The investigator develops various mathematical models for mosquito populations and disease transmission dynamics in this project. This includes models for transgenic mosquitoes, which are resistant to infection by mosquito-borne diseases, and have distinct fitnesses, some of which have advantages over the others. Combined epidemic models are used to study the interactive dynamics of the mosquitoes, characterizing the fact that transgenic mosquitoes have a selective advantage over non-transgenic mosquitoes, and to investigate the effects of transgenic mosquitoes on the disease transmissions. Modeling of transgenic mosquitoes with various genes or strains, as well as modeling of two-sex mosquito populations including both males and females, is also part of this project. All models start with simpler forms, and gradually include more complex structures to better describe the underlying biology. Within each model category, the investigator determines different formulas for the birth and death functions and the contact rates, which facilitates the ability to connect the modelling with real data. With the population models for the mosquitoes well established, various epidemic models for both human and mosquito populations will be incorporated to study the transmission dynamics of the mosquito-borne diseases. The investigator also focuses on modeling of the newly developed paratransgenic technique, which attempts to eliminate a pathogen from mosquito populations through transgenesis of a symbiont, i.e., a genetically modified bacterium, that prevents the mosquitoes from transmitting the pathogen. The dynamics of horizontal bacteria transmission, as well as vertical transmission between mosquitoes, and their effects on the disease transmissions are investigated. The goal is to understand the complexity of the dynamics of the interacting wild mosquitoes and the mosquitoes carrying transgenes or genetically modified bacteria, and predict the impact of releasing the modified mosquitoes. Analysis and numerical simulation is combined to study qualitative and quantitative features of the models, including existence and stability of equilibria, existence of periodic and aperiodic oscillations through bifurcations, and chaotic behavior and transient dynamics. Model parameters are estimated or derived from real biological data and the mathematical analysis of the models covers all parameter regions.
New developments in biology allow researchers to genetically alter mosquitoes so that they are resistant to malaria infection or other mosquito-borne diseases, such as dengue fever and West Nile virus. A more recently developed new paratransgenic approach generates mosquitoes carrying genetically modifies bacteria that impairs in the transmission of pathogens in mosquitoes. The mosquito-borne diseases are transmitted between humans by blood-feeding mosquitoes, and their spread and control have been major concerns for public health. The introduction of modified mosquitoes into wild mosquito populations could be an effective measure in controlling mosquito-borne diseases. To explore this possibility, the investigator, in collaboration with biologists, develops and analyzes mathematical models that represent the population dynamics of wild and transgenic mosquitoes. The models account for the spread of transgenes or genetically modified bacteria through the mosquito population over multiple generations, and predict the impact on the disease transmissions. They help answer such questions as how effectively mosquitoes carrying transgenes or modified bacteria would be able to compete for partners with their wild counterparts, how long it would take for a new resistance gene or bacterium to penetrate the mosquito population, and how effective it would be in preventing the spread of the diseases. In this way, the results of the project can provide useful guidance for public health measures and for disease prevention strategies.