DSpace Repository

Modeling, Dynamics and Optimal Control of West Nile Virus with Seasonality

Modeling, Dynamics and Optimal Control of West Nile Virus with Seasonality

Show full item record

Title: Modeling, Dynamics and Optimal Control of West Nile Virus with Seasonality
Author: Abdelrazec, Ahmed Hassan Manaa
Abstract: West Nile virus (WNv) is a mosquito-borne disease which arrived in Canada in 2001. It has kept spreading across the country and still remains a threat to public health. In this dissertation, we formulate dynamical models and apply theory of dynamical systems to investigate the behavior of the transmission of WNv in the mosquito-bird cycle and humans. In the first part, we propose a system of ordinary differential equations to model the role of corvids and non-corvids birds in the transmission of WNv in the mosquito-bird cycle in a single season and proved the existence of backward bifurcation in the model. In the second part, we consider another deterministic model to study the impact of seasonal variations of the mosquito population on the transmission dynamics of WNv. We prove the existence of periodic solutions under specific conditions. As for the third part, the latter model is extended to assess the impact of some anti-WNv control measures; by re-formulating the model as an optimal control problem. For mosquito-borne diseases, it is essential to access and forcast the virus risk. Therefore in the final part, we generalize the risk index, minimum infection rate (MIR) by using a compartment model for WNv, to define a dynamical minimum infection rate (DMIR) for assessing risk of WNv. By using the data from Peel region, we test and forecast the weekly risk of WNv which can help identify the optimal mitigation strategies.
Subject: Applied mathematics
Epidemiology
Ecology
Keywords: Optimal control
West Nile virus
Mathematical modeling
Backward bifurcation
Seasonality
Type: Electronic Thesis or Dissertation
Rights: Author owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.
URI: http://hdl.handle.net/10315/28202
Supervisor: Zhu, Huaiping
Degree: PhD - Doctor of Philosophy
Program: Mathematics & Statistics
Exam date: 2014-06-12
Publish on: 2015-01-26

Files in this item



This item appears in the following Collection(s)