The next meeting of the seminar of the
Mathematical Modeling and Numerical Analysis Department 
will be held on September 18, 2024, at 2:00 pm in Room 478 of the Institute of Mathematics and Informatics.

A talk on:

Singular perturbation theory in epidemic modelling

will be delivered by Sara Sottile (University of Bologna, Italy).

Abstract: In real world scenarios, the natural phenomena usually evolve on time scales differing by various orders of magnitude. Such separation in time-scales can be found, for example, in the field of chemical oscillations [1], neuroscience [2], ecology [3] or opinion/information spreading [4]. In this context, Geometric Singular Perturbation Theory (GSPT) is a powerful analytical technique which fully exploits the underlying time-scale separation. Epidemiological models also provide a natural fit for these dynamics. Consider, for instance, models that incorporate information dynamics [5, 6], host-vector interactions [7, 8], or even those that account for immunity loss and reinfection processes, which occur over extended time scales [9]. This seminar will introduce the fundamental concepts of Geometric Singular Perturbation Theory (GSPT) and explore its applications in epidemiology, using various tools and techniques to illustrate the range of its potential.

References

[1] Jelbart, S., Pages, N., Kirk, V., Sneyd, J., Wechselberger, M. (2022). Process-oriented geometric singular perturbation theory and calcium dynamics. SIAM Journal on Applied Dynamical Systems, 21(2): 982–1029.

[2] Desroches, M., Krauskopf, B., Osinga, H. M. (2008). Mixed-mode oscillations and slow manifolds in the self-coupled FitzHugh-Nagumo system. Chaos: An Interdisci- plinary Journal of Nonlinear Science, 18(1): 015107.

[3] Rinaldi, S., Scheffer, M. (2000). Geometric analysis of ecological models with slow and fast processes. Ecosystems, 3: 507-521.

[4] S. Schecter. (2021) Geometric singular perturbation theory analysis of an epidemic model with spontaneous human behavioral change. Journal of Mathematical Biology, 82(6):1–26.

[5] Della Marca, R., d’Onofrio, A., Sensi, M., Sottile, S. (2024). A geometric analysis of the impact of large but finite switching rates on vaccination evolutionary games. Nonlinear Analysis: Real World Applications, 75: 103986.

[6] Bulai, I.M., Sensi, M., Sottile, S. (2024). A geometric analysis of the SIRS compartmental model with fast information and misinformation spreading. Chaos, Solitons & Fractals, 185, 115104.

[7] Aguiar, M., Kooi, B. W., Pugliese, A., Sensi, M., Stollenwerk, N. (2021) Time scale separation in the vector borne disease model SIRUV via center manifold analysis. medRxiv

[8] Rashkov, P., Kooi, B. W. (2021) Complexity of host-vector dynamics in a two-strain dengue model. Journal of Biological Dynamics, 15(1), 35–72.

[9] Kaklamanos, P., Pugliese, A., Sensi, M., Sottile, S. (2024). A geometric analysis of the SIRS model with secondary infections. SIAM Journal on Applied Mathematics, 84(2).