Fred Brauer, Honourary Professor in the Mathematics Department at University of British Columbia, passed away on 10-17-2021 in Vancouver, BC. Fred Brauer obtained his Ph.D. in mathematics from MIT in 1956 under Norman Levinson. He was a faculty member of the Department of Mathematics at University of Wisconsin-Madison in the period of 1960-1996 and served as department chair there during 1979-1982. He co-authored 5 highly influential books in population biology and mathematical epidemiology and supervised several outstanding Ph.Ds in the area of mathematical biology. His interests include the mathematical modelling and analysis of nonlinear epidemiological problems and population dynamics, with focuses on the global dynamics and implications of such models.

We would like to invite you to read the following enlightening articles authored by Professor Brauer and his colleagues published in MBE in a span of over 10 years.

Some simple epidemic models

Fred Brauer
Doi: 10.3934/mbe.2006.3.1

Keywords: Kermack-McKendrick, vaccination, epidemic models

Global analysis of discrete-time SI and SIS epidemic models

Jianquan Li, Zhien Ma, Fred Brauer
Doi: 10.3934/mbe.2007.4.699

Keywords: discrete-time epidemic model, dynamic behavior, equilibrium, stability

A final size relation for epidemic models

Julien Arino, Fred Brauer, P. van den Driessche, James Watmough, Jianhong Wu
Doi: 10.3934/mbe.2007.4.159

Keywords: vertical transmission, basic reproduction number, epidemic models, final size relation

Calculation of R0 for age-of-infection models

Christine K. Yang, Fred Brauer
Doi: 10.3934/mbe.2008.5.585

Keywords: basic reproduction number, epidemic models, age-of-infection models, treatment models

Age-of-infection and the final size relation

Fred Brauer
Doi: 10.3934/mbe.2008.5.681

Keywords: final size relation, epidemic models, basic reproduction number, age of infection

Discrete epidemic models

Fred Brauer, Zhilan Feng, Carlos Castillo-Chávez
Doi: 10.3934/mbe.2010.7.1

Keywords: epidemic, final size, single outbreak, continuous time epidemic models, discrete epidemic models

Pandemic influenza: Modelling and public health perspectives

Julien Arino, Chris Bauch, Fred Brauer, S. Michelle Driedger, Amy L. Greer, S.M. Moghadas, Nick J. Pizzi, Beate Sander, Ashleigh Tuite, P. van den Driessche, James Watmough, Jianhong Wu, Ping Yan
Doi: 10.3934/mbe.2011.8.1

Keywords: social distancing, antiviral treatment, final size relation, pandemic influenza, Epidemic models, basic reproduction number, vaccination, control strategies

Dynamics of an age-of-infection cholera model

Fred Brauer, Zhisheng Shuai, P. van den Driessche
Doi: 10.3934/mbe.2013.10.1335

Keywords: Lyapunov functional, Cholera model, final size, global stability, age-of-infection

A novel approach to modelling the spatial spread of airborne diseases: an epidemic model with indirect transmission

Jummy F. David, Sarafa A. Iyaniwura, Michael J. Ward, Fred Brauer
Doi: 10.3934/mbe.2020188

Keywords: disease dynamics, epidemics, airborne disease, indirect transmission, matched asymptotic analysis, Green’s function, ODE, PDE

Carlos Castillo-Chávez¹, Christopher Kribs Zaleta², Yang Kuang³ and Baojun Song⁴

1. School of Human Evolution and Social Change, PO Box 872402 Tempe, AZ 85287-2402
2. UTA Mathematics Dept., P.O. Box 19408, Arlington, TX 76019-0408, United States
3. Department of Math & Statistics, College of Liberal Arts and Sciences, Arizona State University, Tempe, AZ 85287 - 1804
4. Department of Mathematical Sciences, Montclair State University, 1 Normal Avenue, Montclair, NJ 07043

Those of us who met the field of mathematical biology as a well-developed, flourishing, and rewarding discipline owe much to those who made it so. This special issue of Mathematical Biosciences and Engineering is dedicated to two such pioneers: Fred Brauer and Karl Hadeler.

Fred Brauer obtained his Ph.D. from MIT in 1956 under Norman Levinson, and during a long tenure at the University of Wisconsin he co-wrote several texts on ordinary differential equations that have become classics. His research entered mathematical biology first through early studies in predator-prey systems and harvesting, both with and without delays. He then moved into mathematical epidemiology, and the text he co-authored with Carlos Castillo-Chavez in both these areas earlier this decade is already in wide use.

The special issue on a tribute to the Mathematical Epidemiology work of Fred Brauer is available at: https://www.aimsciences.org/journal/1551-0018/2009/6/2

From the Guest Editors

Carlos Castillo-Chávez, Christopher Kribs Zaleta, Yang Kuang and Baojun Song
Doi: 10.3934/mbe.2009.6.2i

Mathematical modelling of tuberculosis epidemics

Juan Pablo Aparicio and Carlos Castillo-Chávez
Doi: 10.3934/mbe.2009.6.209

The reproduction number RtRt in structured and nonstructured populations

Tom Burr and Gerardo Chowell
Doi: 10.3934/mbe.2009.6.239

The estimation of the effective reproductive number from disease outbreak data

Ariel Cintrón-Arias, Carlos Castillo-Chávez, Luís M. A. Bettencourt, Alun L. Lloyd and H. T. Banks
Doi: 10.3934/mbe.2009.6.261

The dynamics of a delay model of hepatitis B virus infection with logistic hepatocyte growth

Steffen Eikenberry, Sarah Hews, John D. Nagy and Yang Kuang
Doi: 10.3934/mbe.2009.6.283

Culling structured hosts to eradicate vector-borne diseases

Xinli Hu, Yansheng Liu and Jianhong Wu
Doi: 10.3934/mbe.2009.6.301

Epidemic models with differential susceptibility and staged progression and their dynamics

James M. Hyman and Jia Li
Doi: 10.3934/mbe.2009.6.321

Mathematical analysis of a model for HIV-malaria co-infection

Zindoga Mukandavire, Abba B. Gumel, Winston Garira and Jean Michel Tchuenche
Doi: 10.3934/mbe.2009.6.333

Examination of a simple model of condom usage and individual withdrawal for the HIV epidemic

Jeff Musgrave and James Watmough
Doi: 10.3934/mbe.2009.6.363

The discounted reproductive number for epidemiology

Timothy C. Reluga, Jan Medlock and Alison Galvani
Doi: 10.3934/mbe.2009.6.377

On the eradicability of infections with partially protective vaccination in models with backward bifurcation

Muntaser Safan and Klaus Dietz
Doi: 10.3934/mbe.2009.6.395

Global stability of a class of discrete age-structured SIS models with immigration

Yicang Zhou and Zhien Ma
Doi: 10.3934/mbe.2009.6.409