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

作　　者：Jacques NdéKengne Calvin Tadmon 

机构地区：[1]Committed Mathematics Team,Research Unit in Mathematics and Applications,Department of Mathematics and Computer Science,University of Dschang,P.O.Box 67 Dschang,Cameroon [2]Institute of Mathematics,University of Mainz,Staudingerweg 9,55128,Mainz,Germany

出　　处：《Infectious Disease Modelling》2024年第3期775-804,共30页传染病建模（英文）

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.

摘　　要：This paper studies an Ebola epidemic model with an exponential nonlinear incidence function that considers the efficacy and the behaviour change.The current model also incorporates a new density-dependent treatment that catches the impact of the disease transmission on the treatment.Firstly,we provide a theoretical study of the nonlinear differential equations model obtained.More precisely,we derive the effective reproduction number and,under suitable conditions,prove the stability of equilibria.Afterwards,we show that the model exhibits the phenomenon of backward-bifurcation whenever the bifurcation parameter and the reproduction number are less than one.We find that the bi-stability and backward-bifurcation are not automatically connected in epidemic models.In fact,when a backward-bifurcation occurs,the disease-free equilibrium may be globally stable.Numerically,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 analysis.To 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 efficacy.Secondly,we propose and analyze a fractional-order Ebola epidemic model,which is an extension of the first model studied.We use the Caputo operator and construct the Grünwald-Letnikov nonstandard finite difference scheme,and show its advantages.

关 键 词：Ebola epidemic models STABILITY BIFURCATION Density-dependent treatment Sensitivity analysis Fractional differential equations Caputo fractional derivative Grünwald-letnikov nonstandard finite difference scheme 

分 类 号：R373.32[医药卫生—病原生物学]