b'Department of MathematicsA Mathematical Model for MosquitoPopulation with Genetics of Insecticide ResistanceC. Thomas EvansSponsors: Dr. Mohammed and Dr. LazariThe widespread and large-scale mosquito resistance to all available insecticides used in mosquito control has emerged as the major stumbling block against mosquito-borne diseases eradication (or control) efforts. In this study, a mathematical model for mosquito population dynamics, which incorporates the population of resistant-type and sensitive-type mosquitoes to insecticides, is developed. The model has four equilibria, namely, mosquito-free, resistant-only, sensitive-only and co-existence equilibrium (where sensitive and resistant genotypes exist). The model was mathematically analyzed and conditions for the existence of the four associated equilibria of the model were derived. The stability of the equilibria will be studied both analytically and numerically.Population Growth Model vs. Covid-19 PandemicKatherine M. Demo and Nicole M. DemmonsSponsor: Dr. LazariCovid-19 has been one of the most relevant world topics discussed over the past few years. Whether it was about where it came from, how deadly it was, or even if it was real, it has created research opportunities. If we wanted to create a model that shows how the disease spreads in a community, we need to understand the rate that the infection spreads. We assume the rate of infection depends on the current population that is infected and the population that is not yet infected to create differential equation to link these growth growth/decay rates. We will use the city of Los Angeles, CA for our data; and by solving the differential equation, we obtain a mathematical model that will predict the number of people that are infected at a given time. We will use the total number of confirmed cases from October to December of 2021 to test against our model.A Mathematical Model for COVID-19 Growth Rate ForecastingC. Thomas Evans and Ebony WilliamsSponsor: Dr. LazariThe experience of the past two years reminds countries that they are as vulnerable to diseases regardless of wealth, technology, and advanced medicine. We wish to reduce vulnerability by facilitating comprehension of infection rates.In this paper we are introducing a basic differential equation model that describes the rate of growth of COVID-19 to predict the number of cases at a given time. We assume that this depends on the current population that has the disease and the remaining people who have yet to catch it. The model used to analyze the infection rate will use these two populations, the maximum possible population to be infected, the time at which the data is being collected/projected, and a constant of proportionality.The accuracy and precision of the given model will be analyzed with data from the total confirmed cases of Atlanta (ATL), GA; with these numbers being collected from October to November 2021.39'