Course title: Introduction to modeling in epidemiology and ecology
Instructor: Michael Robert, Virginia Tech, USA
Course Description: This course provides an introduction to mathematical modeling in epidemiology and ecology, focusing on the development and application of models to understand, predict, and manage biological and ecological systems. We will explore key modeling techniques, such as compartmental models (e.g., SIR models) for infectious disease dynamics and differential equations to describe ecological interactions like predator-prey relationships and population growth. Emphasis will be placed on understanding the assumptions, construction, and interpretation of models, equipping participants with the tools to address real-world challenges in public health and environmental conservation.
Lecture 1 Slides available here. Lecture 2 Slides available here.
Course title: Dynamical Systems - Applications in population dynamics models
Instructor: Ousmane Seydi, University of Université Le Havre Normandie Le Havre, Normandy, France
Course Description: This lecture introduces essential tools in dynamical systems, focusing on existence, uniqueness, and positivity of solutions. Key concepts such as dissipativity, global attractors, Lyapunov functions, stability, and instability will be covered, alongside an introduction to semigroup theory. Applications of these concepts will be demonstrated through ordinary and partial differential equation models in epidemiology, providing insight into the dynamics of disease spread and control.
Course title: Epidemic and ecology models with stochastic differential equations
Instructor: Benito Chen, University of Texas, USA
Course Description: Populations can have large variability. Empirical data may have errors in the measurements. There are unknown factors involved in the processes that are modeled. One way to take into account these uncertainties is to introduce randomness into the models. There are different ways of including randomness into deterministic models described by ordinary differential equations. In this course, we will present several different ways of introducing randomness, but we will concentrate on using stochastic differential equations. We will start with an introduction to random variables and stochastic processes. Then we will present Ito calculus and stochastic differential equations. We will conclude with practical use of numerical methods.
Course title: Identifiability analysis on infectious disease models
Instructor: Omar Saucedo, Virginia Tech, USA
Course description: Description: With the increasing practice of using epidemiological data to assess and parameterize mathematical models, it is important to understand the conditions under which we can reliably recover model parameters from available data. There may be scenarios where we cannot confidently recover the model parameters from existing data, requiring the consideration of parameters’ structural and practical identifiability. Structural identifiability establishes whether model parameters can be uniquely determined, based on the model structure, assuming noise-free data. Practical identifiability focuses on whether we can confidently estimate parameters in the presence of uncertainty or noise in the data. In this talk, I will give an overview on identifiability and provide examples in the context of epidemiological models.
Course title: Modeling heterogeneities of infectious diseases - A structured modeling approach
Instructor: Emmanuel Bakare, International Centre for Applied Mathematical Modelling and Data Analytics
Federal University Oye Ekiti, Ekiti State Nigeria
Course Description: Infectious diseases show complex heterogeneities in transmission dynamics, driven by factors such as age, sex, spatial location, and contact patterns. Incorporating these heterogeneities is crucial for accurate predictions and effective control strategies. This training workshop presents a structured modeling approach to represent the heterogeneities of infectious diseases. This method will combine compartmental models, meta-population models, and network models to represent the interactions between individuals, populations, and environments. We will incorporate heterogeneities in demographic structure, contact patterns, mobility, and environmental factors using a structured modeling framework.
Course title: Individual heterogeneity on infectious disease spread
Instructor: Lauren Childs, Virginia Tech, USA
Course Description: The spread of infectious diseases within a population is altered by many features including biological traits of the pathogen as well as characteristics of the host population such as susceptibility and immunity. Basic epidemic models typically assume uniformity across the host population of such features. This talk will provide extensions to simple epidemic models that incorporate heterogeneity in susceptibility and immunity and discuss implications on variability in outcomes.
Course title: Optimal control in biological systems
Instructors: Eric Numfor and Steve Moore
Augusta University, USA and University of Cape Coast, Ghana
Course Description: Optimal control theory is a common paradigm employed in many fields of science and engineering. It provides a framework for making decisions that govern the behavior of dynamical systems, based on predefined objectives. It is the science of maximizing the returns from and minimizing the costs of the operation of physical, social, and economic processes. In particular, optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. We will focus on the applications of optimal control in ordinary and partial differential equations.
Course title: Introduction to spatial statistics in epidemiology and ecology
Instructor: Folashade Agusto, and Atinuke Adebanji
University of Kansas, USA and Kwame Nkrumah University of Science and Technology, Ghana
Course description: This course introduces participants to the principles and methods used to analyze the spatial distribution and spread of diseases within ecological systems. Students will explore how environmental factors, population movements, and spatial heterogeneity influence disease dynamics, using a combination of geographic information systems (GIS), spatial statistics, and mathematical models. Topics will include disease mapping, spatial clustering, and the role of landscape and habitat in shaping epidemiological patterns. Practical applications will be emphasized through hands-on exercises and case studies, providing students with the tools to analyze real-world ecological and epidemiological data in a spatial context. By the end of the course, students will be able to apply spatial methods to address pressing public health and conservation challenges.
Course title: Ecology: Invasive species control under climate change and habitat fragmentation.
Instructors: Rana Parshad, and Kwadwo Antwi-Fordjour,
Iowa State University and Samford University.
Course Description: Recently, various innovative techniques and tools of mathematics have been utilized in understanding invasive species, their spread, dynamics, and ultimate control. Such processes are further complicated due to environmental changes, such as a changing climate, as well as landscape level changes, such as habitat degradation and fragmentation. However, understanding and improving invasive species/pest control under such circumstances will help us make better managerial decisions in ecosystem management. In this course, participants will learn and explore these directions.
Course title: Network and graph theory in epidemiology and ecology
Instructor: Fadekemi Osaye, Troy University, USA
Course Description: This course provides students with concepts and mathematical/computational tools developed in network theory, for modeling, analyzing and simulating the structures and dynamics of various complex networks. Specific topics to be discussed will include Complex network topologies, methods for network analysis, visualization and simulation, models of dynamical/adaptive networks, network stability and robustness, and applications to social, ecological or biological systems. Python and NetworkX (or igraph in RStudio) will be used for the modeling and analysis of complex networks, in addition to other computational tools.
Course title: Climate change and infectious diseases
Instructor: Luis Escobar, Virginia Tech, USA
Course Description: Historically, climate change has influenced the abundance and distribution of life on Earth. Past and ongoing climate change has impacted the burden of infectious diseases. Future climate change is expected to influence a shift in the ecology of infectious diseases, with new diseases emerging in novel areas and the re-emergence of diseases in areas where they were eradicated. This talk will provide an overview of the influences of climate change on the ecology of infectious diseases with some quantitative examples including waterborne, vector-borne, and directly-transmitted diseases.
Course title: Machine / Deep learning and cancer modeling and control
Instructor: Wandi Ding, Middle Tennessee State University, USA
Course Description: We aim to develop an advanced computational framework that integrates Universal Differential Equations (UDEs), adjoint sensitivity analysis, and quantum computing to optimize control strategies for cancer immunotherapy, while incorporating ethical AI practices. This approach enhances the accuracy, efficiency, and scalability of cancer modeling and intervention strategies, addressing the complexity and nonlinearity of real-world data. Quantum computing will be leveraged to handle high-dimensional data and complex simulations, enabling faster optimizations and more precise, personalized predictions in cancer treatment.