable, that is, the cholera dies out; If R0 〉 1, then the unique endemic equilibrium is global asymptotically stable, which means that the infection persists. The results obtained show that the delay does not lead to periodic oscillations. Finally, some numerical simulations support our theoretical results.
文摘将麦芽糖结合蛋白(maltose-binding protein,MBP)、霍乱毒素B亚基(cholera toxin B subunit,CTB)以及增强型绿色荧光蛋白(enhanced green fluorescent protein,EGFP)基因重组构建MBP-CTB-EGFP并原核表达纯化,利用HEK293T细胞模型探究MBP-CTB-EGFP穿透细胞膜的能力,从而开发新型黏膜佐剂.进一步地,利用原肌球蛋白(tropomyosin,TM)重组融合蛋白MBP-CTB-TM,将其应用于Balb/c小鼠致敏实验,探究融合蛋白的致敏性及其对小鼠食物过敏相关免疫反应的影响,以达到降低过敏原剂量提高建模效率的效果.结果表明:MBP-CTB-EGFP具有作为黏膜佐剂的能力,从而促进外源蛋白进入HEK293T细胞内,且与转染方式相比,携带外源蛋白进入细胞的效率更高.另一方面,利用融合蛋白MBP-CTB-TM免疫小鼠,TM特异性IgE的OD450 nm达到0.4,而天然TM致敏组仅为0.05,此外融合蛋白致敏还导致高水平的TM特异性IgG1、IgG2a产生.本研究表明,融合蛋白MBP-CTB-TM致敏效果更好,有可能达到降低过敏原用量的效果,为后续食物过敏研究提供了有力工具.
