An optimization model for antibiotic use Eduardo Massad a,b, * , Marcelo Nascimento Burattini a,c , Francisco Antonio Bezerra Coutinho a a School of Medicine, University of Sa ˜o Paulo, LIM 01-HCFMUSP, Rua Teodoro Sampaio 115, Sa ˜o Paulo, CEP 05405-000 SP, Brazil b London School of Hygiene and Tropical Medicine, University of London, Keppel Street, London, WC1E 7HT, UK c LIM 03-HCFMUSP, Rua Teodoro Sampaio 115, Sa ˜o Paulo, CEP 05405-000, SP, Brazil Abstract There is a positive correlation between the intensity of use of a given antibiotic and the prevalence of resistant strains. The more you treat, more patients infected with resistant strains appears and, as a consequence, the higher the mortality due to the infection and the longer the hospitalization time. In contrast, the less you treat, the higher the mortality rates and the longer the hospitalization time of patients infected with sensitive strains that could be successfully treated. The hypothesis proposed in this paper is an attempt to solve such a conflict: there must be an optimum treatment intensity that minimizes both the additional mortality and hospitalization time due to the infection by both sensitive and resistant bac- teria strains. In order to test this hypothesis we applied a simple mathematical model that allowed us to estimate the opti- mum proportion of patients to be treated in order to minimize the total number of deaths and hospitalization time due to the infection in a hospital setting. Ó 2007 Elsevier Inc. All rights reserved. Keywords: Antibiotics; Evolution of resistance; Mathematical model; Optimization 1. Introduction Throughout the era of antibiotic use in the treatment of human infections, bacteria have developed resis- tance to one class of antibiotic after another [1–3]. Moreover, resistance to antibiotics is an increasing threat in hospitalized patients [4–8] and many ecological studies have shown a clear association between antimicrobial use and resistance [9,10]. Whenever a new antibiotic is introduced and widespreadly used in people, clinically significant resistance appears and the level of resistance evolution increases proportionally to the intensity of use [1]. Since the first sulfonamides were introduced in the 1930’s, an estimated one million tons of antibiotics have been produced and disseminated, representing a significant selective pressure for the evolution of 0096-3003/$ - see front matter Ó 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2007.12.007 * Corresponding author. Address: School of Medicine, University of Sa ˜o Paulo, LIM 01-HCFMUSP, Rua Teodoro Sampaio 115, Sa ˜o Paulo, CEP 05405-000 SP, Brazil. E-mail address: edmassad@usp.br (E. Massad). Available online at www.sciencedirect.com Applied Mathematics and Computation 201 (2008) 161–167 www.elsevier.com/locate/amc