Abstract:

Probability and mathematical modelling offer complementary ways of understanding biological and health-related phenomena. While statistical distributions help describe individual variability and observed data, dynamical models provide insight into how diseases evolve and how interventions may influence their spread.

In this talk, I will present selected results from our recent research, beginning with flexible lifetime distributions, including the XLindley, New XLindley, Zeghdoudi, and related families. I will discuss their mathematical properties, mixture representations, statistical inference, and applications to lifetime and reliability data. I will then show how continuous distributions can be used to construct count models capable of accounting for heterogeneity and overdispersion.

The second part will focus on discrete epidemic models, particularly SIRS systems. We will discuss equilibrium points, stability conditions, and bifurcation phenomena, illustrating how changes in model parameters can lead to oscillations and more complex epidemic behaviour. I will also present recent work on optimal control strategies that take these dynamical features into account, including applications to COVID-19 data.

Finally, I will briefly introduce ongoing research on an SEIR model for tuberculosis, incorporating nonlinear transmission mechanisms and treatment limitations.

Abstract:

We introduce a stochastic Fisher–KPP equations on Riemannian manifolds, combining reaction–diffusion dynamics with random environmental fluctuations. The model is formulated using the Laplace–Beltrami operator and multiplicative stochastic noise. Particular discussion will be devoted to the positivity and invariant regions, and the influence of stochastic perturbations on propagation phenomena.

Keywords: Stochastic Fisher–KPP equation, Riemannian manifolds, stochastic partial differential equations, Laplace–Beltrami operator, invariant regions,

📊 Statistics & Risk Management Seminar Series

NOVA MATH | NOVA School of Science and Technology

🎓 Talk: Some Recent Advances in Stable Variable Selection
👤 Speaker: Mahdi Nouraie, Macquarie University, Australia
📅 Date: Thursday, 29 October 2026
🕑 Time: 14:00–15:00 (Lisbon time)
💻 Format: Online (Google Meet)
🔗 Join us: Click here to join the seminar
📆 Add to Calendar: See the attached calendar invitation (.ics)

📝 About the Talk

Variable selection is a fundamental challenge in high-dimensional statistical modelling, particularly when predictors are highly correlated. This talk will explore recent advances in improving the stability of Lasso-based variable selection, introducing a novel weighting approach designed to enhance the reliability and reproducibility of selected variables. Results from simulations and real-world applications will illustrate the effectiveness of the proposed method.

📎 For further details, including the full abstract and speaker's biography, please see the seminar announcement available here.

✨ Free entry | All are welcome!

We look forward to seeing you online for an engaging scientific discussion!

Organizers:  Mina Norouzirad and Isabel Natário

Abstract: This course provides an introduction to deterministic and stochastic SIR epidemic models. The deterministic framework is developed through ordinary differential equations, focusing on epidemic thresholds, the basic reproduction number, epidemic peaks, and final epidemic size. The stochastic extension introduces Brownian motion, Itô stochastic differential equations, and the influence of random fluctuations on disease dynamics. Fundamental mathematical properties, including positivity, population conservation, and extinction conditions, are discussed. Numerical simulations using the Euler and Euler–Maruyama methods illustrate the theoretical results and highlight the differences between deterministic and stochastic epidemic dynamics.

Keywords: SIR model, mathematical epidemiology, stochastic differential equations, Itô calculus, epidemic thresholds, numerical simulations.

6 hours mini-course, 2 sessions of 3 hours each
 
Lecture 1: The Continuous Deterministic SIR Model 
Lecture 2: Threshold, Epidemic Peak, and Final Size 
Lecture 3: Formulation of a Continuous Stochastic SIR Model 
Lecture 4: Existence, Uniqueness, Conservation, and Positivity
Lecture 5: Extinction, Persistence and Noise-Adjusted Thresholds
Lecture 6: Numerical Simulation and Model Comparison

Abstract: This mini-course introduces statistical and mathematical tools for studying lifetime data, event counts, and epidemic dynamics. The emphasis will be on understanding the mathematical ideas behind the models and how they can be applied to biological and epidemiological problems.

We will first explore flexible lifetime distributions, focusing on Lindley-type models, Gamma-mixture representations, survival and hazard functions, and reliability properties. We will then consider count-data models, particularly mixed-Poisson distributions, and discuss how they account for overdispersion and population heterogeneity.

The second part will focus on continuous and discrete SIR/SIRS epidemic models. We will examine the basic reproduction number, disease-free and endemic equilibria, local stability, and bifurcation phenomena. We will also discuss how mathematical analysis can help understand epidemic persistence, oscillations, and control strategies.

The course will combine mathematical explanations, worked examples, and exercises. It is intended for graduate students, PhD students, and researchers interested in probability, statistics, differential equations, and mathematical biology.

4h lecture in 2 sessions of 2h each

 Session 1
Flexible Lifetime and Count-Data Models

- Lindley-type distributions and Gamma-mixture representations.
- Survival and hazard functions and reliability properties.
- Statistical inference and model comparison.
- Mixed-Poisson distributions, overdispersion, and biomedical count data.

Session 2 (1h30mm)
Mathematical Modelling of Epidemic Dynamics

- Continuous and discrete SIR/SIRS models.
- Basic reproduction number and epidemic thresholds.
- Disease-free and endemic equilibria.
- Stability analysis and bifurcation phenomena.
- Epidemic control and illustrative examples.

Abstract: This course provides an introduction to deterministic and stochastic SIR epidemic models. The deterministic framework is developed through ordinary differential equations, focusing on epidemic thresholds, the basic reproduction number, epidemic peaks, and final epidemic size. The stochastic extension introduces Brownian motion, Itô stochastic differential equations, and the influence of random fluctuations on disease dynamics. Fundamental mathematical properties, including positivity, population conservation, and extinction conditions, are discussed. Numerical simulations using the Euler and Euler–Maruyama methods illustrate the theoretical results and highlight the differences between deterministic and stochastic epidemic dynamics.

Keywords: SIR model, mathematical epidemiology, stochastic differential equations, Itô calculus, epidemic thresholds, numerical simulations.

6 hours mini-course, 2 sessions of 3 hours each
 
Lecture 1: The Continuous Deterministic SIR Model 
Lecture 2: Threshold, Epidemic Peak, and Final Size 
Lecture 3: Formulation of a Continuous Stochastic SIR Model 
Lecture 4: Existence, Uniqueness, Conservation, and Positivity
Lecture 5: Extinction, Persistence and Noise-Adjusted Thresholds
Lecture 6: Numerical Simulation and Model Comparison

Abstract: This mini-course introduces statistical and mathematical tools for studying lifetime data, event counts, and epidemic dynamics. The emphasis will be on understanding the mathematical ideas behind the models and how they can be applied to biological and epidemiological problems.

We will first explore flexible lifetime distributions, focusing on Lindley-type models, Gamma-mixture representations, survival and hazard functions, and reliability properties. We will then consider count-data models, particularly mixed-Poisson distributions, and discuss how they account for overdispersion and population heterogeneity.

The second part will focus on continuous and discrete SIR/SIRS epidemic models. We will examine the basic reproduction number, disease-free and endemic equilibria, local stability, and bifurcation phenomena. We will also discuss how mathematical analysis can help understand epidemic persistence, oscillations, and control strategies.

The course will combine mathematical explanations, worked examples, and exercises. It is intended for graduate students, PhD students, and researchers interested in probability, statistics, differential equations, and mathematical biology.

4h lecture in 2 sessions of 2h each

 Session 1
Flexible Lifetime and Count-Data Models

- Lindley-type distributions and Gamma-mixture representations.
- Survival and hazard functions and reliability properties.
- Statistical inference and model comparison.
- Mixed-Poisson distributions, overdispersion, and biomedical count data.

Session 2 (1h30mm)
Mathematical Modelling of Epidemic Dynamics

- Continuous and discrete SIR/SIRS models.
- Basic reproduction number and epidemic thresholds.
- Disease-free and endemic equilibria.
- Stability analysis and bifurcation phenomena.
- Epidemic control and illustrative examples.

Room: 3.2 VII
 
Abstract: Given an associative algebra A over a field F, a polynomial identity for A is a polynomial in non-commuting variables that vanishes under all evaluations in A. An algebra satisfying a nontrivial polynomial identity is called a PI-algebra.

In this talk, we introduce some of the main results in PI-theory, with particular emphasis on the use of combinatorial methods and representation theory techniques. Finally, we will present some recent developments in the context of algebras with trace.

This talk is partially based on joint works with S. Argenti, A. Ioppolo and S. Marchesi.