Mathematical Models in Epidemiology (MME)

DATES: 25 March to 17 June 2022. The course will take place once a week, every Wednesday and/or Friday with an Easter Break April 15 and April 22, 2022. Please, check out the programme below.

TIME: 12:00-14:00h (a total of 25 hours)
LOCATION: BCAM Seminar room and online

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 (8 weeks)
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 (4 weeks)
2.a. Epidemiological concepts
2.b. Dengue fever: multi-strain, within-host, vaccine
2.c. COVID-19 pandemic: data analysis, epidemiological measures, projections, prediction
2.d. other public health threads

Mar 25, 2022 (hybrid) 15:30-17:30h
- Dr. Maíra Aguiar: Introduction to MME
- Dr. Nico Stollenwerk: The SIS epidemic Model

Apr 1, 2022 (hybrid) 12:00-14:00h
- Dr. Maíra Aguiar: The SIR epidemic model

Apr 8, 2022 (hybrid) 12:00 - 14:00h
- Dr. Nico Stollenwerk: The SHAR epidemic model | Concepts in Epidemiology: R0 and growth rates

Apr 29, 2022 (hybrid) 12:00 - 14:00h
- Dr. Maira Aguiar: Case study: Modeling COVID-19
- Dr. Nico Stollenwerk: SIR with seasonality and introduction to stochastic processes

May 6, 2022 (hybrid) 12:00 - 14:00h
- Dr. Nico Stollenwerk: Stochastic systems

May 13, 2022 (hybrid) 12:00-14:00h
- Dr. Damián Knopoff: Network theory

May 18, 2022 (hybrid) 12:00 - 14:00h
- Dr. Nicole Cusimano: Spatial systems

May 20, 2022 (hybrid) 12:00 - 14:00h
- Dr. Vanessa Steindorf: Bifurcation analysis | Modeling chagas disease

Jun 3 New date: June 8, 2022 (hybrid) 12:00 - 14:00h
- Dr. Nico Stollenwerk: Parameter estimation | Model selection

Jun 10, 2022 (hybrid) 12:00 - 14:00h
- Dr. Akhil Srivastav: Optimal control (vector-borne diseases)
- Carlo Estadilla: Optimal control (HIV)

Jun 15, 2022 (on-line) 12:00 - 14:00h
- Dr. Maíra Aguiar: Multi-strain dengue models

Jun 17, 2022 (on-line) 15:00 - 18:00h
- Dr. Maíra Aguiar and Dr. Fernando Saldaña: Modeling COVID-19



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] Ma ra 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] Ma ra Aguiar, Vizda Anama, Konstantin B. Blyuss, Carlo Delfin S. Estadilla, Bruno V. Guerrero, Dami n
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



*Registration is free, but mandatory before March 16th. To sign-up go to https://forms.gle/j2SBVkVQNNikPzpS9 and fill the registration form.

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