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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. 

As COVID-19 cases continue to rise globally, many researchers have developed mathematical models to help capture the dynamics of the spread of COVID-19. Specifically, the compartmental SEIR model andits variations have been widely employed. These models differ in the type of compartments included, nature of the transmission rates, seasonality, and several other factors. Yet, while the spread of COVID-19 is largely attributed to a wide range of social behaviors in the population, several of these SEIR models do not account for such behaviors. In this project, we consider novel SEIR-based models that incorporate various behaviors. We created a baseline model and explored incorporating both explicit and implicit behavioral changes. Furthermore, using the Next Generation Matrix method, we derive a basic reproduction number, which indicates the estimated number of secondary cases by a single infected individual. Numerical simulations for the various models we made were performed and user-friendly graphical user interfaces were created. In the future, we plan to expand our project to account for the use of face masks, age-based behaviors and transmission rates, and mixing patterns.