### US-Africa Advanced Study Institute on Mathematical Modeling of Infectious Diseases in Africa

#### June 11 - 22, 2007 AIMS, Cape Town, South Africa

Organizers:
Brenda Latka, (Program Chair), DIMACS, latka@dimacs.rutgers.edu
Wayne Getz, UC Berkeley, getz@nature.berkeley.edu
Abba Gumel, University of Manitoba, gumelab@cc.umanitoba.ca
Fritz Hahne, AIMS, fjwh@aims.ac.za
John Hargrove, SACEMA, jhargrove@sun.ac.za
Simon Levin, Princeton University, slevin@eno.princeton.edu
Edward Lungu, University of Botswana, lunguem@mopipi.ub.bw
Fred Roberts, DIMACS, froberts@dimacs.rutgers.edu
Alex Welte, Wits University, awelte@cam.wits.ac.za
Presented under the auspices of the DIMACS Special Focus on Computational and Mathematical Epidemiology.

This Advanced Study Institute is jointly organized with African Institute for Mathematical Sciences (AIMS), and
South African Centre for Epidemiological Modelling and Analysis (SACEMA).

#### Workshop Program:

Program in table form.

Abstracts:

Fred S. Roberts, DIMACS, Rutgers University, Piscataway, NJ USA

Title: Graph-theoretical Models of the Spread and Control of Disease and of Fighting Fires

Mathematical models using graphs and networks are increasingly important in understanding ways to combat the spread of disease, whether due to natural outbreaks such as influenza or deliberate outbreaks caused by bioterrorists. We will discuss the role of the mathematical sciences in modeling the spread of disease and describe specific models that use the tools of graph theory to understand strategies for vaccination, quarantine, etc. We will describe recent work on abstract models of the control of fires that are mathematically analogous to the disease spread models. The talk will be self-contained. Background in graph theory, epidemiology, or firefighting is not required.

Martin I. Meltzer, CDC

Title: Making Models Useful for Policy Makers

Public health policy makers often need reliable estimates of potential impact of diseases and the possible consequences of interventions. Willingness to accept results from mathematical models, however, depends on how the modeler's) approach the problem and present the results. Typically, adoption of the results of a mathematical model as a basis for framing public health strategy and tactics is dependent upon the basic understanding of the model. This presentation will outline some guidelines, with examples, for building models that policy makers are likely to rely upon.

The 2-week Advanced Study Institute (ASI) course will have two parts. The first part (first week) provides a basic introduction to mathematical modeling in epidemiology at a fast pace. This introductory week is designed to allow students who have never taken an epidemiological modeling course to acquire the necessary background they need for the second week. The second part (second week) covers advanced material. The following is an outline of the program.

Week 1: June 11 - June 15, 2007

Introduction to epidemiological modeling
Background information on diseases, epidemiology, and statistical approaches to model fitting; modeling methods driven by data and simulation; epidemiological and data aspects of classical epidemic models (Kermack McKendrick) SIR, SIS, SEIR; various modeling paradigms, particularly network, agent-based; overview of some key diseases such as HIV/AIDS, malaria, tuberculosis etc. (including their social and economic consequences); the modeling of emerging diseases; parameter estimation; the concept of Ro and whether or not it tells the whole story in some situations; introduction to some mathematical and graphical software.

Main instructor: James Lloyd-Smith (Penn State)

Review of basic mathematical techniques used in modeling and of key diseases of Africa
The 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; review of mathematical tools (e.g., nonlinear dynamical systems theory, linear algebra, statistical and optimization issues); 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); introduction to uncertainty and sensitivity analysis in epidemiology (Latin hypercube sampling and partial rank correlation coefficients); work on student projects.

Main instructor: Edward Lungu (U. of Botswana)

Week 2: Monday, June 18 - Tuesday, June 19, 2007

Advanced mathematical topics and epidemiological modeling
Optimal control of ordinary differential equations and applications to disease models.

Main instructors: Jonathan Dushoff (Princeton U.), Suzanne Lenhart (U. of Tennessee)

Week 2: Wednesday, June 20 - Friday, June 22, 2007

Review of selected papers from the current literature, covering theory and also HIV, TB, and other applications
Meta-population models: Two-patch systems (community and hospital), modeling transmission within and between patches; constructing Markov transition matrices; modeling control strategies (quarantine, isolation, vaccines, anti-virals).

Main instructor: Jonathan Dushoff (Princeton U.)

Stochastic Modeling
Continuous and discrete-time stochastic models; comparison between stochastic and deterministic modeling; projects.

Main instructors: James Lloyd-Smith (Penn State), Suzanne Lenhart (U. of Tennessee)