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

Infectious Disease Modelling 2024年第3期9卷 775-804页

作者： Jacques NdéKengne calvin tadmon Committed Mathematics Team Research Unit in Mathematics and ApplicationsDepartment of Mathematics and Computer ScienceUniversity of DschangP.O.Box 67 DschangCameroon Institute of Mathematics University of MainzStaudingerweg 955128MainzGermany

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.

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

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A transmission dynamics model of COVID-19:Case of Cameroon

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Infectious Disease Modelling 2022年第2期7卷 211-249页

作者： calvin tadmon Severin Foko Department of Mathematics and Computer Science Faculty of ScienceUniversity of DschangP.O.Box:67DschangCameroon The Abdus Salam International Centre for Theoretical Physics Strada Costiera 1134151TriesteItaly

In this work,we propose and investigate an ordinary differential equations model describing the spread of COVID-19 in *** model takes into account the asymptomatic,unreported symptomatic,quarantine,hospitalized individuals and the amount of virus in the environment,for evaluating their impact on the transmission of the *** establishing the basic properties of the model,we compute the control reproduction number Rc and show that the disease dies out whenever Rc1 and is endemic whenever Rc>***,an optimal control problem is derived and investigated theoretically by mainly relying on Pontryagin's maximum *** illustrate the theoretical analysis by presenting some graphical results.

关键词： COVID-19 ODE model Global stability Lyapunov function Optimal control

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New exact solutions to the Eddingtoninspired-Born-Infeld equations for a relativistic perfect fluid in a Bianchi type Ⅰ spacetime

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Communications in Theoretical Physics 2022年第6期74卷 122-134页

作者： calvin tadmon Guichard Djiodjo-Seugmo Department of Mathematics and Computer Science Faculty of ScienceUniversity of DschangPO Box 67DschangCameroon The Abdus Salam International Centre for Theoretical Physics Strada Costiera 11I-34151 TriesteItaly

We consider a Bianchi type Ⅰ physical metric g, an auxiliary metric q and a density matter ρ in Eddington-inspired-Born-Infeld theory. We first derive a system of second order nonlinear ordinary differential equations. Then, by a suitable change of variables, we arrive at a system of first order nonlinear ordinary differential equations. Using both the solution-tube concept for the first order nonlinear ordinary differential equations and the nonlinear analysis tools such as the Arzelá-Ascoli theorem, we prove an existence result for the nonlinear system obtained. The resolution of this last system allows us to obtain new exact solutions for the model ***, by studying the asymptotic behaviour of the exact solutions obtained, we conclude that this solution is the counterpart of the Friedman-Lemaitre-Robertson-Walker spacetime in Eddington-inspired-Born-Infeld theory.

关键词： Eddington-inspired-Born-Infeld theory Bianchi typeⅠspacetime solution-tube Friedmann-Lema?tre-Robertson-Walker spacetime density matter ordinary differential equations

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