Abstract: This presentation summarizes the findings from three interrelated projects conducted throughout my PhD research. By deploying differential equation models, this research explores issues concerning the dynamics of the mosquito population and diseases transmitted by mosquitoes. In the first project, we introduce a non-autonomous model for the transmission of a mosquito-borne disease, specifically Dengue fever, between two distinct regions: (A) rural areas with a fraction of the human population and a higher mosquito presence, and (B) urban areas where most workplaces are located, where the majority of people reside, and where mosquito numbers are relatively low. This model integrates periodic mosquito-biting rates and periodic shifts in the workforce. This project calculates the basic reproduction number, $\mathcal{R}_0$, and establishes the epidemic threshold. In particular, we illustrate how changes in the workforce's shift patterns impact the disease's spread. In the second project, we present a mathematical model that characterizes the interactions between wild mosquitoes and genetically modified mosquitoes that carry the {\it Serratia AS1} bacteria. The primary concern is determining whether AS1 can establish itself in the mosquito population, and if so, in what manner: either replacing or co-existing with wild mosquitoes. After confirming the well-posedness of the model, we investigate two sub-models: one disregards environmental AS1 infection, and the other assumes no cross-vertical transmission of AS1 within mosquitoes. We perform an in-depth analysis of each sub-model to identify the conditions under which AS1-carrying mosquitoes either replace or suppress wild mosquitoes or fail to establish. In addition, we performed numerical simulations to support our theoretical results. The third project builds on the second one by examining the influence of AS1 in malaria control. Using the model presented in the second project, we construct an extensive model that categorizes mosquitoes into three groups: wild, AS1-carrying, and malaria-carrying. By analyzing the dynamics of the model and comparing the results with those of a sub-model that omits \textit{Serratia AS1} (termed the malaria-only model), we investigate the potential role of the AS1 bacterium, introduced as a malaria control measure, in mitigating or eradicating malaria.