Mathematical Modeling, Analysis, and Simulation of the COVID-19 Pandemic with Behavioral Patterns and Group Mixing

Due to the rise of COVID-19 cases, many mathematical models have been developed to study the disease dynamics of the virus. However, despite its role in the spread of COVID-19, many SEIR models neglect to account for human behavior. In this project, we develop a novel mathematical modeling framework for studying the impact of mixing patterns and social behavior on the spread of COVID-19. Specifically, we consider two groups, one exhibiting normal behavior who do not reduce their contacts and another exhibiting altered behavior who reduce their contacts by practicing non-pharmaceutical interventions such as social distancing and self-isolation. The dynamics of these two groups are modeled through a coupled system of ordinary differential equations that incorporate mixing patterns of individuals from these groups, such that contact rates depend on behavioral patterns adopted across the population. Additionally, we derive the basic reproduction number, perform numerical simulations, and create an interactive dashboard