# Modeling epidemics: an introduction to the use of compartmental models for the simulation of epidemics in time and space [MAT/05, 3 ECTS]

## Next seminars

Supervisor
Alexander Viguerie - Emory University and GSSI
Date and time
Wednesday, October 28, 2020 at 4:15 PM - 12 hours - online - live streaming
Programme Director
Giandomenico Orlandi
External reference
Publication date
September 22, 2020
Department
Computer Science

## Summary

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)

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 1: Background, and motivation. The SIR model in detail, basic viral reproduction number R0 and susceptible thresholds. Equilibrium solutions and asymptotic behaviors. Demonstration in Python
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

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