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This volume is a product of two activities under the auspices of DIMACS Special Focus on Computational and Mathematical Epidemiology, namely the US-Africa Advanced Study Institute (ASI) on Mathematical Modeling of Infectious Diseases in Africa, which took place at the African Institute for Mathematical Sciences (AIMS), Muizenberg, South Africa, June 11-22, 2007, and the DIMACS Workshop on Mathematical Modeling of Infectious Diseases in Africa, hosted by the South Africa Centre for Epidemiological Modeling and Analysis (SACEMA), Stellenbosch, South Africa, on June 25-27, 2007. About 50 graduate students, from across Africa and the USA, attended the ASI, and a total of about 80 people attended the workshop.
The volume consists of two types of papers: tutorial papers and research papers. While the tutorial papers introduce the basic and general principles, concepts, challenges and types of disease modeling, the research papers focus on advanced topics associated with the mathematical modeling (and analysis) of diseases relevant to Africa.
The tutorial-type papers cover topics such as basic principles and framework for modeling diseases, classical (Kermack-McKendrick type) epidemic models, modeling challenges, basic methods of analysis, epidemiological thresholds, uncertainty and sensitivity analysis and the interpretation of the analytical and simulation results obtained. In addition to the aforementioned basic topics, the volume also contains papers on more advanced topics. These include papers on optimal control techniques in disease modeling, design and analysis of discrete-time models, the role of stochasticity in disease modeling, economic aspects of disease modeling and control (including the use of greedy algorithms to obtain optimal solutions) and some advanced dynamical systems techniques for qualitatively analyzing relatively large disease transmission models. Some of these papers address the problem of the transmission dynamics and control of some diseases that inflict major socio-economic and public health burden in Africa, notably HIV and HIV-TB co-infection.
The Editors are very grateful to all those who contributed papers to the volume (S. Shrestha, J.O. Lloyd-Smith, E.M. Lungu, M. Kgosimore, F. Nyabadza, R. Miller Neilan, S. Lenhart, A.-A.Yakubu, W. Ding, J. Dushoff, M.S. Sancheza, B.G. Williams, W. Getz, S. D. Hove-Musekwa, V. Runyowa, Z. Mukandavire, O. Sharomi, A.B. Gumel and F. Roberts). In addition to the great scholarly contributions of the authors, this volume would not have been possible without the support of the sponsors of the ASI and the workshop in Stellenbosch, namely AIMS, DIMACS, The US National Science Foundation and SACEMA.
The Editors are immensely grateful to Fred Roberts, who made the whole US-Africa program possible. We are thankful to the DIMACS staff (notably, Margaret Barry Cozzens, Gene Fiorini, Brenda Latka, Christine Spassione and Ricardo Collado) and Ms. Christine Thivierge (Editorial Assistant, AMS) for their support. Finally, we are very grateful to the many anonymous reviewers who helped in reviewing the contributed papers. The Editors are also very thankful to Simon Levin for writing the Prologue of this volume.
Abba Gumel and Suzanne Lenhart
January 23, 2010
Foreword F.S. Roberts vii Preface A. Gumel and S. Lenhart xi Prologue S. Levin xiii Introduction to Mathematical Modeling of Infectious Disease Dynamics S. Shrestha and J.O. Lloyd-Smith 1 Tools for Mathematical Epidemiology E.M. Lungu, M. Kgosimore, and F. Nyabadza 47 An Introduction to Optimal Control with an Application in Disease Modeling R. Miller Neilan and S. Lenhart 67 Introduction to Discrete-time Epidemic Models A.-A.Yakubu 83 Introduction to Optimal Control for Discrete Time Models with an Application to Disease Modeling W. Ding and S. Lenhart 109 Incorporating Stochasticity in Simple Models of Disease Spread J. Dushoff 121 Using Mathematical Models to Monitor and Evaluate the Impact of Public Health Interventions on Epidemics: The Case of the TB/HIV Co-pandemic in Africa M.S. S´ancheza, J.O. Lloyd-Smith, B.G. Williams, and W. Getz 135 Modeling the Epidemiological and Economic Impact of HIV/AIDS with Particular Reference to Zimbabwe S.D. Hove-Musekwa, V. Runyowa, and Z. Mukandavire 187 Mathematical Analysis of HIV Treatment Model with Variable Viral Load and Infection Stages O. Sharomi and A.B. Gumel 209 Greedy Algorithms in Economic Epidemiology F.S. Roberts 249