The MITACS Canada-Africa Biomath Network
Summer School in Mathematical Biology


University of Botswana; August 18-29, 2008.

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General Information

This is the first Summer School organized by the MITACS' Canada-Africa Biomathematics Network (launched in Kampala, Uganda, November 2007). The School will consist of series of lectures and tutorials on the design and analyses of models for the spread of emerging and re-emerging diseases.  Various modeling paradigms will be discussed, in addition to giving introductory lectures on materials pertinent to the course.  The summer school will include a number of hands-on and computer exercises, together with group projects to reinforce and extend the various concepts covered during lectures.  Leading and young experts, from Africa and Canada, will conduct this course.  It is expected that medical and public health specialists from Africa will also partake in this exercise (both as speakers and as participants). 

List of Instructors:

Marie-Claude Boily (Imperial College, UK)
Troy Day (Queen's University, Canada)
Elamin H. Elbasha (Merck Inc., USA)
Abba Gumel (University of Manitoba, Canada)
John Hargrove (SACEMA, South Africa)
Edward Lungu (University of Botswana)
Joseph Mugisha (Makerere University, Uganda)
Dorothy Musekwa (National University of Science and Technology, Zimbabwe)


Week 1:  Monday-Friday:  Basic Mathematical and Epidemiology Course

 Review of basic mathematical techniques used in modeling (e.g., nonlinear dynamical systems theory, linear algebra, statistical and optimization issues); an overview of some key diseases such as HIV/AIDS, malaria, tuberculosis etc. (including their social and economic consequences); introduction to some mathematical and graphical software (e.g., LaTex, Matlab, Maple, Gnuplot, Octave etc.); computational issues in epidemic modeling.

 Introduction to epidemiological modeling:  Purpose of modeling; compartmental modeling; incidence functions; disease-related quantities (average duration of infectiousness, incubation period, mortality rate, infection rate); threshold phenomena (reproduction numbers); vaccination models and herd immunity; continuous, deterministic modeling (using  ODEs);  classical epidemic models (Kermack McKendrick) SIR, SIS, SEIR;  local stability analysis (next generation operator); existence and stability of equilibria; structured modeling (modeling spread of sexually transmitted diseases; core group; populations structured by gender and risk behavior; random versus associative mixing); modeling vector-borne diseases; determining optimal control strategies; discrete time models (SIR; comparison with continuous ODE models); computer project.

Instructors:  Troy Day, John Hargrove and Edward Lungu

Week 2:   Monday/Tuesday: Advanced Models and Mathematical Techniques  
                Wednesday-Friday: Case Studies (Theory, HIV, Malaria, TB, Co-infections).

Meta-population models:  Two-patch systems (community and hospital), modeling transmission within and between patches; constructing Markov transition matrix for movements; modeling control strategies (quarantine, isolation, vaccines and anti-virals).

Mathematical Immunology: modelling in-host dynamics (dynamics of HIV and TB in-vivo); optimal control of scarce public health resources (vaccines, antivirals etc.); evolutionary considerations in disease modelling

Stochastic Modeling:  continuous and discrete-time stochastic models; comparison between stochastic and deterministic modeling; computer projects.

Uncertainty and Sensitivity Analysis:  Parameter estimation; latin hypercube sampling; partial rank correlation coefficients; applications in epidemiology.       

Advanced Models:  Incidence functions (mass-action, standard incidence, saturated incidence and preferred-mixing incidence); models with vertical transmission, resistance development, periodicity, staged-progression, differential infectivity; spatial and individual-based models; network models; age structure; age of infection.

Group Projects: Participants will be sub-divided into groups, with each group assigned a specific research project pertaining to modelling the transmission dynamics of diseases. Each group will consist of four to six participants with a diverse background in training (mathematics, statistics, computer science, epidemiology, and public health). Each group will present its project at the end of the Summer School.

Instructors:  Marie-Claude Boily, Troy Day, Abba Gumel, Dorothy Musekwa and Joseph Mugisha.


Pictures Taken at Summer School

Check out a Movie (produced by Amy Hurford)