Bull Math Biol (2011) 73:2916–2931 DOI 10.1007/s11538-011-9652-6 ORIGINAL ARTICLE The Role of Immunity and Seasonality in Cholera Epidemics Rosângela P. Sanches · Claudia P. Ferreira · Roberto A. Kraenkel Received: 16 October 2010 / Accepted: 15 March 2011 / Published online: 6 April 2011 © Society for Mathematical Biology 2011 Abstract This paper presents a mathematical model for cholera epidemics which comprises seasonality, loss of host immunity, and control mechanisms acting to re- duce cholera transmission. A collection of data related to cholera disease allows us to show that outbreaks in endemic areas are subject to a resonant behavior, since the intrinsic oscillation period of the disease (∼1 year) is synchronized with the annual contact rate variation. Moreover, we argue that the short period of the host immunity may be associated to secondary peaks of incidence observed in some regions (a bi- modal pattern). Finally, we explore some possible mechanisms of cholera control, and analyze their efficiency. We conclude that, besides mass vaccination—which may be impracticable—improvements in sanitation system and food/personal hygiene are the most effective ways to prevent an epidemic. Keywords Cholera · Mathematical model · Endemic state · Resonance · Bimodal · Control mechanisms R.P. Sanches Programa de Pós-graduação em Biometria, Universidade Estadual Paulista, 18618-000 Botucatu, SP, Brazil e-mail: rps@ibb.unesp.br C.P. Ferreira ( ) Departamento de Bioestatística, Instituto de Biociências, Universidade Estadual Paulista, 18618-000 Botucatu, SP, Brazil e-mail: pio@ibb.unesp.br R.A. Kraenkel Instituto de Física Teórica, Universidade Estadual Paulista, R. Dr. Bento Teobaldo Ferraz 271, 01140-070 São Paulo, SP, Brazil e-mail: kraenkel@ift.unesp.br