Course 1

Introduction to population dynamics modeling

The objective of this course is to present the fundamentals of modeling real-world problems, particularly population dynamics.

The application of linear difference equations to population growth encompasses various biological models, including those concerning insect populations and the propagation of annual plants, examining the qualitative behavior of solutions within this framework. Meanwhile, nonlinear difference equations explore into population biology, particularly density dependence in single-species populations. Transitioning to continuous models, the focus shifts to the growth of microorganisms, such as bacterial growth in a chemostat, involving the formulation and dimensional analysis of these models, investigating steady-state solutions, stability, linearization, and the stability of steady states within the chemostat context.

Course 2

Title: Mathematical epidemiology: Between-hosts modeling

The objective of this course is to present various between-hosts modeling techniques to describe infectious disease spread. We will cover a variety of infectious diseases, such as COVID-19, HIV, malaria, dengue, - measles and influenza. Topics will also include vaccines, drug resistance, the basic reproductive ratio, and contact networks.

Course 3

Title: Mathematical immunology: Within-host modeling

Within-host models have made significant contributions to the understanding of pathogen-host interactions: entry, dissemination, transmission and drug treatment and immune responses. We will introduce various within host models (ordinary, delay, and partial differential equations), and analysis (infection free equilibrium point, infected equilibrium point, stability, etc.) of different model virus infections (HIV, hepatitis, influenza etc.).

Course 4

Title: Biological data, parameter estimation and model validation

The objective of this course is to analyze biological data and incorporate them into models. The topics include data analysis, data visualization, parameter estimation, model validation, sensitivity analysis, Latin Hypercube method, selection of mathematical models, uncertainty of parameters, Identifiability of parameters, confidence interval, bootstrapping method etc.

Course 5

Title: Machine learning techniques for disease modeling

The course covers the fundamentals of machine learning and neural network and the current research trends on AI for disease modeling. The course mainly focuses on neural network-based machine learning methods for solving differential equations arose on disease modeling.