Mathematical Biology Mathematics for Health
Data Knowledge
Care and Ageing Big Data 


 Machine Learning
Evolution & Genetics  


  • Modeling dengue fever epidemiology, prevention, and control: insights for public health intervention measures
  • Vaccination models and human behavior
  • Transmission and control models of tuberculosis


Project: Modelling dengue fever epidemiology, prevention, and control: insights for public health intervention measures

Description: In recent years, mathematical modeling became an important tool for understanding infectious disease epidemiology and dynamics, leading to great advances for disease control, providing tools for assessing the potential impact of different public health intervention measures. M. Aguiar has large experience in modeling infectious diseases dynamics with special focus in dengue fever epidemiology. Multi-strain dengue dynamics have been modeled with extended Susceptible-Infected-Recovered (SIR)-type models including immunological aspects of the disease such as the Antibody Dependent-Enhancement (ADE) phenomenology; Aguiar et al. have investigated a minimalist two-infection dengue model, with at least two different dengue serotypes to describe differences between primary and secondary infections. Deterministic chaos was found in much wider parameter regions (not predicted by previous models), no longer needing to restrict the infectivity on a secondary infection to be much larger than the infectivity on primary infection. The minimalist model successfully described large fluctuations observed in empirical outbreak data, estimating lower infection rate for secondary dengue infections than for primary infections, anticipating results published recently in Duong et al. PNAS 2015. Aguiar has also shown that the combination of immunological aspects of the disease such as temporary cross-immunity (TCI) and ADE are the most important features to drive the complex dynamics in the system, more than the detailed number of serotypes to be added in the model. However, this work is focusing on the multi-strain aspect of the disease and its effects on the host population only, taking effects of the vector dynamics into account only by the model parameters. Regarding the newly licensed dengue vaccine, opposing the predictions made by other groups, Aguiar et al. have discussed the risks behind this vaccine recommendation, after analyzing an age-structured model. Using the public available vaccine trial data, vaccine efficacy was estimated via the Bayesian approach, predicting a significant reduction of hospitalizations only when the vaccine is given to seropositive individuals. This work is still ongoing.

Methods: Differential Equations | Bifurcation analysis | Bayesian Analysis | Epidemiological data analysis

CMA Researchers: Maíra Aguiar

Selected Pubications:

  • Aguiar, M. (2018) Dengue vaccination: a more ethical approach is needed. Lancet. 2018 May 5;391(10132):1769-1770
  • Aguiar, Maira; Stollenwerk, Nico. (2018) Dengvaxia: age as surrogate for serostatus Lancet Infect Dis. 2018 Mar;18(3):245.
  • Aguiar, Maira; Stollenwerk, Nico. Dengvaxia Efficacy Dependency on Serostatus: A Closer Look at More Recent Data. Clin Infect Dis. 2018 Feb 1;66(4):641-642
  • Aguiar, Maira; Halstead, Scott B.; Stollenwerk, Nico. Consider stopping dengvaxia administration without immunological screening. Expert Rev Vaccines. 2017 Apr;16(4):301-302
  • Aguiar, Maira; Stollenwerk, Nico; Halstead, Scott B. The Impact of the Newly Licensed Dengue Vaccine in Endemic Countries. PLoS Negl Trop Dis. 2016 Dec 21;10(12):e000517
  • Aguiar, Maira; Stollenwerk, Nico; Halstead, Scott B. The risks behind Dengvaxia recommendation Lancet Infect Dis. 2016 Aug;16(8):882-3
  • Halstead, Scott B.; Aguiar, Maira. Dengue vaccine and the 2016 Olympics. Lancet. 2016 Jul 16;388(10041):237-8
  • Halstead, Scott B.; Aguiar, Maira Dengue vaccines: Are they safe for travelers? Travel Med Infect Dis. 2016 Jul-Aug;14(4):378-83
  • Rocha, Filipe; Mateus, Luis; Skwara, Urszula; et al. Understanding dengue fever dynamics: a study of seasonality in vector-borne disease models. INT J OF COMP MATH 2016. 93(8):1405-1422
  • Aguiar, Mara; Coelho, Giovanini Evelim; Rocha, Filipe; et al. Dengue transmission during the 2014 FIFA World Cup in Brazil. Lancet Infect Dis. 2015 Jul;15(7):765-6
  • Aguiar, M.; Paul, R.; Sakuntabhai, A.; et al. Are we modelling the correct dataset? Minimizing false predictions for dengue fever in Thailand. Epidemiol Infect. 2014 Nov;142(11):2447-59
  • Kooi, Bob W.; Aguiar, Maira; Stollenwerk, Nico . Analysis of an asymmetric two-strain dengue model. Math Biosci. 2014 Feb;248:128-39
  • Rocha, Filipe; Aguiar, Maira; Souza, Max; et al. Time-scale separation and centre manifold analysis describing vector-borne disease dynamics. INT J OF COMP MATH. 2016 Oct. 90(10): 2105-2125
  • Aguiar, M., Kooi, B., & Stollenwerk, N. (2008). Epidemiology of dengue fever: A model with temporary cross-immunity and possible secondary infection shows bifurcations and chaotic behaviour in wide parameter regions. Math. Model. Nat. Phenom.; 3:48-70.
  • Aguiar, M., et al. (2011). 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. J. Theor. Biol.; 289:181-196.
  • Aguiar, M., Stollenwerk, N. and Kooi, W. B. (2012). Scaling of stochasticity in dengue hemorrhagic fever epidemics. Math. Model. Nat. Phenom., 7, 1-11.


Project: Vaccination models and human behavior

Description: This project results from the effort we started, some years ago, to find a research topic that would bring together the expertise and interests of the elements of the group, in particular, game theory and epidemiology. An increasing effort has been made to include human behavior in epidemiological models. One way to model this behavior is through game theory, which assumes that individuals make their decisions in order to maximize their gain or minimize a particular risk. We started by studying the impact of individual decision for diseases with seasonal transmission and vaccination and, more recently we have studied the impact of voluntary vaccination on childhood diseases with increased risk in adulthood.

Methods: Theory of games | Differential Equations

CMA Researchers: Fabio A. C. C. Chalub, Paulo Doutor, Paula Patrício, Maria do Céu Soares

Funding: Project EXPL/MAT-CAL/0794/2013. Game theory and epidemiology; PI: Paula Rodrigues (CMA); Total funding: 25.000,00 €


  • P. Doutor, P. Rodrigues, M. d. C. Soares, and F. A. C. C. Chalub. Optimal vaccination strategies and rational behavior in seasonal epidemics. J. Math. Biol., 73(6-7):1437–1465, DEC 2016.


Project: Transmission and control models of tuberculosis

Description: A model for tuberculosis transmission is analyzed to better understand the transmission dynamics of tuberculosis. The model is changed to accommodate different treatment strategies and to evaluate its impact on tuberculosis transmission in the population.

Methods: Differential Equations | Optimal Control

CMA Researchers: Paula Patrício


  • Pinho, S.T.R., Rodrigues, P., Andrade, R.F.S., Serra, H., Lopes, J.S., Gomes, M.G.M. (2015) Impact Of Tuberculosis Treatment Length And Adherence Under Different Transmission Intensities Theor Popul Biol 104 : 68-77.
  • Lopes JS, Rodrigues P, Pinho ST, Andrade RF, Duarte R, Gomes MG. (2014) Interpreting measures of tuberculosis transmission: a case study on the Portuguese population. BMC Infect Dis. 2014 Jun 18;14:340.
  • Rodrigues P, Silva CJ, Torres DF. (2014) Cost-effectiveness analysis of optimal control measures for tuberculosis. Bull Math Biol. 2014 Oct;76(10):2627-45.