Introductory and Advanced Courses

Course 1

Title: Mathematical epidemiology I
Duration: 6 hours
Level: Introductory
Lecturer’s NAME: Professor Robert Smith? The University of Ottawa, Canada

Abstract of the course: The objective of this course is to present a detailed introduction to modelling infectious diseases. We will discuss disease modelling at the population level, as these models represent some of the most classical results. We will cover a variety of topics on the mathematical modelling of infectious diseases (HIV, malaria, COVID-19, human papillomavirus, West Nile virus, measles, anthrax and smallpox). Interventions will include vaccines, drug resistance, social distancing and quaranting. Theoretical tools will include differential equation models, the basic reproductive ratio, uncertainty/sensitivity analysis, Latin Hypercube Sampling and impulsive differential equations

Course 2

Title: Mathematical Epidemiology II
Duration: 5 hours lessons + 3 hours computer room sessions and tutorials
Level: Graduate
Lecturer’s NAME: Professor María Vela Perez, Universidad Complutense de Madrid, Spain

Abstract of the course: This course is a continuation to the course  “Mathematical Epidemiology I”. It includes model building and fitting to data using various techniques. Furthermore, some computational methods and techniques related to epidemiological models using MATLAB code will be explained

Course 3

Title: Survival analysis
Duration: 3 hours of lessons + 3 training sessions
Level: Graduate
Lecturer’s NAME: Professor Valérie Gares, Univ Rennes, INSA, CNRS, IRMAR – UMR 6625, F-35000 Rennes, France

Abstract of the course: Survival analysis is a branch of statistics for analyzing data on time to an event such as death, heart attack, a specific disease. We first introduce censored failure time and probabilistic tools for survival analysis (survival function, instantaneous risk, cumulative hazard function). We then describe  nonparametric methods for estimating the survival function and the cumulative hazard function (Kaplan-Meier and Nelson-Aalen estimators respectively). The Logrank test is developed to compare survival distributions between groups in a two sample problem. Finally, we discuss a semi-parametric regression model for censored data, the proportional hazards model. All methods are illustrated with artificial or real data sets. The practical session will be realized on R software.

Course 4

Title: Introduction to clinically-oriented, image-based computational modeling and simulation of cancer growth
Duration: 12 hours (6 hours of lectures + 6 hours of hands-on coding lab)
Level: Graduate/doctorate
Lecturer’s NAME: Professor Guillermo Lorenzo Gomez, Marie Sklodowska-Curie fellow; Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, USA; Dipartimento di Ingegneria Civile e Architettura, Università di Pavia, Italy

Abstract of the course: The use of mechanistic mathematical models and computer simulations to forecast tumor growth has enabled the prediction of clinical outcomes for multiple types of cancers and provides a promising approach to optimize their treatment. Mechanistic models of cancer usually consist of a set of partial differential equations describing the key mechanisms involved in cancer growth and treatment. Longitudinal clinical and imaging data enable the calibration of these mechanistic models to render a personalized forecast of tumor evolution, hence accounting for the unique heterogeneity of each patient’s tumor. In particular, quantitative medical imaging (e.g., multi-parametric magnetic resonance imaging, positron emission tomography) can probe different biological features of cancerous tissues and provide spatiotemporally-resolved data for model calibration and the assessment of tumor progression.

This course will begin by reviewing the main approaches of organ-scale, patient-specific mechanistic mathematical modeling of tumors using different imaging data types for model initialization and calibration. We will also describe standard computational technologies enabling model simulation, model calibration, model selection, and treatment optimization. Then, we will focus on the use of finite element and iso-geometric methods to solve mechanistic models of cancer and hence run computer simulations to forecast tumor evolution. The course will cover the derivation of the standard finite-element/isogeometric formulation of the model, an outline of the usual algorithms to solve the resulting systems, and a description of the technical details for code implementation. Additionally, the course includes a series of hands-on coding sessions aimed at solving several problems using standard finite-element/isogeometric methods, and ultimately leading to the construction of a code to solve a usual reaction-diffusion model of cancer growth

Course 5

Title: Mathematics of Infectious Diseases
Level: Introductory
Duration: 5-6 hours lectures + 3-4 hours discussion, lab sessions and tutorials + 1.5 hours of public lecture
Lecturer’s NAME: Professor Abba Gumel, Arizona State University, Tempe, Arizona, USA

Abstract of the course: The objective of the course is to introduce the mathematical methods and theories used to study the transmission dynamics and control of emergent and re-emergent infectious diseases of public health importance.  In addition to introducing the various principles and underlying assumptions associated with the formulating of realistic models for disease transmission and control, techniques, and tools for rigorously analyzing the qualitative dynamics of the models will be discussed. The analyses entail the determination of the existence and asymptotic stability properties of the associated steady-state solutions (equilibria, limit cycles etc.), as well as characterizing the kind of bifurcations the resulting models undergo. Knowledge of such qualitative properties of the steady-state solutions is crucial in determining epidemiological thresholds that govern the persistence or elimination of the disease being studied

Case studies in application areas, such as modeling the impact of (a) climate change on the spread of mosquito-borne diseases, (b) evolution of insecticide resistance on the spread of mosquito-borne diseases, (c) non-pharmaceutical interventions on the control and mitigation of respiratory diseases, such as the 2003 SARS-CoV, the 2016 MERS and the 2019 (COVID-19) coronavirus pandemics and (d) biological control methods (such as CRISPR-Cas9 gene drive, sterile insect technology and release of Wolbachia-infected mosquitoes) on controlling the population abundance of mosquito species that are vectors of important mosquito-borne diseases (such as malaria, dengue, Zika, chikungunya and West Nile virus) will be presented

Course 6

Title: Introduction age structured population models
Duration: 5-6 hours lectures + 3-4 hours discussion
Level: Graduate
Lecturer’s NAME: Professor Xingfu Zou, University of Western Ontario, Canada

Abstract: These lectures aim to provide the audience with some basic skills and methods in developing mathematical models for populations with various structures, including spatial structure and age structure. Some fundamental problems about such models will be discussed, and some mathematical theories and tools for tackling these problems will be introduced and demonstrated