Global stability and uniform persistence in an SVEIR model with saturating fomite-mediated transmission

Speaker(s)

Emanuela Penitente

Affiliation

University of Naples Federico II

Language of the talk

English

Date

Feb. 25, 2026, 2:15 p.m.

Link

https://uw-edu-pl.zoom.us/j/97187479863?pwd=4ERaSaNt4dbYv77P5T9Ru1AawSYnia.1

Information about the event

Tym razem spotkanie online

Seminar

Seminar of Biomathematics and Game Theory Group

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In this talk, I will consider the recently developed SVEIR (Susceptible–Vaccinated–Exposed–Infected–Recovered) epidemic model proposed by G¨okc¸e and coauthors [1], which describes the transmission of a vaccine-preventable disease through two routes: direct host-to-host transmission and indirect fomite-mediated infection, represented by an environmental contamination variable. The contribution of fomites to the transmission is modelled via a bounded saturating Holling-type response function. I will first review some of the main findings obtained in [1], i.e., the local stability of the disease–free equilibrium for R0 < 1, and the occurrence of either backward or forward transcritical bifurcations at R0 = 1, depending on the choice of the saturating response. Then, I will focus on the global dynamical behaviour. After proving positivity, boundedness, and the existence of a compact attracting set, I will focus on the Holling type II case and derive a sufficient condition for the global asymptotic stability of the disease–free equilibrium by exploiting a monotone/Metzler decomposition in the spirit of the Kamgang–Sallet approach [2].
Finally, for R0 > 1, I will show a result on the uniform persistence of the disease and the existence of at least one endemic equilibrium using persistence theory for continuous semiflows via an acyclicity analysis of the boundary dynamics [3]. Overall, these results provide rigorous extinction/persistence criteria and contribute to the theoretical understanding of environmentally mediated infectious disease dynamics.

[1] Gokce, A., Gurbuz, B., Rendall, A. D. (2024). Dynamics of a mathematical model of virus spreading incorporating the effect of a vaccine. Nonlinear Analysis: Real World Applications, 78, 104097

[2] Kamgang, J. C., Sallet, G. (2008). Computation of threshold conditions for epidemiological models and global stability of the disease-free equilibrium (DFE). Mathematical
Biosciences, 213(1), 1-12

[3] Thieme, H. R. (1993). Persistence under relaxed point-dissipativity (with application to an endemic model). SIAM Journal on Mathematical Analysis, 24(2), 407-435

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