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Title: An epidemic model for cholera with optimal control treatment
Author: Lemos-Paião, A. P.
Silva, C. J.
Torres, D. F. M.
Keywords: Disease-free and endemic equilibria
Local asymptotic stability
Numerical case study of Haiti
Optimal control
SIQRB cholera model
Basic reproduction number
Disease free
Local asymptotic stability
Issue Date: 2017
Abstract: We propose a mathematical model for cholera with treatment through quarantine. The model is shown to be both epidemiologically and mathematically well posed. In particular, we prove that all solutions of the model are positive and bounded; and that every solution with initial conditions in a certain meaningful set remains in that set for all time. The existence of unique disease-free and endemic equilibrium points is proved and the basic reproduction number is computed. Then, we study the local asymptotic stability of these equilibrium points. An optimal control problem is proposed and analyzed, whose goal is to obtain a successful treatment through quarantine. We provide the optimal quarantine strategy for the minimization of the number of infectious individuals and bacteria concentration, as well as the costs associated with the quarantine. Finally, a numerical simulation of the cholera outbreak in the Department of Artibonite (Haiti), in 2010, is carried out, illustrating the usefulness of the model and its analysis. © 2016 Elsevier B.V.
Description: This research was supported by the Portuguese Foundation for Science and Technology (FCT) within projects UID/MAT/04106/2013 (CIDMA) and PTDC/EEI-AUT/2933/2014 (TOCCATA), funded by Project 3599 - Promover a Produção Científica e Desenvolvimento Tecnológico e a Constituição de Redes Temáticas and FEDER funds through COMPETE 2020, Programa Operacional Competitividade e Internacionalização (POCI). Lemos-Paião is also supported by the Ph.D. fellowship PD/BD/114184/2016; Silva by the post-doc fellowship SFRH/BPD/72061/2010.
Peer review: yes
DOI: 10.1016/
ISSN: 0377-0427
Appears in Collections:CIDMA - Artigos
SCG - Artigos

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