Ebola virus disease model with a nonlinear incidence rate and density-dependent treatment

作     者：Jacques NdéKengne Calvin Tadmon 

作者机构：Committed Mathematics TeamResearch Unit in Mathematics and ApplicationsDepartment of Mathematics and Computer ScienceUniversity of DschangP.O.Box 67 DschangCameroon Institute of MathematicsUniversity of MainzStaudingerweg 955128MainzGermany 

出 版 物：《Infectious Disease Modelling》 (传染病建模（英文）)

年 卷 期：2024年第9卷第3期

页      面：775-804页

学科分类：1007[医学-药学(可授医学、理学学位)] 100705[医学-微生物与生化药学] 1001[医学-基础医学(可授医学、理学学位)] 100103[医学-病原生物学] 10[医学] 

基　　金：C.Tadmon acknowledges good working conditions at the institute of Mathematics University of Mainz where this paper has been finalised during a research stay supported by the Alexander von Humboldt Foundation 

主　　题：Ebola epidemic models Stability Bifurcation Density-dependent treatment Sensitivity analysis Fractional differential equations Caputo fractional derivative Grünwald-letnikov nonstandard finite difference scheme 

摘      要：This paper studies an Ebola epidemic model with an exponential nonlinear incidence function that considers the efficacy and the behaviour *** current model also incorporates a new density-dependent treatment that catches the impact of the disease transmission on the ***,we provide a theoretical study of the nonlinear differential equations model *** precisely,we derive the effective reproduction number and,under suitable conditions,prove the stability of ***,we show that the model exhibits the phenomenon of backward-bifurcation whenever the bifurcation parameter and the reproduction number are less than *** find that the bi-stability and backward-bifurcation are not automatically connected in epidemic *** fact,when a backward-bifurcation occurs,the disease-free equilibrium may be globally ***,we use well-known standard tools to fit the model to the data reported for the 2018–2020 Kivu Ebola outbreak,and perform the sensitivity *** control Ebola epidemics,our findings recommend a combination of a rapid behaviour change and the implementation of a proper treatment strategy with a high level of ***,we propose and analyze a fractional-order Ebola epidemic model,which is an extension of the first model *** use the Caputo operator and construct the Grünwald-Letnikov nonstandard finite difference scheme,and show its advantages.