https://doi.org/10.1140/epjp/s13360-025-07104-3
Regular Article
Dynamical analysis and optimal control of an ebola virus model with animal reservoir and human spillover
1
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan
2
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia
3
Mathematics Department, Faculty of Science, Taibah University, 41411, Al-Madinah Al-Munawarah, Saudi Arabia
a
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Received:
2
November
2025
Accepted:
21
November
2025
Published online:
11
December
2025
Abstract
This paper develops a compartmental mathematical model to study the transmission model exhibits nonlinear dynamical features, including feedback, threshold effects, and interactions between human and animal populations of the Ebola virus, formulated as an 
system that incorporates zoonotic spillover from animal reservoirs to human populations. Nonlinear interactions in the epidemic model produce rich dynamical behaviors, multiple equilibria, symbolic computation, stability theory, and robust nonlinear control are used to analyze these behaviors and to design effective strategies to mitigate outbreaks. The basic reproduction number 
is derived using the next-generation matrix method, with local stability of both the disease-free and endemic equilibria analyzed through Jacobian-based techniques. Global stability (GS) of the disease-free equilibrium is established via the Metzler matrix approach, while a Lyapunov function is constructed to prove the GS of the DEE. A Nonstandard Finite Difference (NSFD) scheme is formulated to numerically simulate the system while preserving positivity, boundedness, and dynamical consistency. Sensitivity analysis identifies the human infection rate, animal-to-animal transmission rate, and animal mortality as key parameters influencing , guiding targeted intervention strategies. To mitigate the epidemic, an Integral Sliding Mode Controller (ISMC) is designed, which effectively reduces infection prevalence, stabilizes the system dynamics, and demonstrates robustness even under parameter uncertainties. Numerical simulations confirm that ISMC substantially lowers peak infections and helps maintain healthier human and animal populations. Overall, this integrated framework combining rigorous mathematical modeling, robust nonlinear control, and numerical simulations provides both theoretical insights and practical tools for understanding, forecasting, and controlling Ebola outbreaks, particularly in regions where zoonotic transmission plays a critical role.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
