Thesis Format
Integrated Article
Degree
Doctor of Philosophy
Program
Applied Mathematics
Supervisor
Dr. Xingfu Zou
Abstract
This thesis uses differential equation models to investigate some problems related to mosquito population dynamics and mosquito-borne disease dynamics. It consists of three projects. The first project was motivated by the drastic change in work modes during and after the Covid-19 pandemic. We propose a non-autonomous model for a mosquito-borne disease, specifically, dengue disease transmission between two areas: (A) rural areas where a fraction of the human population lives, characterized by a higher presence of mosquitoes; (B) urban areas where the majority of workplaces (if not all) are found, the rest of the human population inhabits, and fewer mosquitoes are observed. We incorporate periodic mosquito bite patterns and periodic switch of working force in the model. We derive the basic reproduction number, $\mathcal{R}_0$ and determine the epidemic threshold. In particular, we demonstrate how variations in the work shift pattern of the work force will affect the disease's dynamics. In the second project, we propose a mathematical model to describe the interactions of wild mosquitoes and genetically modified mosquitoes that carry {\it Serratia AS1} bacteria. The main concern is whether AS1 can be established in the mosquito population, and if so, in what form: replacing or co-existing with the wild mosquitoes. After verifying the well-posedness, we examine two submodels: one neglects the infection by AS1 in the environment, and the other assumes no cross-vertical transmission of AS1 within mosquitoes. We conduct a thorough analysis for each submodel to obtain conditions for AS1 carrying mosquitoes to replace or suppress the wild mosquitoes, or fail to establish. We also performed numerical simulations to illustrate our theoretical findings. The third project is a continuation of the second, in which we investigate the impact of AS1 on the control of malaria disease. Based on the model in Chapter 3, we first develop a full model that divides the mosquitoes into three compartments: wild, AS1-carrying, and malaria-carrying. By analyzing the dynamics of the model and comparing the results with that for the sub-model that excludes \textit{Serratia AS1} (referred to as the malaria-only model), we explore the role that the AS1 bacterium, introduced as a control measure of malaria, can play in inhibiting or eliminating malaria.
Summary for Lay Audience
Diseases spread by mosquitoes have gained enormous attention in the field of mathematical biology. These small, blood-feeding insects are vital carriers of illnesses, mainly due to their dynamic interactions with humans. Female mosquitoes are particularly significant in this context because they are primarily responsible for biting humans and transmitting diseases. Diseases transmitted by mosquitoes including dengue and malaria pose serious risks to public health and put immense pressure on the healthcare system. Factors like globalization and climate change have facilitated the spread of these diseases to the areas that were previously unaffected. Additionally, short-distance travel can quickly spread these diseases from one location to another. To better understand this problem, we apply mathematical models to examine how travel between rural and urban areas influences the spread of dengue fever. This research considers the daily biting habits of mosquitoes and how these behaviors impact whether the disease continues to spread or can be eliminated. Effective control measures are essential for reducing the disease burden. However, current control strategies may not fully capture the complexities of mosquito-borne diseases. Therefore, this thesis aims to gain a deeper understanding of the biological control mechanisms that can help combat these diseases. In this context, we propose employing a mathematical model to examine mosquito population dynamics, particularly emphasizing the role of biologically controlled mosquitoes in mitigating disease transmission. This thesis later expands this research to also address malaria control using similar biologically controlled mosquitoes-based approaches.
Recommended Citation
Pal, Doli Rani, "Modeling and Analysis of Mosquito population dynamics and Mosquito-borne disease dynamics" (2024). Electronic Thesis and Dissertation Repository. 10483.
https://ir.lib.uwo.ca/etd/10483