Using Mathematical Models in Controlling the Spread of Malaria

http://hdl.handle.net/10150/195486
Title:
Using Mathematical Models in Controlling the Spread of Malaria
Author:
Chitnis, Nakul Rashmin
Issue Date:
2005
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Malaria is an infectious disease, transmitted between humans through mosquito bites, that kills about two million people a year. We derive and analyze a mathematical model to better understand the transmission and spread of this disease. Our main goal is to use this model to compare intervention strategies for malaria control for two representative areas of high and low transmission. We model malaria using ordinary differential equations. We analyze the existence and stability of disease-free and endemic (malaria persisting in the population) equilibria. Key to our analysis is the definition of a reproductive number, R₀ (the number of new infections caused by one individual in an otherwise fully susceptible population through the duration of the infectious period). We prove the loss of stability of the disease-free equilibrium as R0 increases through R₀ = 1. Using global bifurcation theory developed by Rabinowitz, we show the bifurcation of endemic equilibria at R₀ = 1. This bifurcation can be either supercritical (leading to stable endemic equilibria for R₀ > 1) or subcritical (leading to stable endemic equilibria for R₀ < 1 in the presence of hysteresis). We compile two reasonable sets of values for the parameters in the model: for areas of high and low transmission. We compute sensitivity indices of R₀ and the endemic equilibrium to the parameters around the baseline values. R₀ is most sensitive to the mosquito biting rate in both high and low transmission areas. The fraction of infectious humans at the endemic equilibrium is most sensitive to the mosquito biting rate in low transmission areas, and to the human recovery rate in high transmission areas. This sensitivity analysis allows us to compare the effectiveness of different control strategies. According to our model, the most effective methods for malaria control are the use of insecticide-treated bed nets and the prompt diagnosis and treatment of infected individuals.
Type:
text; Electronic Dissertation
Keywords:
mathematical modeling; malaria; epidemiology; ordinary differential equations; sensitivity analysis; reproductive number
Degree Name:
PhD
Degree Level:
doctoral
Degree Program:
Degree Grantor:
University of Arizona
Cushing, Jim M.; Hyman, James M.
Committee Chair:
Cushing, Jim M.; Hyman, James M.

DC FieldValue Language
dc.language.isoENen_US
dc.titleUsing Mathematical Models in Controlling the Spread of Malariaen_US
dc.creatorChitnis, Nakul Rashminen_US
dc.contributor.authorChitnis, Nakul Rashminen_US
dc.date.issued2005en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractMalaria is an infectious disease, transmitted between humans through mosquito bites, that kills about two million people a year. We derive and analyze a mathematical model to better understand the transmission and spread of this disease. Our main goal is to use this model to compare intervention strategies for malaria control for two representative areas of high and low transmission. We model malaria using ordinary differential equations. We analyze the existence and stability of disease-free and endemic (malaria persisting in the population) equilibria. Key to our analysis is the definition of a reproductive number, R₀ (the number of new infections caused by one individual in an otherwise fully susceptible population through the duration of the infectious period). We prove the loss of stability of the disease-free equilibrium as R0 increases through R₀ = 1. Using global bifurcation theory developed by Rabinowitz, we show the bifurcation of endemic equilibria at R₀ = 1. This bifurcation can be either supercritical (leading to stable endemic equilibria for R₀ > 1) or subcritical (leading to stable endemic equilibria for R₀ < 1 in the presence of hysteresis). We compile two reasonable sets of values for the parameters in the model: for areas of high and low transmission. We compute sensitivity indices of R₀ and the endemic equilibrium to the parameters around the baseline values. R₀ is most sensitive to the mosquito biting rate in both high and low transmission areas. The fraction of infectious humans at the endemic equilibrium is most sensitive to the mosquito biting rate in low transmission areas, and to the human recovery rate in high transmission areas. This sensitivity analysis allows us to compare the effectiveness of different control strategies. According to our model, the most effective methods for malaria control are the use of insecticide-treated bed nets and the prompt diagnosis and treatment of infected individuals.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectmathematical modelingen_US
dc.subjectmalariaen_US
dc.subjectepidemiologyen_US
dc.subjectordinary differential equationsen_US
dc.subjectsensitivity analysisen_US
dc.subjectreproductive numberen_US
thesis.degree.namePhDen_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineApplied Mathematicsen_US