**DATES:** 17 March - 5 May 2023 (6 sessions) | April 7 and April 14, 2023 – Easter Break

**TIME:** 11:45-17:15 (a total of 24 hours)

**LOCATION:** Maryam Mirzakhani Seminar Room (BCAM)

**ABSTRACT:**
Epidemiological models are important tools to understand the dynamics of infectious diseases, contributing to public health authorities' capacity to implement the available intervention measures to control disease transmission. As the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential, to understand the epidemiological dynamics of disease spreading and control under different scenarios. This course provides an introduction to mathematical epidemiology, from mathematical concepts and applications up to discussion of real world case studies, including the COVID-19 pandemic.

**PROGRAMME**
**1. Mathematical concepts and applications**
Intro deterministic and stochastic epidemiological models

Stability analysis, complex eigenvalues, bifurcation diagrams, state space plots

Basic concepts on epidemiology: reproduction number, growth rates, relative risk and vaccine efficacy

Data on epidemiology

Model validation with empirical data

Model projections

Infectious disease epidemiology

Multi-strain models

Chaotic dynamics

Lyapunov exponents, predictability

Model validation and data analysis

Control measures (vaccination and other)

Epidemic processes in complex networks

**2.Case studies**
a. Epidemiological concepts

b. Dengue fever: multi-strain, within-host, vaccine

c. COVID-19 pandemic: data analysis, epidemiological measures, projections, prediction

d. other public health threads

(Fri.) March 17, 2023 (4 lectures h)

11:45-12:30

15 min break

12:45- 13:30

lunch (13:30-15:30)

15:30-16:15

15 min break

16:30-17:15

(Fri.) March 24, 2023 (4 lectures h)

11:45-12:30

15 min break

12:45- 13:30

lunch (13:30-15:30)

15:30-16:15

15 min break

16:30-17:15

(Fri.) March 31, 2023 (4 lectures h)

11:45-12:30

15 min break

12:45- 13:30

lunch (13:30-15:30)

15:30-16:15

15 min break

16:30-17:15

April 7 and April 14, 2023 – Easter Break

(Fri.) April 21, 2023 (4 lectures h)

11:45-12:30

15 min break

12:45- 13:30

lunch (13:30-15:30)

15:30-16:15

15 min break

16:30-17:15

(Fri.) April 28, 2023 (4 lectures h)

11:45-12:30

15 min break

12:45- 13:30

lunch (13:30-15:30)

15:30-16:15

15 min break

16:30-17:15

(Fri.) May 5, 2023 (4 lectures h)

11:45-12:30

15 min break

12:45- 13:30

lunch (13:30-15:30)

15:30-16:15

16:15- 16:45 coffee break

16:45-17:30

**March 17**: Introduction to MME | The SIS epidemic Model | The SIR epidemic model

**March 24**: The SHAR epidemic model | Concepts in Epidemiology: R0 and growth rates | Case study: Modeling COVID-19 | SIR with seasonality and introduction to stochastic processes

**March 31**: Stochastic systems | Dengue, HIV, etc | Mathematical models applied to infectious disease dynamics: case studies

**April 21**: Network theory | Bifurcation analysis | Modeling chagas disease

**April 28**: Parameter estimation | Model selection | Optimal control (vectorborne diseases) | Optimal control (HIV)

**May 5**: Multi-strain dengue models | COVID-19 models

**PREREQUISITES:**
Basic knowledge of ordinary differential equations, linear algebra, and probabilities/statistics

**REFERENCES:**
[1] Maíra Aguiar, Nico Stollenwerk and Bob W. Kooi (April 20th 2012). Modeling Infectious Diseases Dynamics: Dengue Fever, a Case Study, Epidemiology Insights, Maria de Lourdes Ribeiro de Souza da Cunha, IntechOpen, DOI: 10.5772/31920. Available from: https://www.intechopen.com/chapters/35765

[2] Stollenwerk, N., Jansen, V.: Population Biology and Criticality: From Critical Birth–Death Processes to Self- Organized Criticality in Mutation Pathogen Systems. World Scientific, London (2011)

[3] Aguiar, M., Kooi, B., Stollenwerk, N. Epidemiology of Dengue Fever: A model with temporary cross immunity and possibly secondary infection shows bifurcations and chaotic behaviors in wide parameter region. Math. Model. Nat. Phenom. Vol 3 (4) 48-70 (2008).

[4] Aguiar, M., Ballesteros, S., Kooi, B.W., Stollenwerk, N. The role of seasonality and import in a minimalistic multi-strain dengue model capturing differences between primary and secondary infections: complex dynamics and its implications for data analysis. Journal of Theoretical Biology, 289, 181-196 (2011).

[5] Aguiar, M., Stollenwerk, N., Kooi, W.B. Scaling of stochasticity in dengue hemorrhagic fever epidemics. Mathematical Modelling of Natural Phenomena. 7, 1-11, (2012)

[6] L. Mateus, N. Stollenwerk and J.C. Zambrini, Stochastic Models in Population Biology: From Dynamic Noise to Bayesian Description and Model Comparison for Given Data Sets, Int. Journal. Computer Math., 90, 2161-2173, (2013).

[7] Kooi W. B., Aguiar, M.and Stollenwerk, N. Analysis of an asymmetric two-strain dengue model. Mathematical Biosciences. 248, 128-139, (2014).

[8] Aguiar, M., Paul, R., Sakuntabhai, A., Stollenwerk, N.: Are we modeling the correct data set? Minimizing false predictions for dengue fever in Thailand. Epidemiol. Infect. 142, 2447--59 (2014).

[9] Aguiar, M.; Stollenwerk, N.; and Halstead. S.B. Modeling the impact of the newly licensed dengue vaccine in endemic countries. PLoS Neglected Tropical Diseases 10(12), e0005179 (2016)

[10] Aguiar, M., Stollenwerk, N. The impact of serotype cross-protection on vaccine trials: DENVax as a case study (2020). Vaccines. 8(4) , 674 (2020).

[11] Aguiar, M., Millán Ortuondo, E., Bidaurrazaga Van‐Dierdonck, J., Mar, J., Stollenwek, N.: Modelling COVID 19 in the Basque Country from introduction to control measure response. Sci. Rep. 10, 17306 (2020)

[12] Aguiar, M., Bidaurrazaga Van-Dierdonck, J., Stollenwerk, N.: Reproduction ratio and growth rates: measures for an unfolding pandemic. PLoS ONE 15, e0236620 (2020)

[13] Aguiar, M., Bidaurrazaga Van‐Dierdonck, J., Mar, J., Cusimano, N., Knopoff, D., Anam, V., Stollenwek, N.: Critical fluctuations in epidemic models explain COVID-19 post-lockdown dynamics. Sci. Rep. 11, 13839 (2021)

[14] Pastor Satorras, R., Castellano, C., Van Mieghem, P., Vespignani, A. Epidemic processes in complex networks. Reviews of Modern Physics 87, 925 (2015).

[15] Maíra Aguiar, Joseba Bidaurrazaga Van-Dierdonck, Javier Mar, Nico Stollenwerk (2021). The role of mild and asymptomatic infections on COVID-19 vaccines performance: a modeling study. Journal of Advanced Research (In Press). https://doi.org/10.1016/j.jare.2021.10.012

[16] Maíra Aguiar, Vizda Anama, Konstantin B. Blyuss, Carlo Delfin S. Estadilla, Bruno V. Guerrero, Damián Knopoff, Bob W. Kooi, Akhil Kumar Srivastava, Vanessa Steindorf, Nico Stollenwerk. (2022). Mathematical models for dengue fever epidemiology: a 10-year systematic review. Physics of Life Review, Volume 40, March 2022, Pages 65-92.

https://doi.org/10.1016/j.plrev.2022.02.001
[17] Steindorf, V.; Srivastav, A.K, Stollenwerk, N., Kooi, B.W., Aguiar, M. (2022). Modelling secondary infections with temporary immunity and disease enhancement factor: mechanics for complex dynamics in simple epidemiological models. Chaos, Solitons & Fractals 164:112709.

** *Registration is free, but mandatory before 10 March 2023.** To sign-up go to

https://forms.gle/cpA3B7zcGnFBB7FX6 and fill the registration form.