A network reaction–transport model for Ebola dynamics with adaptive mobility, spillover, and behavioral feedback

Olumuyiwa James Peter; Azhar Iqbal Kashif Butt; Sharifah Sakinah Syed Ahmad; and Muneerah AL Nuwairan; Olumuyiwa James Peter; Azhar Iqbal Kashif Butt; Sharifah Sakinah Syed Ahmad; and Muneerah AL Nuwairan

doi:10.3934/math.20261077

AIMS Mathematics

2026, Volume 11, Issue 8: 26834-26867. doi: 10.3934/math.20261077

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Research article

A network reaction–transport model for Ebola dynamics with adaptive mobility, spillover, and behavioral feedback

1.
Department of Mathematics, Saveetha School of Engineering, SIMATS, Saveetha University, Chennai, Tamil Nadu, India
2.
Department of Mathematical and Computer Sciences, University of Medical Sciences, Ondo City, Ondo State, Nigeria
3.
Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa 31982, Saudi Arabia
4.
Faculty of Artificial Intelligence and Cyber Security, Universiti Teknikal Malaysia Melaka, Malaysia

Received: 13 June 2026 Revised: 09 August 2026 Accepted: 19 August 2026 Published: 26 August 2024
MSC : 91A40, 34D23

Ebola virus disease is an ever-present threat to public health, driven by the interplay of zoonotic transmission, human mobility, high-risk social behaviors, and behavioral responses to infection. In the present work, we proposed and thoroughly analyzed a network-based reaction–transport model of Ebola virus disease transmission, which simultaneously accounts for the dynamics of adaptive human mobility, higher-order transmission, and zoonotic spillover. Our model precisely incorporates routine pairwise transmission, group transmission through funerals and healthcare settings, survivor relapse, and continuous reseeding from animal reservoirs, as well as human mobility responses to local prevalence through fear-based suppression. We rigorously proved the positivity, global boundedness, and well-posedness of the resulting nonlinear system, despite state-dependent transport and continuous external forcing. We derived a network-based basic reproduction number using an operator-theoretic next-generation method, which integrates transmission, recovery, and mobility-driven spatial transport. Our analysis precisely shows that zoonotic transmission fundamentally alters classical epidemic thresholds: in the subcritical human-to-human transmission regime, continuous reseeding invariably drives the system toward a positive endemic equilibrium. Using resolvent and spectral analysis, we meticulously demonstrated the anti-diffusive effect of fear-based mobility suppression, which generates spatial trapping, hysteresis, eigenvector localization, and Turing-type instabilities leading to the formation of geographically localized and persistent Ebola virus disease hotspots. Numerical simulations on synthetic mobility networks confirmed the theoretical results and thoroughly demonstrated sharp phase transitions governing hotspot dominance and persistence. Our results rigorously showed that zoonotic transmission controls the persistence of Ebola Virus Disease, while mobility and behavioral responses determine the spatial localization of the endemic equilibrium. Overall, this work provides a mechanistic explanation for the observed coexistence of low global prevalence and strong spatial localization of Ebola Virus Disease and offers new insight into the complex interplay among behavioral responses, network structure, and zoonotic transmission.
- Ebola virus,
- zoonotic spillover,
- adaptive human mobility,
- network reaction–transport models,
- fear-driven behavior,
- spatial heterogeneity,
- nonlinear transmission
Citation: Olumuyiwa James Peter, Azhar Iqbal Kashif Butt, Sharifah Sakinah Syed Ahmad, and Muneerah AL Nuwairan. A network reaction–transport model for Ebola dynamics with adaptive mobility, spillover, and behavioral feedback[J]. AIMS Mathematics, 2026, 11(8): 26834-26867. doi: 10.3934/math.20261077

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Abstract

Ebola virus disease is an ever-present threat to public health, driven by the interplay of zoonotic transmission, human mobility, high-risk social behaviors, and behavioral responses to infection. In the present work, we proposed and thoroughly analyzed a network-based reaction–transport model of Ebola virus disease transmission, which simultaneously accounts for the dynamics of adaptive human mobility, higher-order transmission, and zoonotic spillover. Our model precisely incorporates routine pairwise transmission, group transmission through funerals and healthcare settings, survivor relapse, and continuous reseeding from animal reservoirs, as well as human mobility responses to local prevalence through fear-based suppression. We rigorously proved the positivity, global boundedness, and well-posedness of the resulting nonlinear system, despite state-dependent transport and continuous external forcing. We derived a network-based basic reproduction number using an operator-theoretic next-generation method, which integrates transmission, recovery, and mobility-driven spatial transport. Our analysis precisely shows that zoonotic transmission fundamentally alters classical epidemic thresholds: in the subcritical human-to-human transmission regime, continuous reseeding invariably drives the system toward a positive endemic equilibrium. Using resolvent and spectral analysis, we meticulously demonstrated the anti-diffusive effect of fear-based mobility suppression, which generates spatial trapping, hysteresis, eigenvector localization, and Turing-type instabilities leading to the formation of geographically localized and persistent Ebola virus disease hotspots. Numerical simulations on synthetic mobility networks confirmed the theoretical results and thoroughly demonstrated sharp phase transitions governing hotspot dominance and persistence. Our results rigorously showed that zoonotic transmission controls the persistence of Ebola Virus Disease, while mobility and behavioral responses determine the spatial localization of the endemic equilibrium. Overall, this work provides a mechanistic explanation for the observed coexistence of low global prevalence and strong spatial localization of Ebola Virus Disease and offers new insight into the complex interplay among behavioral responses, network structure, and zoonotic transmission.

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