Asymptotic stability analysis of a fractional epidemic model for Ebola virus disease in Caputo sense

Samson Olaniyi; Furaha M. Chuma; Sulaimon F. Abimbade

doi:10.46481/jnsps.2025.2304

Authors

Samson Olaniyi Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso, Nigeria https://orcid.org/0000-0001-6492-1405
Fuhara M. Chuma Department of Physics, Mathematics and Informatics, Dar es Salaam University College of Education, Tanzania
Sulaimon F. Abimbade
[email protected]
Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso, Nigeria https://orcid.org/0000-0002-1992-9560

Keywords:

Mathematical model, Fractional order, Caputo derivative operator, Ebola virus disease, Lyapunov stability

Abstract

In this work, a non-integer-order epidemic system modelling the nonlinear dynamics of Ebola virus disease is formulated in the sense of Caputo-ractional derivative. The existence and uniqueness of solution of the model is established. More importantly, the theoretical analysis carried out is aimed at establishing the local and global asymptotic stability properties of the disease-free steady state of the epidemic model using the fractional Routh-Hurwitz criterion and Lyapunov functional technique, respectively. It is proved that the steady state is locally and globally asymptotically stable at the value of the key epidemiological threshold quantity lower than unity. The result is numerically validated for different values of fractional order to show the asymptotic behavior of the disease dynamics. This result is significant for fighting and preventing Ebola epidemic in the population, since the Caputo derivative operator allows for effective description of the disease dynamics with memory, where the future evolution of the disease is governed by its prior history.

Dimensions

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