A delayed fractional-order model of Ebola virus disease with human behavioral dynamics
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Date
2026-05-20
Authors
Lusekelo Eva, Helikumi Mlyashimbi, Daudi Salamida
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Abstract
This study presents a fractional-order mathematical model to examine the transmission dynamics
of Ebola Virus Disease, explicitly incorporating incubation delays, human behavioral
responses, and socio-cultural funeral practices. Caputo fractional derivatives are employed to
represent memory effects, capturing the complex temporal evolution of outbreaks. Conditions
for the local stability of disease-free and endemic equilibria are derived. Numerical bifurcation
analysis indicates that increasing the incubation delay 𝜏 beyond a critical threshold 𝜏∗ ≈ 2.5 days
induces a Hopf bifurcation, resulting in sustained oscillations in infection levels. Additionally,
increasing 𝜏 from 1 to 3 days delays the epidemic peak by approximately 10 days and elevates
peak infections from 1200 to over 10,000 cases. The model further demonstrates that higher
proportions (𝑝1 > 0.4) of unmonitored deaths due to socio-cultural burial practices increase
the outbreak size by 35%, highlighting the importance of cultural interventions. The fractional
order 𝑞 influences oscillatory behaviors; as 𝑞 approaches 1, peak infection levels rise by 20%.
These findings emphasize the significance of integrating cultural, behavioral, and delay effects
into Ebola control strategies.
Description
Keywords
Ebola virus disease, Human behavioral response, Mathematical modeling, Infectious disease dynamics