- Seminars
- Modeling epidemics: an introduction to the use of compartmental models for the simulation of epidemics in time and space [MAT/05, 3 ECTS]
Modeling epidemics: an introduction to the use of compartmental models for the simulation of epidemics in time and space [MAT/05, 3 ECTS]
Speaker
Alexander Viguerie - Emory University and GSSI
Date
Oct 28, 2020 - Time:
16:15
12 hours - online - live streaming
The outbreak of COVID-19 in 2020 has led to a surge in interest of the mathematical modeling of
epidemics. Many of the introduced models are so-called compartmental models, in which the total quan-
tities characterizing a certain system may be decomposed into two (or more) species distributed
into two (or more) homogeneous units called compartments. This short course will introduce the notion
of a compartment model and the basics of their development, beginning with the standard SIR
(susceptible-infected-recovered) model and gradually introducing more realistic models that account for
factors such as age-structured populations, asymptomatic patients, and interventions such as lockdowns,
mandatory mask-wearing etc. The course will also address how one may incorporate spatial variation
via a partial differential equation (PDE) model or additional compartments in an ordinary differential
equation (ODE) model. Some sample python code will be provided for numerical examples. The course is
open to all students; however previous exposure to differential equations and basic programming concepts
is recommended.
(Zoom, link in the e-learning course platform)
Lesson 2: Compartment modelling in general: derivation of a predator-prey type model and differences/similarities with SIR. Using graphs for intuition, discussion of various types of compartment models. More sophisticated SIR-type models and R0 generalizations with next-generation matrices.
Lesson 3: Incorporating spatial information. ODE spatial incorporation via spatial-compartment structure. Introduction of PDEs and diffusion. Parallels with computational mechanics and interpretation in terms of constitutive relation and balance equations. Brief discussion of data fitting/machine learning techniques
Lesson 4: Interactive session: extension of basic SIR code. Students will be provided the base code in python and asked to extend the model via a provided flow-chart. Then they will answer several questions based on the new model
contact e-mail: giandomenico.orlandi@univr.it
1. 28/10 16.15 - 17.45
2. 29/10 09.30 - 11.45
3. 04/11 16.15 - 17.45
4. 05/11 09/30 - 11.45
5. Project assignments
Lesson 2: Compartment modelling in general: derivation of a predator-prey type model and differences/similarities with SIR. Using graphs for intuition, discussion of various types of compartment models. More sophisticated SIR-type models and R0 generalizations with next-generation matrices.
Lesson 3: Incorporating spatial information. ODE spatial incorporation via spatial-compartment structure. Introduction of PDEs and diffusion. Parallels with computational mechanics and interpretation in terms of constitutive relation and balance equations. Brief discussion of data fitting/machine learning techniques
Lesson 4: Interactive session: extension of basic SIR code. Students will be provided the base code in python and asked to extend the model via a provided flow-chart. Then they will answer several questions based on the new model
contact e-mail: giandomenico.orlandi@univr.it
- Data pubblicazione
- Sep 22, 2020
- Contact person
- Giandomenico Orlandi
- Department
- Computer Science
- School
- Science and Engineering
ATTACHMENTS
- poster - locandina corso